**Course: **MATH 1350

**Title: **Survey of Calculus

**Section: **101 (Class Number 7894)

**Campus: **Ohio University, Athens Campus

**Department: **Mathematics

**Academic Year: **2019 - 2020

**Term: **Fall Semester

**Instructor: **Mark Barsamian

**Contact Information: **My contact information is posted on my web page.

**Office Hours for 2018 - 2019 Fall Semester: **8:45am - 9:30am Mon - Fri in Morton 538

**Course Description: **A survey of basic concepts of calculus for students who want an introduction to calculus, but who do not need the depth of MATH 2301

**Prerequisites: **MATH 1321 or (C or better in 1200) or math placement level 2 or higher and WARNING: No credit for this course and MATH 2301 (MATH 1350 always deducted)

**Special Needs: **If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.

**Meeting Times and Locations: **Section 101 (Class Number 7894), taught by Mark Barsamian, meets at these times and locations:

- Mon, Wed, Fri: 10:45am - 11:40am in Morton Hall Room 235
- Tue: 10:30am - 11:25am in Morton Hall Room 235

**Course Packet Information: **

**What is it? **a 64-page packet, spiral bound in a yellow cover, containing

- Complete Set of 10 Reference Pages
- Complete Set of 31 Class Drills
- Complete List of Homework Assignments
- Information about Tutoring and Supplemental Instruction (SI) on the Athens Campus

**Is it required? **It is required for students in Section 101 (Class Number 7894), taught by Mark Barsamian.

**Where do you get it? **Minuteman Press, 17 W. Washington Street, Athens (next to Donkey Coffee), (740) 593-7393

**What does it cost? **10.25, including tax

**What do you ask for? **Tell them that you need the MATH 1350 Packet.

**MyLab Math: **

Ohio University MATH 1350 is part of the *Inclusive Access Program* at Ohio University. That means that when you register for MATH 1350, you automatically get access to the *MyLab Math* system run by *Pearson*, the publisher of our textbook. This system includes an online copy of the textbook and also an extensive system for online homework and other resources. (A charge for this access is added to your fees.) You will access this system, including the *eText*, through the *Blackboard* site for the course. Initial access to the system involves a few steps. Those steps are explained on the web page Accessing My Lab Math.

**Syllabus: **For Section 101 (Class Number 7894), taught by Mark Barsamian, this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next three portions of hidden content (Textbook, Learning Outcomes, Calendar) and then print this web page.

**Textbook Information: **

**Title: ***Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version, 14 ^{th} Edition*

**Authors: **Barnett, Ziegler, Byleen, Stocker

**Publisher: **Pearson, 2019

**Obtaining the book: **Ohio University MATH 1350 is part of the *Inclusive Access Program* at Ohio University. That means that when you register for MATH 1350, you automatically get access to the *MyLab Math* system run by *Pearson*, the publisher of our textbook. This system includes an online copy of the textbook. (A charge for this access is added to your fees.) You will access this system, including the *eText*, through the *Blackboard* site for the course. Initial access to the system involves a few steps. Those steps are explained on the web page Accessing My Lab Math.

**Learning Outcomes: **

- Concepts Covered in Chapter 2 and 3 of Our Textbook
- Find limits analytically, numerically and graphically including one-sided limits and limits at infinity.*
- Analyze the limit behavior of a function at a point in its domain to determine if the function is continuous at that point. Determine intervals in which a function is continuous. Analyze and classify the discontinuities of a function.*
- Find the derivative of a function using the limit definition.*
- Find the derivative of a function by identifying and applying the appropriate derivative formula.*
- Understand the interpretation of the derivative as the slope of a line tangent to a graph and as a rate of change.*
- Understand the business terminology of demand, cost, price, revenue, and profit, and solve applied problems including marginal analysis applications. Explain the relationship between marginal cost and average cost.*

- Concepts Covered in Chapter 4 of Our Textbook
- Find higher order derivatives of a function.*
- Use the first derivative to determine intervals on which the graph of a function is increasing or decreasing and to determine critical points of the function.*
- Use the second derivative to determine intervals on which the graph of a function is concave upwards or concave downwards and to determine points of inflection.*
- Find and classify relative extrema of a function.*
- Find the absolute extrema of a continuous function on a closed interval.*

- Concepts Covered in Chapter 5 and 6 of Our Textbook
- Find antiderivatives and indefinite integrals using integration formulas and the method of substitution*
- Identify definite integrals of functions as the areas of regions between the graph of the function and the
*x*-axis.* - Estimate the numerical value of a definite integral using a Riemann sum.**
- Use the Fundamental Theorem of Calculus to evaluate definite integrals.*
- Use definite integrals to calculate the area of the region under a curve and the area of the region between two curves.*
- Use definite integrals to calculate the average value of a function on an integral.**
- Find present value and future value for an investment with interest compounded continuously.*
- 4.10 For given supply and demand functions, find and interpret the consumer's surplus and the producer's surplus.*

Note: This list of Learning Outcomes has been designed to adhere to the *Transfer Assurance Guides* (TAGS) provided by the University System of Ohio.

- General information about TAGS can be found at the following link: (TAGS).
- The specific list of TAGS requirements for Business Calculus can be found at the following link: (Business Calculus).
- The symbol * denotes essential learning outcomes from the TAGS.
- The symbol ** denotes optional topics from the TAGS.

**Calendar: **

**Day #1:**2.1 Intro to Limits: Graphical Approach**Topic:**2.1 Introduction to Limits: Graphical Approach**Book Section:**2.1 Introduction to Limits**Class Drills:**Class Drill 1: Limits for a Function Given by a Graph**Lecture Notes:**Lecture Notes Day 1**Homework:**- H00: Using the online MyLab Math System
- H01: Functions, Graphs, Factoring (1.1#39,44) (1.2#11,13,19,29) (1.4#3,11,13) (2.1#5,8)
- H02: Given graph of \( f \), find limit (2.1#15,16,21,23)
- H03: Given specified limit behavior, sketch graph of \( f \). (2.1#47,49)

**Day #2:**2.1 Introduction to Limits: Analytical Approach**Topic:**Analytical Approach to Limits**Book Section:**2.1 Introduction to Limits**Reference:**Reference 2: Facts About Limits from Section 2.1**Lecture Notes:**Lecture Notes Day 2**Homework:**- H04: Using Theorem 2 Limit Properties to find Limits (2.1#33,35,37,41)
- H05: Limits of Rational Functions (2.1#59,61,63,73,75)
- H06: Limits of Piecewise-Defined Functions (2.1#53,57,91)
- H07: Limits of Difference Quotients (2.1#81,83)
- H08: Conceptual Questions (2.1#67,69,71)

**Day #3:**2.2 Graphical Approach to Infinite Limits and Vertical Asymptotes**Topic:**Introduce Limits Involving Infinity and Discuss Examples for a Function Given by a Graph**Book Section:**2.2 Infinite Limits and Limits at Infinity**Reference:**Reference 3: Summarizing Limit Terminology from Sections 2.1 and 2.2**Class Drill:**Class Drill 2: Limits Involving Infinity for a Function Given by a Graph**Lecture Notes:**Lecture Notes Day 3**Homework:**- H09: Prerequisite Skills: Equations for Horizontal & Vertical Lines (2.2#3,4)
- H10: Given graph of \( f \), find limit (2.2#9,11,13,15)

**Day #4:**2.2 Analytical Approach to Infinite Limits and Vertical Asymptotes**(Quiz 1)****Topic:**Analytical Approach to Infinite Limits and Vertical Asymptotes**Book Section:**2.2 Infinite Limits and Limits at Infinity**Reference:****Class Drills:**Class Drill 3: Finding*y*-values and Limits for a Rational Function**Lecture Notes:**Lecture Notes Day 4**Homework:**H11: Given formula for \( f \), find limit (2.2#17,19,21,23,41,43,45)**Quiz:**Quiz 1

**Monday is Labor Day Holiday: No Class****Day #5:**2.2 Limits at Infinity; Horizontal Aysmptotes**Topic:**Limits at Infinity and Horizontal Aysmptotes**Book Section:**2.2 Infinite Limits and Limits at Infinity**Reference:**Reference 5: Limits as \( x \rightarrow \infty \) and What They Tell Us About Graph End Behavior**Lecture Notes:**Lecture Notes Day 5**Homework:**- H12: Polynomial End Behavior (2.2#27,30,32)
- H13: Limits at Infinity; End Behavior (2.2#33,37,39,67,68,69,71)
- H14: Applied: Time Going to Infinity (2.2#85,86,88)
- H15: Find all horizontal & vertical asymptotes (2.2#51,53,55,57,59,61,63)

**Day #6:**2.3 Introduction to Continuity**Topic:**Introduction to Continuity**Book Section:**2.3 Continuity**Class Drill:**Class Drill 4: Limits and Continuity of a Function Given by a Graph**Lecture Notes:**Lecture Notes Day 6**Homework:**- H16: Prerequisite Skills: Interval Notation (2.3#1,2,4)
- H17: Given graph of \( f \), find limit and continuity behavior (2.3#19,20,27)
- H18: Given specified limit and continuity behavior, sketch graph (2.3#11,13)
- H19: Given formula for \( f \), where is \( f \) continuous? (2.3#35,37,69)
- H20: Conceptual Questions (2.3#77,79,81)

**Day #7:**2.3 Determining the Sign Behavior of a Function**(Quiz 2)****Topic:**Determining the Sign Behavior of a Function**Book Section:**2.3 Continuity**Lecture Notes:**Lecture Notes Day 7**Homework:**- H21: Positive and Negative Behavior of Graphs and Functions (2.3#55,85)
- H22: Solving Inequalities (2.3#47,49,51,53)

**Quiz 2**

**Day #8:**2.4 Rates of Change**Topic:**Rates of Change**Book Section:**2.4 The Derivative**Reference:**Reference 6: Definitions of Rates of Change**Class Drills:**Class Drill 5: Representations of Slopes**Lecture Notes:**Lecture Notes Day 8**Homework:**- H23: Prerequisite Skills: Line Equations (1.3#9,13,21,33,37,39) (2.2#5,6,7,8)(2.4#1)
- H24: Prerequisite Skills: Building and Simplifying Expressions (1.1#61,63,73,78)
- H25: Secant & Tangent Line Slopes (2.4#9,11,13,45,47,57)

**Day #9:**2.4 The*Definition of the Derivative***Topic:**The*Definition of the Derivative***Book Section:**2.4 The Derivative**Reference:**Reference 6: Definitions of Rates of Change**Class Drills:**Class Drill 6: Finding Derivatives Graphically Using a Ruler**Teacher Prep:**Class Drill 6 Extra Graphs**Lecture Notes:**Lecture Notes Day 9**Homework:**- H26: Computing \( f' \) for Polynomial (2.4#19,21,27,29)

**Day #10:**2.4 Using the*Definition of the Derivative*to find More Difficult Derivatives**Topic:**Using the*Definition of the Derivative*to find More Difficult Derivatives**Book Section:**2.4 The Derivative**Lecture Notes:**Lecture Notes Day 10**Homework:**H27: Computing \( f' \) for \( \frac{1}{x} \) and \( \sqrt{x} \) type functions (2.4#35,37)

**Day #11:**2.5 Constant Function Rule; Power Rule**(Quiz 3)****Topic:**Constant Function Rule; Power Rule**Book Section:**2.5 Basic Differentiation Properties**Lecture Notes:**Lecture Notes Day 11**Homework:**- H28: Prerequisite Skills: Rewrite as power function (2.5#1,2,4,5)
- H29: Constant Function Rule and Power Rule (2.5#9,11,13,15,17,19)
**Quiz 3**

**Day #12:**2.5 Sum Rule; Constant Multiple Rule**Topic:**Sum Rule; Constant Multiple Rule**Book Section:**2.5 Basic Differentiation Properties**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:****Lecture Notes:**Lecture Notes Day 12**Homework:**- H30: Sum Rule, Const Multiple rule, Power rule (2.5#35,37,39)
- H31: Rewrite function as sum of \( constant \times x^p \), then differentiate (2.5#45,51,53,55,81)
- H32: Tangent Line and Instantaneous Velocity (2.4#15,17) (2.5#59,63)
- H33: Applied Problems (2.5#89,91,97)

**Day #13:**2.7 Introduction to Marginal Analysis and Estimation**Topic:**Introduction to Marginal Analysis and Estimation**Book Section:**2.7 Marginal Analysis in Business and Economics**Reference:**Reference 8: Business Terminology**Class Drills:**Class Drill 9: Questions about Tangent Lines**Lecture Notes:**Lecture Notes Day 13**Homework:**- H34: Skills Warmup: Computing Cost (2.7#4,5,6)
- H35: Computing Marginal Quantities (2.7#9,13,17)
- H36: Applied Problems (2.7#33,43,45,49,51)

**Day #14:**2.7 Marginal Analysis: More Estimation Problems**Topic:**Marginal Analysis: More Estimation Problems**Book Section:**2.7 Marginal Analysis in Business and Economics**Reference:**Reference 8: Business Terminology**Lecture Notes:**Lecture Notes Day 14**Homework:**H36: Applied Problems (2.7#33,43,45,49,51)

**Day #15:****In-Class Exam 1 on Chapter 2**- No books, No Notes, No Calculators, No Cell Phones
- The exam starts after 10:45am as soon as all your stuff is put away.
- The exam ends at 11:40
- The exam is seven problems:
- A problem about Ordinary Limits (Section 2.1 concepts)
- A problem about Limits Involving Infinity (Section 2.2 concepts)
- A problem about Continuity (Section 2.3 concepts)
- A problem finding a Derivative using the Definition of the Derivative (Section 2.4 concepts)
- A problem involving finding a Derivative using the Sum Rule, Constant Multiple Rule, and Power Rule (Section 2.5 concepts)
- A problem involving the Slope of a Tangent Line (Section 2.4 & 2.5 concepts)
- A problem involving Marginal Analysis (Section 2.7 concepts)

- All exam problems are based on Homework Exercises and/or Class Drills

**Day #16:**3.1 Simple Interest; Periodically Compounded Interest; the Constant*e***Topic:**Simple Interest; Periodically Compounded Interest; the Constant*e***Book Section:**3.1 The Constant \( e \) and Continuously Compounded Interest**Lecture Notes:**Lecture Notes Day 16**Homework:**- H37: Skills Warmup: Solving For Specified Variable (3.1#4,5,9,13)
- H38: Using Table of Values to Investigate Limit (3.1#21,23)

**Day #17:**3.1 Continuously Compounded Interest**Topic:**Continuously Compounded Interest**Book Section:**3.1 The Constant*e*and Continuously Compounded Interest**Lecture Notes:**Lecture Notes Day 17**Homework:**- H39: Continuously Compounded Interest (3.1#11,27,29,31,35,37)
- H40: Radioactive Decay (3.1#43,45)

**Day #18:**3.2 Derivatives of Exponential Functions**Topic:**Derivatives of Exponential Functions**Book Section:**3.2 Derivatives of Exponential and Logarithmic Functions**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:**Class Drill 10 Derivatives of Functions Involving Exponents**Lecture Notes:**Lecture Notes Day 18**Homework:**- H41: Differentiating Exponential Functions (3.2#13,28,49,51,53,57)
- H42: Tangent Line and Applied Problems: Exponential (3.2#33,67,75)

**Day #19:**3.2 Derivatives of Logarithmic Functions**(Quiz 4)****Topic:**Derivatives of Logarithmic Functions**Book Section:**3.2 Derivatives of Exponential and Logarithmic Functions**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:**Class Drill 11: Derivatives of Functions Involving Logarithms**Lecture Notes:**Lecture Notes Day 19**Homework:**- H43: Prerequisite Skills: Rewriting Log Expressions (3.2#7,8,9,10)
- H44: Differentiating Logarithmic Functions (3.2#15,21,43,44,51,55)
- H45: Tangent Line Problems: Logarithmic (3.2#31,35)
**Quiz 4**

**Day #20:**3.3 Derivatives of Products**Topic:**Derivatives of Products**Book Section:**3.3 Derivatives of Products and Quotients**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Lecture Notes:**Lecture Notes Day 20**Homework:**H46: Differentiating Products (3.3#17,19,21,55)

**Day #21:**3.3 Derivatives of Quotients**Topic:**Derivatives of Quotients**Book Section:**3.3 Derivatives of Products and Quotients**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:**Class Drill 12: Don't Forget the Easy Derivative Rules**Lecture Notes:**Lecture Notes Day 21**Homework:**- H47: Differentiating Quotients (3.3#25,31,33,69)
- H48: Trick: Rewrite First to Eliminate Quotient (3.3#59,73)

**Day #22:**3.3 More difficult Quotient Rule problems**Topic:**More difficult Quotient Rule problems**Book Section:**3.3 Derivatives of Products and Quotients**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Lecture Notes:**Lecture Notes Day 22**Homework:**- H49: Tangent Line Problems Involving Quotients (3.3#63,65)
- H50: Applied Problems Involving Quotients (3.3#93,95,97)

**Friday is Fall Break: No Class**

**Day #23:**3.4 The Chain Rule**(Quiz 5)****Topic:**Chain Rule Applied to Nested Functions with a Power Function as the Outer Function**Book Section:**3.4 The Chain Rule**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Lecture Notes:**Lecture Notes Day 23**Homework:**H51: Chain Rule Problems with Power Function Outer Function (3.4#21,27,29,33,37,55,67)**Quiz 5**

**Day #24:**3.4 The Chain Rule**Topic:**Chain Rule Applied to General Nested Functions**Book Section:**3.4 The Chain Rule**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Lecture Notes:**Lecture Notes Day 24**Homework:**- H52: Chain Rule Problems with Exponential or Logarithmic Outer Function (3.4#25,31)
- H53: Tangent Line Problems Involving the Chain Rule (3.4#39,40)
- H54: Applied Problems Involving the Chain Rule (3.4#91,95,97)
- H55: Product Rule then Chain Rule (3.4#47,79)

**Day #25:**Rate of Change Class Problems**Topic:**Rate of Change Problems**Book Section:**Concepts from Book Sections 2.5, 3.2, 3.3, 3.4**Class Drills:**Rate of Change Class Drills 13a, 13b, 13c, 13d**Lecture Notes:**Lecture Notes Day 25**Homework:**Do the Rate of Change Class Drills that were not done in class.

**Day #26:****In-Class Exam 2 on Chapter 3 and Rate of Change Class Drills**- No calculators, no books, no notes, no cell phones.
- The exam starts after 10:45am, as soon as all your stuff is put away
- The exam ends at 11:40am, no exceptions
- The exam covers Chapter 3 Sections 1,2,3,4 and the Rate of Change Class Drills
- exam is 9 problems, on 4 pages, printed on front & back of 2 sheets of paper
- A problem involving bank account interest or the concept of the number
*e*(concepts from Section 3.1) - Six problems of this type: Given
*f(x)*(a) find*f '(x)*(b) possibly also find*f '(c)*for some*x = c*. The kinds of functions will be as follows:- A problem involving an exponential function and the Exponential Function Rules (concepts from Section 3.2)
- A problem involving logarithmic functions and the Logarithmic Function Rules (concepts from Section 3.2)
- A problem involving a product of functions and the Product Rule (concepts from Section 3.3)
- A problem involving a quotient of functions and the Quotient Rule (concepts from Section 3.3)
- A problem involving nested functions and the Chain Rule (concepts from Section 3.4)
- A problem involving nested functions and the Chain Rule (concepts from Section 3.4)

- A problem about the tangent line (Chapter 3 Sections 2,3,4 and Class Drills have tangent line problems.)
- A problem about rate of change (Chapter 3 Sections 2,3,4 and Class Drills have rate of change problems.)
**Note: All exam problems are based on the list of Homework Problems and Class Drills.****Note: On all problems, you should show all steps of the solution and use correct notation. (Remember that in this course, the objective is to not only get correct answers, but also present clear solutions to the problems.)**

**Day #27:**4.1 Horizontal Tangent Lines; Increasing & Decreasing Functions**Topic:**Horizontal Tangent Lines; Increasing & Decreasing Functions**Book Section:**4.1 First Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Class Drills:****Lecture Notes:**Lecture Notes Day 27**Homework:**- H56: Graphical Problems (4.1#9,11,13,14,19,21,23,25,61,65,79,83)
- H57: Increasing and Decreasing intervals for function given by formula (4.1#49,51,53,55)

**Day #28:**4.1 Local Extrema & 1st Derivative Test**Topic:**Local Extrema and the 1^{st}Derivative Test**Book Section:**4.1 First Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Class Drills:**Class Drill 16: Using the 1^{st}Derivative Test**Lecture Notes:**Lecture Notes Day 28**Homework:**- H58: Partition numbers, Critical numbers (4.1#27,29,31)
- H59: 1
^{st}Derivative Test (4.1#17,43,45,85,97)

**Day #29:**4.1 More Examples Involving the 1^{st}Derivative Test**Topic:**More Examples Involving the 1^{st}Derivative Test**Book Section:**4.1 First Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Class Drills:**Class Drill 17: Using the 1^{st}Derivative Test on a Function Given by a Formula**Lecture Notes:**Lecture Notes Day 29**Homework:**H59: 1^{st}Derivative Test (4.1#17,43,45,85,97)

**Day #30:**4.2 Concavity and 1^{st}Derivative**(Quiz 6)****Topic:**Concavity and the 1^{st}Derivative**Book Section:**4.2 Second Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Class Drills:****Lecture Notes:**Lecture Notes Day 30**Homework:**H60: Shapes of graphs (4.2#9,13,14,15,16)**Quiz 6**

**Day #31:**4.2 Concavity and 2nd Derivative**Topic:**Concavity and the 2^{nd}Derivative**Book Section:**4.2 Second Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Lecture Notes:**Lecture Notes Day 31**Homework:**- H61: Find Second Derivative (4.2#17,19)
- H62: Given formula for \( f \), determine concavity (4.2#33,35,37,87,89)

**Day #32:**4.2 Curve Sketching**Topic:**Curve Sketching**Book Section:**4.2 Second Derivative and Graphs**Reference:**Reference 9: Derivative Relationships**Class Drills:****Lecture Notes:**Lecture Notes Day 32**Homework:**H63: Graphing (4.2#45,49,57,77)

**Day #33:**4.5 Absolute Max & Min; Closed Interval Method**Topic:**Absolute Max & Min; Finding Absolute Max & Min Using Closed Interval Method**Book Section:**4.5 Absolute Maxima and Minima**Lecture Notes:**Lecture Notes Day 33**Homework:**- H64: Identifying Absolute Extrema on Graph (4.5#9,11,15,17,18)
- H65: Closed Interval Method (4.5#26,67)

**Day #34:**4.5 Absolute Max & Min on Open Interval; 2^{nd}Derivative Test**(Quiz 7)****Topic:**Finding Absolute Max & Min on Open Interval; Second Derivative Test**Book Section:**4.5 Absolute Maxima and Minima**Class Drills:**Class Drill 22: Local and Absolute Extrema**Lecture Notes:**Lecture Notes Day 34**Homework:**- H66: Finding Absolute Extrema on Open Interval (4.5#43,49,51,53)
- H67: Second Derivative Test (4.5#35,37,73,79)

**Quiz 7**

**Day #35:**4.6 Single Variable Optimization: Maximizing Revenue and Profit**Topic:**Single Variable Optimization: Maximizing Revenue and Profit**Book Section:**4.6 Optimization**Class Drills:**Class Drill 23: Maximizing Revenue**Lecture Notes:**Lecture Notes Day 35**Homework:**H68: Single Variable Maximizing Revenue (4.6#19,25,27)

**Day #36:**4.6 Two Variable Abstract Optimization Problems**Topic:**Two Variable Abstract Optimization Problems**Book Section:**4.6 Optimization**Lecture Notes:**Lecture Notes Day 36**Homework:**H69: Two Variable Abstract Max Min Problems (4.6#9,13,15,17)

**Day #37:**4.6 Two Variable Applied Optimization Problems**Topic:**Two Variable Applied Optimization Problems**Book Section:**4.6 Optimization**Lecture Notes:**Lecture Notes Day 37**Homework:**H70: Two Variable Applied Max Min Fence Problems (4.6#33,34,35,36)

**Day #38:****In-Class Exam 3 on Chapter 4**- Exam is on Friday, November 1 in Morton 235.
- No calculators, no books, no notes, no cell phones.
- The exam starts after 1:45am, as soon as all your stuff is put away
- The exam ends at 11:40am, no exceptions
- The exam covers Chapter 4 Sections 1,2,5,6
- exam is 6 problems, on 4 pages, printed on front & back of 2 sheets of paper
- a problem intervals of increase & decrease and local max/min (concepts from Section 4.1)
- a problem intervals of concavity and inflection points (concepts from Section 4.2)
- a problem involving the relationship between the graph of
*f*and given information about the sign of*f '*and*f ''*(concepts from Sections 4.1 & 4.2) - a problem about absolute max/min on a closed interval (concepts from Section 4.5)
- a problem about absolute max/min on an interval that is not closed (concepts from section 4.5)
- an optimization problem (concepts from section 4.6)
**Notes:****Note: All exam problems are based on the list of Homework Problems and Class Drills.**- There will be at least one problem involving increasing/decreasing, local extrema, concavity, inflection points for a function involving \( xe^{-x} \). Related Homework Problems are 4.1#43 and 4.2#89. Related Class Drill is Class Drill 17. There are no related Book Examples. Related Class Examples were done on Day 31 (Mon Oct 21) and Day 32 (Tue Oct 22) and Day 33 (Wed Oct 23).
- There will be at least one problem involving local and/or absolute extrema for a function involving 1/
*x*or 1/*x*^{2}. Related Homework Problems are 4.1#85 and 4.5#51,53 and 4.6#13,15,33,36. Related Book Examples are 4.5[Example 3A] and 4.6[Example 2]. Related Class Examples were done on Day 31 (Mon Oct 21) and Day 36 (Tue Oct 29) and Day 37 (Wed Oct 30) (Examples #2 and #4 on that day). - On all problems, you should show all steps of the solution and use correct notation. (Remember that in this course, the objective is to not only get correct answers, but also present clear solutions to the problems.)

**Day #39:**5.1 Antiderivatives**Topic:**Antiderivatives**Book Section:**5.1 Antiderivatives and Indefinite Integrals**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:**Class Drill 24: Is One Given Function an Antiderivative of Another Given Function?**Lecture Notes:**Lecture Notes Day 39**Homework:**- H71: Rewrite function as sum of \( constant \times x^p \), (5.1#1,3,5)
- H72: Is one function antiderivative of another? (5.1#25,27,28,29,31,33,34,35,36,37,38)
- H73: Graphs of antiderivatives of a function (5.1#39,41)

**Day #40:**5.1 Indefinite Integrals**Topic:**Indefinite Integrals**Book Section:**5.1 Antiderivatives and Indefinite Integrals**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Lecture Notes:**Lecture Notes Day 40**Homework:**H74: Basic Indefinite Integrals (5.1#9,11,13,17,19,21,23)

**Day #41:**5.1 Indefinite Integrals**Topic:**Indefinite Integrals**Book Section:**5.1 Antiderivatives and Indefinite Integrals**Reference:**Reference 7: Derivative and Indefinite Integral Rules**Class Drills:**Class Drill 25: Good and Bad Indefinite Integral Solutions**Lecture Notes:**Lecture Notes Day 41**Homework:**- H75: Rewrite integrand then integrate (5.1#43,45,47,49,51,53)
- H76: Find particular antiderivative satisfying extra condition (5.1#55,61)

**Day #42:**5.2 Intro to Substitution Method; Basic Substitution Integrals**(Quiz 8)****Topic:**Introduction to the Substitution Method and Basic Substitution Integrals**Book Section:**5.2 Integration by Substitution**Reference:**Reference 10: The Substitution Method for Indefinite Integrals**Lecture Notes:**Lecture Notes Day 42**Homework:**- H77: Review of Chain Rule Derivatives (5.2#3,5,7)
- H78: Basic Substitution Integrals: Power Function Outer Function and No Leftover Constant (5.2#11,15,17,19)

**Quiz 8**

**Monday is Veterans Day Holiday: No Class****Day #43:**5.2 Harder Substitution Integrals**Topic:**Harder Substitution Integrals**Book Section:**5.2 Integration by Substitution**Reference:**Reference 10: The Substitution Method for Indefinite Integrals**Class Drills**Class Drill 26: The Substitution Method**Lecture Notes:**Lecture Notes Day 43**Homework:**- H79: Harder Substitution Integrals: General Outer Functions and Leftover Constant (5.2#23,27,29,31,33,41,65,67)
- H80: Application of Substitution Integrals to Total Change Problems (5.2#81,85)

**Day #44:**5.4 Approximating Areas by Left and Right Sums**Topic:**Approximating Areas by Left and Right Sums**Book Section:**5.4 The Definite Integral**Class Drills:****Lecture Notes:**Lecture Notes Day 44**Homework:**H81: Approximating areas with Sums (5.4#7,13,15,17,19,23,61,73)

**Day #45:**5.4 The Definite Integral as a Limit of Sums**Topic:**The Definite Integral as a Limit of Sums**Book Section:**5.4 The Definite Integral**Lecture Notes:**Lecture Notes Day 45**Homework:**- H82: Using Properties of Definite Integral (5.4#33,41,45,49,51,53)
- H83: Conceptual Problems (5.4#55,56)

**Day #46:**5.5 Fundamental Theorem of Calculus**(Quiz 9)****Topic:**The Fundamental Theorem of Calculus**Book Section:**5.5 The Fundamental Theorem of Calculus**Class Drills:**Class Drill 29: The Fundamental Theorem of Calculus**Lecture Notes:**Lecture Notes Day 46**Homework:**H84: Basic Definite Integrals (5.5#11,13,15,17,19,21,23,25,27,29,31)**Quiz 9**

**Day #47:**5.5 Fund. Thm. of Calculus Applied to Total Change Problems**Topic:**The Fundamental Theorem of Calculus Applied to Total Change Problems**Book Section:**5.5 The Fundamental Theorem of Calculus**Lecture Notes:**Lecture Notes Day 47**Homework:**- H85: Harder Definite Integrals (5.5#35,36,37,39,41,45)
- H86: Total Change Problems (5.5#69,70,71,89)

**Day #48:**5.5 Average Value of Continuous Function over an Interval**Topic:**The Average Value of a Function Over an Interval**Book Section:**5.5 The Fundamental Theorem of Calculus**Lecture Notes:**Lecture Notes Day 48**Homework:**H87: Average Value of a Function Over an Interval (5.5#49,51,55,92)

**Day #49:****In-Class Exam 4 on Chapter 5****Exam 4 will be six problems:**- Is one given function an antiderivative of another given function?
- Homework Problems: H72 5.1 # 25,27,28,29,31,33,34,35,36,37,38
- Class Drills: #24, 26
- Class Examples: Mon Nov 4 (Day #39)
- Quiz: Quiz 8

- Find a particular antiderivative satisfying an extra condition
- Homework Problems: H76 5.1 # 55, 61
- Class Examples: Friday, November 8 (Day 42)

- Indefinite Integrals
- Homework Problems:
- H74: Basic Indefinite Integrals (5.1#9,11,13,17,19,21,23)
- H75: Rewrite integrand then integrate (5.1#43,45,47,49,51,53)

- Class Drill: # 25
- Class Examples: Tues Nov 5, Wed Nov 6 (Day #40,41)

- Homework Problems:
- Definite Integral Problem
- Homework Problems:
- H81: Approximating areas with Sums (5.4# 15,17,19)
- H82: Using Properties of Definite Integral (5.4# 33,41)

- Class Drills # 27,28
- Class Examples: Fri Nov 15 (Day #45)

- Homework Problems:
- Substitution Problem
- Homework Problems:
- H78: Basic Substitution Integrals: Power Function Outer Function and No Leftover Constant (5.2#11,15,17,19)
- H79: Harder Substitution Integrals: General Outer Functions and Leftover Constant (5.2#23,27,29,31,33,41,65,67)

- Class Drill # 26
- Class Examples: Tue Nov 12, Wed Nov 13 (Day # 43,44)
- Quiz: Quiz 9

- Homework Problems:
- Fundamental Theorem of Calculus Problem
- Homework Problems:
- H84: Basic Definite Integrals (5.5#11,13,15,17,19,21,23,25,27,29,31)
- H85: Harder Definite Integrals (5.5#35,36,37,39,41,45)

- Class Drill #28
- Class Examples Tue Nov 19, Wed Nov 20 (Days #47,48)

- Homework Problems:

- Is one given function an antiderivative of another given function?

**Day #50:**6.1 The Area Between a Curve and the*x*-axis; The Area Between Two Curves;**Topic:**The Area Between a Curve and the*x*-axis; The Area Between Two Curves**Book Section:**6.1 Area Between Curves**Class Drill:**Class Drill 30: Finding Area Bounded by Curves Using Two Different Methods**Lecture Notes:**Lecture Notes Day 50**Homework:**- H88: Area between curve and x-axis (6.1#9,11,17,21,23,25,57)
- H89: Area between two curves (6.1#3,5,37,47,53,55,63)

**Day #51:**6.1 Application of Area Between Curves to Total Change and Gini Index**Topic:**Applications of the Area Between Two Curves**Book Section:**6.1 Area Between Curves**Handout:**Quantifying Income Inequality by the Gini Index**Lecture Notes:**Lecture Notes Day 51**Homework:**H90: Applications of the Area Between Two Curves (6.1#83,85,89)

**Wednesday through Friday is Thanksgiving Break: No Class**

**Day #52:**6.2 Total Income & Future Value for Continuous Income Stream**Topic:**Total Income and Future Value for a Continuous Income Stream**Book Section:**6.2 Applications of the Area Between Curves in Business and Economics**Lecture Notes:**Lecture Notes Day 52**Homework:**- H91: Total Income from a Continuous Income Stream (6.2#37,39,41,43)
- H92: Future Value of Continuous Income Stream (6.2#45,47,49,51,53,67)

**Day #53:**6.2 Consumers' Surplus, Producers' Surplus**Topic:**Consumers' Surplus; Producers' Surplus**Book Section:**6.2 Applications of the Area Between Curves in Business and Economics**Lecture Notes:**Lecture Notes Day 53**Homework:**H93: Consumers' Surplus; Producers' Surplus, Equilibrium Price (6.2#69,71,73,75,77)

**Day #54:**Equilibrium Price**(Quiz 10)****Topic:**Equilibrium Price**Book Section:**6.2 Applications of the Area Between Curves in Business and Economics**Lecture Notes:**Lecture Notes Day 54**Homework:**H93: Consumers' Surplus; Producers' Surplus, Equilibrium Price (6.2#69,71,73,75,77)**Quiz 10**

**Day #55:**6.2 Equilibrium Price, Consumers' Surplus, Producers' Surplus**Topic:**Equilibrium Price**Book Section:**6.2 Applications of the Area Between Curves in Business and Economics**Class Drills:**Class Drill 31: Finding Equilibrium Price and Consumers' and Producers' Surplus**Lecture Notes:**Lecture Notes Day 55**Homework:**H93: Consumers' Surplus; Producers' Surplus, Equilibrium Price (6.2#69,71,73,75,77)

**Day #56: Mon Dec 9 Final Exam 10:10am - 12:10pm in Morton 25**- The final Exam is on Monday, December 9, 2019 in Morton 235.
- The exam starts after 10:10am, as soon as all your stuff is put away
- The exam ends at 12:10pm, no exceptions
- No calculators, no books, no notes, no cell phones.
- The Exam is 10 problems
- Compute a derivative using the Power Rule, Sum & Constant Multiple Rule, Exponential or Logarithmic Function, Product, Quotient, or Chain Rules Rules (
the**NOT***Definition of the Deriviative*. That is,the Limit)**NOT****Homework Problems:**- From Homework H30 Sum Rule, Const Multiple rule, Power rule: 2.5 # 37
- From Homework H31 Rewrite function as sum of \( constant \times x^p \), then differentiate: 2.5 # 45, 51, 53, 55
- From Homework H41 Differentiating Exponential Functions: 3.2 # 13, 51, 53, 57
- From Homework H44 Differentiating Logarithmic Functions: 3.2 # 15, 21, 43, 44, 51, 55
- From Homework H46 Differentiating Products: 3.3 # 17, 19, 55
- From Homework H47 Differentiating Quotients: 3.3 # 25, 31, 33, 69
- From Homework H48 Trick: Rewrite First to Eliminate Quotient: 3.3 # 59, 73
- From Homework H51 Chain Rule Problems with Power Function Outer Function: 3.4 # 21, 27, 29, 33, 55
- From Homework H52 Chain Rule Problems with Exponential or Logarithmic Outer Function: 3.4 # 25, 31
- From Homework H55 Product Rule then Chain Rule: 3.4 # 47

**Quizzes:**Quiz 5 (Monday, October 7)**Exam Problems:**- Exam 1 # [5],[6]
- Exam 2 # [2], [3], [4], [6]

**Class Drills:**

- Tangent line problem or Rate of Change Problem.
**Homework Problems:**- From Homework H32 Tangent Line and Instantaneous Velocity: 2.5 # 59, 63
- From Homework H42 Tangent Line and Applied Problems: Exponential 3.2 # 33, 75
- From Homework H45 Tangent Line Problems: Logarithmic 3.2#31,35
- From Homework H49 Tangent Line Problems Involving Quotients: 3.3 # 63
- From Homework H51 Chain Rule Problems with Power Function Outer Function: 3.4 # 33
- From Homework H53 Tangent Line Problems Involving the Chain Rule: 3.4 # 39, 40

**Exam Problems:**Exam 2 # [5], [7]**Class Drills:**- Class Drill 9: Questions about Tangent Lines
- Class Drill 11: Derivatives of Functions Containing Logarithms
- Rate of Change Class Drills 13a, 13b, 13c, 13d

- Problem about intervals of increase & decrease, local extrema, intervals of concavity, inflection points (One of the 13 problems listed below.)
**Homework Problems:**- From Homework H56 Graphical Problems: 4.1 # 61, 65
- From Homework H57 Increasing and Decreasing intervals for function given by formula: 4.1 # 49, 51
- From Homework H59 First Derivative Test:: 4.1 # 43, 45
- From Homework H62 Given formula for \( f \), determine concavity: 4.2 # 33, 35, 37, 89
- From Homework H63 Graphing: 4.2 # 45, 49, 57

**Quizzes:**Quiz 6 (Which was mistitled Quiz 5), Quiz 7**Exam Problems:**Exam 3 # [1], [2], [3]**Class Drills:**

- Problem about finding absolute max/min or optimization.
**Homework Problems:**- From Homework H65 Closed Interval Method 4.5: # 26, 67
- From Homework H66 Finding Absolute Extrema on Open Interval: 4.5 # 43, 51, 53
- From Homework H68 Single Variable Maximizing Revenue: 4.6 # 19, 27
- From Homework H70 Two Variable Applied Max Min Fence Problems: 4.6 # 33, 34, 35, 36

**Exam Problems:**Exam 3 # [4], [5], [6]**Class Drills:**Class Drill 23: Maximizing Revenue

- Compute an Indefinite Integral
**Homework Problems:**- From Homework H74 Basic Indefinite Integrals: 5.1 # 9, 11, 17, 19, 21
- From Homework H75 Rewrite integrand then integrate: 5.1 # 43, 45, 49, 51, 53
- From Homework H76 Find particular antiderivative satisfying extra condition: 5.1 # 55, 61

**Exam Problems:**Exam 4 # [2], [3]

- Find a Definite Integral using the Fundamental Theorem of Calculus.
**Homework Problems:**- From Homework H84 Basic Definite Integrals: 5.5 # 13, 15, 17, 19, 21, 23, 25, 27, 29
- From Homework H85 Harder Definite Integrals: 5.5 # 35, 36

**Exam Problems:**Exam 4 # [6]**Class Drills:**Class Drill 29: The Fundamental Theorem of Calculus

- Problem involving the area between curves.
**Homework Problems:**- From Homework H89 Area between two curves: 6.1# 47, 53, 55, 63
- From Homework H90 Applications of the Area Between Two Curves: 6.1 # 89

**Quizzes:**Quiz 10**Class Drills:**Class Drill 30: Finding Area Bounded by Curves Using Two Different Methods

- Problem about Lorenz Curve & Gini Index.
**Handout:**Quantifying Income Inequality by the Gini Index**Homework Problems:**From Homework H90 Applications of the Area Between Two Curves: 6.1 # 83, 85

- Problem about Total Total Income for a Continuous Income Stream or Future Value of a Continuous Income Stream
**Homework Problems:**- From Homework H91 Total Income from a Continuous Income Stream: 6.2 # 37, 39, 41, 43
- From Homework H92 Future Value of Continuous Income Stream: 6.2 # 45, 47, 49

- Problem about Consumers' Surplus / Consumers' Surplus / Equilibrium Point
**Homework Problems:**From Homework H93 Consumers' Surplus; Producers' Surplus, Equilibrium Price: 6.2 # 69, 71, 73, 75, 77**Class Drills:**Class Drill 31: Finding Equilibrium Price and Consumers' and Producers' Surplus

- Compute a derivative using the Power Rule, Sum & Constant Multiple Rule, Exponential or Logarithmic Function, Product, Quotient, or Chain Rules Rules (
**Remark: Six of the ten Final Exam problems are based on problems from our quizzes and in-class exams!**

**Grading: **

During the semester, you will accumulate a * Points Total* of up to

**Online Homework:**93 assignments, with total points rescaled to 40 points possible**Quizzes:**Best 8 of 10 quizzes @ 25 points each = 200 points possible**In-Class Exams:**Best 3 of 4 exams @ 170 points each = 510 points possible**Final Exam:**250 points possible

At the end of the semester, your * Points Total* will be converted into your

- A grade of
**A, A-**means that you mastered all concepts, with no significant gaps.- 900 - 1000 points (or more) = 90% - 100% (or more) =
**A** - 850 - 899 points = 85% - 89.9% =
**A-**

- 900 - 1000 points (or more) = 90% - 100% (or more) =
- A grade of
**B+, B, B-**means that you mastered all essential concepts and many advanced concepts, but have some significant gaps.- 800 - 849 points = 80% - 84.9% =
**B+** - 750 - 799 points = 75% - 79.9% =
**B** - 700 - 749 points = 70% - 74.9% =
**B-**

- 800 - 849 points = 80% - 84.9% =
- A grade of
**C+, C, C-**means that you mastered most essential concepts and some advanced concepts, but have many significant gaps..- 650 - 699 points = 65% - 69.9% =
**C+** - 600 - 649 points = 60% - 64.9% =
**C** - 550 - 599 points = 55% - 59.9% =
**C-**

- 650 - 699 points = 65% - 69.9% =
- A grade of
**D+, D, D-**means that you mastered some essential concepts.- 500 - 549 points = 50% - 54.9% =
**D+** - 450 - 499 points = 45% - 49.9% =
**D** - 400 - 449 points = 40% - 44.9% =
**D-**

- 500 - 549 points = 50% - 54.9% =
- A grade of
**F**means that you did not master essential concepts.- 0 - 399 points = 0% - 39.9% =
**F**

- 0 - 399 points = 0% - 39.9% =

Note that although this grading scale may look easy compared to the usual 90,80,70,60 scale, it is actually not easier. The reasons are:

- The letter grades in this course mean the same thing as the letter grades in other courses.
- When I grade homework and exams, I give out fewer points. (In this course, if you do grade C work on a 20 point exam problem, you will get between 11, 12, or 13 points for the problem. That is in the range 55% - 69.9%. But in somebody else's course that uses the 90,80,70,60 scale, you would have gotten 14 or 15 points for the problem. That is in the range 70% - 79.9%.)
**There is no curve.**

**Course Structure: **

One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways.

**Textbook Readings:**To succeed in the course, you will need to read the textbook, study the examples in it, and work on the "matched problems" that accompany the examples. Many of the examples are exactly like exercises on the Homework, Quizzes and Exams.**Lectures:**In lecture, I will sometimes highlight textbook material that is particularly important, sometimes present material in a manner different from the presentation in the book, and sometimes solve sample problems. We have 51 lectures, totaling 2805 minutes. It is not possible to cover the entire content of the course in 2805 minutes, and the lectures are not meant to do that. Lectures are meant to be a supplement to your reading the textbook and solving problems.**Office Hours:**Come to my office for help! My regular office hours are 8:45am - 9:30am Mon - Fri. If those times are not good for you, I am sometimes available at other times as well, but just not at a regular day & time. Call me, or email me, or talk to me after class to set something up.**Tutoring & SI:**For information about Tutoring and Supplemental Instruction (SI), go to the following link: Student Resources**Online Homework:**Farther down this web page, you will find a long list of Homework Exercises. (The list is also printed inside the back cover of the Course Packet.) The goal of the course is for you to be able to solve the exercises on that list. These exercises will be the content of your*online homework*.**Written Work that is Graded:**During class meetings, you will take*Quizzes*, and*Exams*. They are all based on the Homework Exercise List (mentioned above) and on Class Drills.**Quizzes:**There are ten Quizzes. These are roughly 10-15 minutes long and are given at the end of class on the dates shown in the calendar above.**In-Class Exams:**There are four In-Class Exams. These take an entire class period and are given on the dates shown in the calendar above. The amount of content on an In-Class Exam is roughly four times the amount of content on a Quiz.**Final Exam:**The final exam is given on the date shown in the calendar above. The amount of content on the Final Exam is roughly twice the amount of content on an In-Class Exam.**Importance of Clarity in Written Work:**Note that on the quizzes and exams that you take, the goal is to present solutions to problems, not merely come up with answers.*You are graded on the clarity and correctness of your presentation of the solutions to the problems.*Here is a short*Style Guide*for your written work:### Style Guide for Written Solutions to Mathematical Problems

On the quizzes and exams that you take, the goal is to present solutions to problems, not merely come up with answers.

- All details of calculations should be presented clearly, with explanations for key steps.
- All steps of a calculation need to be correct for the calculation to be considered correct. A calculation where multiple mistakes somehow cancel each other and give a correct answer is just as incorrect as a calculation where a mistake leads to a wrong answer.
- Answers should be simplified, unless you are specifically instructed to not simplify.
- Everything that you write should be in sentences.
- Of course, any prose that you write should be in sentences.
- But also note that mathematical symbols are just abbreviations for things that can be written in prose sentences. So really, all your mathematical symbols should be written in sentences, too.

- Mathematical expressions should be presented in equations with a correct left side.
- When you start a calculation of a new quantity, write it on a new line.
- Work in fractions and symbols, not mixed fractions or decimals.
- For example, write \(\frac{7}{3}\) instead of \(2\frac{1}{3}\) or 2.33
- For example, write \(\sqrt{3}\) instead of 1.73
- For example, write \(\frac{1}{e^2}\) instead of .135

- The square root symbol is fine. But for more complicated expressions, use fractional exponents instead of complicated radical notation.
- For example, both \(x^{1/2}\) and \(\sqrt{x}\) are fine.
- But write \(x^{5/3}\) instead of \(\sqrt[3]{x^5}\)

- Final answers should be written with positive exponents.
- For example, write \(\frac{1}{e^2}\) instead of \(e^{-2}\)

**Homework Assignments: **

The goal of the course is for you to be able to solve the exercises on the list below. (The list is also printed inside the back cover of the Course Packet.) You will work on these assignments within an online homework system called *MyLab Math*. Your work will be graded by the *MyLab Math* system and the total homework score shown in the gradebook.

- H00: Using the online MyLab Math System
- H01: Functions, Graphs, Factoring (1.1#39,44) (1.2#11,13,19,29) (1.4#3,11,13) (2.1#5,8)

- H02: Given graph of \( f \), find limit (2.1#15,16,21,23)
- H03: Given specified limit behavior, sketch graph of \( f \). (2.1#47,49)
- H04: Using Theorem 2 Limit Properties to find Limits (2.1#33,35,37,41)
- H05: Limits of Rational Functions (2.1#59,61,63,73,75)
- H06: Limits of Piecewise-Defined Functions (2.1#53,57,91)
- H07: Limits of Difference Quotients (2.1#81,83)
- H08: Conceptual Questions (2.1#67,69,71)

- H09: Prerequisite Skills: Equations for Horizontal & Vertical Lines (2.2#3,4)
- H10: Given graph of \( f \), find limit (2.2#9,11,13,15)
- H11: Given formula for \( f \), find limit (2.2#17,19,21,23,41,43,45)
- H12: Polynomial End Behavior (2.2#27,30,32)
- H13: Limits at Infinity; End Behavior (2.2#33,37,39,67,68,69,71)
- H14: Applied: Time Going to Infinity (2.2#85,86,88)
- H15: Find all horizontal & vertical asymptotes (2.2#51,53,55,57,59,61,63)

- H16: Prerequisite Skills: Interval Notation (2.3#1,2,4)
- H17: Given graph of \( f \), find limit and continuity behavior (2.3#19,20,27)
- H18: Given specified limit and continuity behavior, sketch graph (2.3#11,13)
- H19: Given formula for \( f \), where is \( f \) continuous? (2.3#35,37,69)
- H20: Conceptual Questions (2.3#77,79,81)
- H21: Positive and Negative Behavior of Graphs and Functions (2.3#55,85)
- H22: Solving Inequalities (2.3#47,49,51,53)

- H23: Prerequisite Skills: Line Equations (1.3#9,13,21,33,37,39) (2.2#5,6,7,8)(2.4#1)
- H24: Prerequisite Skills: Building and Simplifying Expressions (1.1#61,63,73,78)
- H25: Secant & Tangent Line Slopes (2.4#9,11,13,45,47,57)
- H26: Computing \( f' \) for Polynomial (2.4#19,21,27,29)
- H27: Computing \( f' \) for \( \frac{1}{x} \) and \( \sqrt{x} \) type functions (2.4#35,37)

- H28: Prerequisite Skills: Rewrite as power function (2.5#1,2,4,5)
- H29: Constant Function Rule and Power Rule (2.5#9,11,13,15,17,19)
- H30: Sum Rule, Const Multiple rule, Power rule (2.5#35,37,39)
- H31: Rewrite function as sum of \( constant \times x^p \), then differentiate (2.5#45,51,53,55,81)
- H32: Tangent Line and Instantaneous Velocity (2.4#15,17) (2.5#59,63)
- H33: Applied Problems (2.5#89,91,97)

- H34: Skills Warmup: Computing Cost (2.7#4,5,6)
- H35: Computing Marginal Quantities (2.7#9,13,17)
- H36: Applied Problems (2.7#33,43,45,49,51)

- H37: Skills Warmup: Solving For Specified Variable (3.1#4,5,9,13)
- H38: Using Table of Values to Investigate Limit (3.1#21,23)
- H39: Continuously Compounded Interest (3.1#11,27,29,31,35,37)
- H40: Radioactive Decay (3.1#43,45)

- H41: Differentiating Exponential Functions (3.2#13,28,49,51,53,57)
- H42: Tangent Line and Applied Problems: Exponential (3.2#33,67,75)
- H43: Prerequisite Skills: Rewriting Log Expressions (3.2#7,8,9,10)
- H44: Differentiating Logarithmic Functions (3.2#15,21,43,44,51,55)
- H45: Tangent Line Problems: Logarithmic (3.2#31,35)

- H46: Differentiating Products (3.3#17,19,21,55)
- H47: Differentiating Quotients (3.3#25,31,33,69)
- H48: Trick: Rewrite First to Eliminate Quotient (3.3#59,73)
- H49: Tangent Line Problems Involving Quotients (3.3#63,65)
- H50: Applied Problems Involving Quotients (3.3#93,95,97)

- H51: Chain Rule Problems with Power Function Outer Function (3.4#21,27,29,33,37,55,67)
- H52: Chain Rule Problems with Exponential or Logarithmic Outer Function (3.4#25,31)
- H53: Tangent Line Problems Involving the Chain Rule (3.4#39,40)
- H54: Applied Problems Involving the Chain Rule (3.4#91,95,97)
- H55: Product Rule then Chain Rule (3.4#47,79)

- H56: Graphical Problems (4.1#9,11,13,14,19,21,23,25,61,65,79,83)
- H57: Increasing and Decreasing intervals for function given by formula (4.1#49,51,53,55)
- H58: Partition numbers, Critical numbers (4.1#27,29,31)
- H59: First Derivative Test (4.1#17,43,45,85,97)

- H60: Shapes of graphs (4.2#9,13,14,15,16)
- H61: Find Second Derivative (4.2#17,19)
- H62: Given formula for \( f \), determine concavity (4.2#33,35,37,87,89)
- H63: Graphing (4.2#45,49,57,77)

- H64: Identifying Absolute Extrema on Graph (4.5#9,11,15,17,18)
- H65: Closed Interval Method (4.5#26,67)
- H66: Finding Absolute Extrema on Open Interval (4.5#43,49,51,53)
- H67: Second Derivative Test (4.5#35,37,73,79)

- H68: Single Variable Maximizing Revenue (4.6#19,25,27)
- H69: Two Variable Abstract Max Min Problems (4.6#9,13,15,17)
- H70: Two Variable Applied Max Min Fence Problems (4.6#33,34,35,36)

- H71: Rewrite function as sum of \( constant \times x^p \), (5.1#1,3,5)
- H72: Is one function antiderivative of another? (5.1#25,27,28,29,31,33,34,35,36,37,38)
- H73: Graphs of antiderivatives of a function (5.1#39,41)
- H74: Basic Indefinite Integrals (5.1#9,11,13,17,19,21,23)
- H75: Rewrite integrand then integrate (5.1#43,45,47,49,51,53)
- H76: Find particular antiderivative satisfying extra condition (5.1#55,61)

- H77: Review of Chain Rule Derivatives (5.2#3,5,7)
- H78: Basic Substitution Integrals: Power Function Outer Function and No Leftover Constant (5.2#11,15,17,19)
- H79: Harder Substitution Integrals: General Outer Functions and Leftover Constant (5.2#23,27,29,31,33,41,65,67)
- H80: Application of Substitution Integrals to Total Change Problems (5.2#81,85)

- H81: Approximating areas with Sums (5.4#7,13,15,17,19,23,61,73)
- H82: Using Properties of Definite Integral (5.4#33,41,45,49,51,53)
- H83: Conceptual Problems (5.4#55,56)

- H84: Basic Definite Integrals (5.5#11,13,15,17,19,21,23,25,27,29,31)
- H85: Harder Definite Integrals (5.5#35,36,37,39,41,45)
- H86: Total Change Problems (5.5#69,70,71,89)
- H87: Average Value of a Function Over an Interval (5.5#49,51,55,92)

- H88: Area between curve and x-axis (6.1#9,11,17,21,23,25,57)
- H89: Area between two curves (6.1#3,5,37,47,53,55,63)
- H90: Applications of the Area Between Two Curves (6.1#83,85,89)

- H91: Total Income from a Continuous Income Stream (6.2#37,39,41,43)
- H92: Future Value of Continuous Income Stream (6.2#45,47,49,51,53,67)
- H93: Consumers' Surplus; Producers' Surplus, Equilibrium Price (6.2#69,71,73,75,77)

**Attendance Policy: **

Attendance is required for all lectures and exams, and will be recorded using sign-in sheets.

**Missing Class: **If you miss a class for any reason, it is your responsibility to copy someone's notes or download my notes from the course web page, and study them. I will not use office hours to teach topics discussed in class to students who were absent.

**Missing a Quiz or Exam Because of Illness: **If you are too sick to take a quiz or exam, then you must

- send me an e-mail before the quiz/exam, telling me that you are going to miss it because of illness, then
- then go to the Hudson Student Health Center.
- Later, you will need to bring me documentation from Hudson showing that you were treated there.

**Missing Quizzes or Exams Because of University Activity: **If you have a University Activity that conflicts with one of our quizzes or exams, you must contact me before the quiz or exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying me in advance, you will not be given a make-up.

**Missing Quizzes or Exams Because of Personal Travel Plans: **Seven of the ten quizzes and all four of the in-class exams are on Fridays. Students often ask me if they can make up a quiz or exam, or take it early, because their ride home is leaving earlier in the day. The answer is always, *No you may not have a make-up or take the quiz or exam early. You will just have to change your travel plans or forfeit that quiz or exam.*

**Policy on Cheating: **

If cheat on a quiz or exam, you will receive a zero on that quiz or exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR).

If you cheat on another quiz or exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.

**Calculators and Free Online Math Resources: **

**Calculators:**

Calculators will not be allowed on quizzes or exams.

**Websites with Useful Math Resources: **

In lectures, I often use a computer for graphing and calculating. The computer tools that I use are free online resources that are easily accessible at the following link.

Link to Free Online Math Resources

I use the same online resources in my office, instead of a calculator. You are encouraged to use these same free resources at home, instead of a calculator.

page maintained by Mark Barsamian, last updated Dec 3, 2019