**Course: **MATH 1350

**Title: **Survey of Calculus

**Section: **105 and 109 (Class Numbers 6525 and 6529)

**Campus: **Ohio University, Athens Campus

**Department: **Mathematics

**Academic Year: **2018 - 2019

**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 113 or MATH 1200 or Placement level 2 or higher.

**Note: **Students cannot earn credit for both MATH 1350 and either of MATH 2301

**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 105 (Class Number 6525) meets at these times and locations:
- Mon, Wed, Fri 10:45am - 11:40am in Morton Hall Room 115
- Tue 10:30am - 11:25am in Morton Hall Room 115

- Section 109 (Class Number 6529) meets at these times and locations:
- Mon, Wed, Fri 11:50am - 12:45pm in Morton Hall Room 215
- Thu 12:00pm - 12:55pm in Morton Hall Room 215

**Syllabus: **For Sections 105 and 109 (Class Numbers 6525 and 6529), this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next two portions of hidden content (Learning Outcomes, Textbook) and then print this web page.

**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.

**Textbook Information: **

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

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

**Publisher: **Pearson, 2019

**ISBN 13: **978-0-13-486264-4

**Remark: **The ISBN number listed above is for

- the 14
^{th}Edition of the book - Brief Version
- Includes the access code for the
*MyLab Math*online homework system.

**Course Packet Information: **

**What is it? **a 68-page packet, spiral bound in a blue cover, containing

- Complete Set of 10 Reference Pages
- Complete Set of 34 Class Drills
- List of Homework Assignments
- Information about Tutoring and Supplemental Instruction (SI) on the Athens Campus

**Is it required? **It is required for students in Sections 105 and 109 (Class Numbers 6525 and 6529), 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.

**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.

**Student Resources: **
Link to Info about Tutoring and Supplemental Instruction (SI)

**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 our ten quizzes and three of our four in-class exams are on Fridays. We have a quiz on the Tuesday before Thanksgiving Break. Please don't bother asking me if you can make up a quiz or exam, or take it early, because your ride home is leaving earlier in the day, or because you already bought a plane ticket with an early departure time in order to lengthen your weekend or your Thanksgiving Break. The answer is, *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.

**Grading: **

During the semester, you will accumulate points as described in the table below.

Quizzes (best 8 of 10 quizzes, 20 points each): | 160 points possible |

In-Class Exams (best 3 of 4 exams, 200 points each): | 600 points possible |

Cumulative Final Exam: | 240 points possible |

Total: | 1000 points possible |

At the end of the semester, your Total will be converted to your Course Grade as described in the table below. **(Note that there is no curve.)**

Total Score | Percentage | Grade | Interpretation |
---|---|---|---|

900 - 1000 | 90% - 100% | A | You mastered all concepts, with no significant gaps |

850 - 899 | 85% - 89.9% | A- | |

800 - 849 | 80% - 84.9% | B+ | You mastered all essential concepts and many advanced concepts, but have some significant gaps. |

750 - 799 | 75% -79.9% | B | |

700 - 749 | 70% - 74.9% | B- | |

650 - 699 | 65% - 69.9% | C+ | You mastered most essential concepts and some advanced concepts, but have many significant gaps. |

600 - 649 | 60% - 64.9% | C | |

550 - 599 | 55% - 59.9% | C- | |

500 - 549 | 50% - 54.9% | D+ | You mastered some essential concepts. |

450 - 499 | 45% - 49.9% | D | |

400 - 449 | 40% - 44.9% | D- | |

0 - 399 | 0% - 39.9% | F | You did not master essential concepts. |

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.

**Written Exercises:**In the course packet, you will find a table of exercises. The list can also be found at the following link: (list of exercises) The goal of the course is for you to be able to solve the exercises on this list. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study.**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 your suggested exercise list.**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**Quizzes and Exams:**Your course grade is determined mostly by your performance on Quizzes and Exams. The quizzes and exams are based on exercises from the list of exercises and on Class Drills.**Extra Credit Online Homework:**The MyLab Math online homework system has homework assignments that correspond to the assignments on the list of exercises. These online homework assignments can be done for extra credit. Keep in mind two very important things:- The number of extra credit points that you can earn by doing the online homework is much smaller than the number of points that you can earn from quizzes and exams, so it is very important to have a study strategy that improves your chances of doing well on the quizzes and exams.
- The online homework system can be used to get an idea of whether you are getting the correct answers to the problems. But your quiz and exam scores depend not just on getting a correct answer, but also on having a clear, correct written presentation of the solution. The online homework system does not help you improve your writing; only the written homework does that. To succeed on the quizzes and exams, you really have to practice writing out solutions to the exercises on the list of exercises. There is no substitue for practicing writing down solutions to exercises. So think of the online homework system as a supplement to your written homework.

**Calendar: **

**Day #1:**2.1 Intro to Limits: Graphical Approach**Topic:**Graphical Approach to Limits**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:**- H01: Skills Warmup: Factoring (1,3,5)
- H02: Given graph of
*f*, find limit. (15,16,21,23) - H03: Given specified limit behavior, sketch graph of
*f*. (47,49)

**Day #2:**2.1 Intro 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 (33,35,37,41)
- H05: Limits of Rational Functions (59,61,63,73,75)
- H06: Limits of Piecewise-Defined Functions (53,57,91)
- H07: Limits of Difference Quotients (81,83)
- H08: Conceptual Questions (67,68,69,70,71,72)

**Day #3:**2.2 Infinite Limits; Vertical Asymptotes**Topic:**Infinite Limits and Vertical Asymptotes**Book Section:**2.2 Infinite Limits and Limits at Infinity**Reference:**Reference 3: Summarizing Limit Terminology from Sections 2.1 and 2.2**Class Drills:**Class Drill 2: Limits Involving Infinity for a Function Given by a Graph**Lecture Notes:**Lecture Notes Day 3**Homework:**- H09: Skills Warmup: Line Equations (3,4)
- H10: Given graph of
*f*, find limit. (9,10,11,12,13,14,15,16) - H11: Given formula for
*f*, find limit. (17,19,21,23,41,43,45)

**Day #4:**2.2 Infinite Limits; Vertical Asymptotes**(Quiz 1)****Topic:**Infinite Limits and Vertical Asymptotes**Book Section:**2.2 Infinite Limits and Limits at Infinity**Reference:**Reference 4: Contrasting Limit Methods from Sections 2.1 and 2.2**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. (17,19,21,23,41,43,45)**>>> 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*→ ∞ and What They Tell Us About Graph End Behavior**Lecture Notes:**Lecture Notes Day 5**Homework:**- H12: Polynomial End Behavior (27,31,79)
- H13: Limits at Infinity; End Behavior (33,37,39,65,67,68,69)
- H14: Applied: Time Going to Infinity (85,88)
- H15: Find all horizontal & vertical asymptotes (51,53,57,61,63)
- H16: Conceptual Questions (73,74,75,76,77,78)

**Day #6:**2.3 Introduction to Continuity**Topic:**Introduction to Continuity**Book Section:**2.3 Continuity**Class Drills:**Class Drill 4: Limits and Continuity of a Function Given by a Graph**Lecture Notes:**Lecture Notes Day 6**Homework:**- H17: Skills Warmup: Interval Notation (2,3,7)
- H18: Given graph of
*f*, find limit and continuity behavior (19,20,27) - H19: Given specified limit and continuity behavior, sketch graph (11,14)
- H20: Given formula for
*f*, where is*f*continuous? (35,37,69) - H21: Conceptual Questions (77,78,79,80,81)

**Day #7:**2.3 Determining the Sign of a Function on an Interval**(Quiz 2)****Topic:**Determining the Sign of a Function on an Interval**Book Section:**2.3 Continuity**Lecture Notes:**Lecture Notes Day 7**Homework:**- H22: Positive and Negative Behavior of Graphs and Functions (55,85)
- H23: Solving Inequalities (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:**- H24: Skills Warmup: Compute Slope of Line (1)
- H25: Secant & Tangent Line Slopes (9,11,13,15,45,47,57)

**Day #9:**2.4 Introduction to the Derivative**Topic:**Introduction to 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**Lecture Notes:**Lecture Notes Day 9**Homework:**- H26: Computing
*f '*for Polynomial (19,21,27,29,81,89)

- H26: Computing

**Day #10:**2.4 Computing Derivatives**Topic:**Computing Derivatives**Book Section:**2.4 The Derivative**Lecture Notes:**Lecture Notes Day 10**Homework:**- H27: Computing
*f '*for 1/*x*and*sqrt*(*x*) Type Functions (35,37) - H28: Given graph of
*f*, where does*f '*exist? (49,50,51,52,53,54) - H29: Conceptual Questions: (63,64,65,66,68)

- H27: Computing

**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:**- H30: Skills Warmup: Rewrite as power function (1,2,3,4,5,6,7,8)
- H31: Constant Function Rule and Power Rule (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:**- H32: Sum Rule, Const Multiple rule, Power rule (35,37,49)
- H33: Rewrite as sum of
*const*×*x*, then differentiate (45,51,53,55,81)^{p} - H34: Tangent Line and Instantaneous Velocity (59,63)
- H35: Conceptual Question (83,84,85,86)
- H36: Applied Problems (89,91,97)

**Day #13:**2.7 Marginal Analysis in Business and Economics**Topic:**Marginal Anaylsis**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:**- H37: Skills Warmup: Computing Cost and Average Cost (1,2,3,4)
- H38: Computing Marginal Quantities (9,13,17)
- H39: Applied Problems (33,43,45,47,49,51)

**Day #14:**2.7 Marginal Analysis in Business and Economics**Topic:**Marginal Anaylsis**Book Section:**2.7 Marginal Analysis in Business and Economics**Reference:**Reference 8: Business Terminology**Lecture Notes:**Lecture Notes Day 14**Homework:**- H39: Applied Problems (33,43,45,47,49,51)

**Day #15:****In-Class Exam 1 on Chapter 2**

**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:**- H40: Skills Warmup: Solving For Specified Variable (3,7)
- H41: Using Table of Values to Investigate Limit (21,23)

**Day #17:**3.1 Continuously Compound Interest**Topic:**Continuously Compounded Interest**Book Section:**3.1 The Constant*e*and Continuously Compounded Interest**Lecture Notes:**Lecture Notes Day 17**Homework:**- H42: Continuously Compounded Int (11,13,27,29,31,35,37,41)
- H43: Radioactive Decay (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:**- H44: Differentiating Exponential Functions (13,27,53,57)
- H45: Tangent Line and Applied Problems: Exponential (33,67,69,75)

**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:**- H46: Skills Warmup: Rewriting Log Expressions (7,8,9,10)
- H47: Differentiating Logarithmic Functions (15,21,43,44,51,55)
- H48: Tangent Line Problems: Logarithmic (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:**H49: Differentiating Products (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:**- H50: Differentiating Quotients (25,31,33,69)
- H51: Trick: Rewrite First to Eliminate Quotient (59,73)

**Day #22:**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**Lecture Notes:**Lecture Notes Day 22**Homework:**- H52: Tangent Line Problems Involving Quotients (63,65)
- H53: Applied Problems Involving Quotients (93,95,97)

**Fri Oct 5 is Fall Semester Reading Day: 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:**H54: Power Function Outer Function (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**Class Drills:**Class Drill 13: Don’t Forget the Easy Derivative Rules Part II**Lecture Notes:**Lecture Notes Day 24**Homework:**- H55: Exponential or Logarithmic Outer Function (25,31,39,40)
- H56: Applied Problems (91,95,97)
- H57: Product Rule then Chain Rule (47,63)

**Day #25:**Rate of Change Class Drills**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 14a, 14b, 14c, 14d**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**

**Day #27:**4.1 Horiz Tang Lines; Incr/Decr Funct.**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:**- H58: Graphical Probs (9,11,13,14,19,21,23,25,61,65,79,83)
- H59: Incr and Decr intervals for function given by formula (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:****Lecture Notes:**Lecture Notes Day 28**Homework:**H60: Partition numbers, Critical numbers (27,29,31)

**Day #29:**4.1 More Examples Involving the 1st 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 19: Using the First Derivative Test on a Function Given by a Formula**Lecture Notes:**Lecture Notes Day 29**Homework:**H61: First Derivative Test (17,43,45,85,97)

**Day #30:**4.2 Concavity and 1st 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:**H62: Shapes of graphs (9,13)**>>> 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:**- H63: Find Second Derivative (17,19)
- H64: Given formula for f, determine concavity (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:**H65: Graphing (45,49,57,77)

**Day #33:**4.5 Absolute Max and Min; Closed Interval Method**Topic:**Absolute Max and Min; Finding Absolute Max and Min Using Closed Interval Method**Book Section:**4.5 Absolute Maxima and Minima**Lecture Notes:**Lecture Notes Day 33**Homework:**- H66: Identifying Absolute Extrema on Graph (9,17)
- H67: Closed Interval Method (26,67)

**Day #34:**4.5 Absolute Max and Min on Open Interval; 2^{nd}Derivative Test**(Quiz 7)****Topic:**Finding Absolute Max and Min on Open Interval; Second Derivative Test**Book Section:**4.5 Absolute Maxima and Minima**Class Drills:**Class Drill 24: Local and Absolute Extrema**Lecture Notes:**Lecture Notes Day 34**Homework:**- H68: Finding Absolute Extrema on Open Interval (43,49,51,53)
- H69: Second Derivative Test (35,37,73,75)

**>>> 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 25: Maximizing Revenue**Lecture Notes:**Lecture Notes Day 35**Homework:**H70: Single Variable Maximizing Revenue (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:**H71: Two Variable Abstract Max Min Problems (9,13,15,17)

**Day #37:**4.6 Two Variable Applied Optimization Problems Involving Fences**Topic:**Two Variable Applied Optimization Problems Involving Fences**Book Section:**4.6 Optimization**Lecture Notes:**Lecture Notes Day 37**Homework:**H72: Two Variable Applied Max Min Fence Problems (33,34,35,36)

**Day #38:****In-Class Exam 3 on Chapter 4**

**Day #39:**5.1 Antiderivatives**Topic:**Antiderivatives**Book Section:**5.1 Antiderivatives and Indefinite Integrals**Class Drills:**Class Drill 26: Is One Given Function an Antiderivative of Another Given Function?**Lecture Notes:**Lecture Notes Day 39**Homework:**- H73: Rewrite function as sum of
*const*×*x*: (1,3,5)^{p} - H74: Is one function antiderivative of another? (25,27,28,29,31,33,34,35,36,37,38)
- H75: Graphs of antiderivatives of a function (39,41)

- H73: Rewrite function as sum of

**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:**H76: Basic Indefinite Integrals (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 27: Good and Bad Indefinite Integral Solutions**Lecture Notes:**Lecture Notes Day 41**Homework:**- H77: Rewrite integrand then integrate (43,45,47,49,51,53)
- H78: Find particular antiderivative satisfying extra condition (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**Class Drills:**Class Drill 28: Is One Given Function an Antiderivative of Another Given Function?**Lecture Notes:**Lecture Notes Day 42**Homework:**- H79: Review of Chain Rule Derivatives (3,5,7)
- H80: Is one function an antiderivative of another? (51,52,53,55,56,57)
- H81: Basic Substitution Integrals: Power Function Outer Function and No Leftover Constant (11,15,17,19)

**>>> Quiz 8 <<<**

**Mon Nov 12 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 29: The Substitution Method**Lecture Notes:**Lecture Notes Day 43**Homework:**H82: Harder Substitution Integrals: Leftover Constants and General Outer Functions (23,27,29,31,33,41,65,67)

**Day #44:**5.2 Applications of Substitution Integrals**Topic:**Application of Substitution Integrals**Book Section:**5.2 Integration by Substitution**Lecture Notes:**Lecture Notes Day 44**Homework:**H83: Application of Substitution Integrals to Total Change Problems (81,85)

**Day #45:**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 45**Homework:**H84: Approximating areas with Sums (7,13,15,17,19,23,61,73)

**Day #46:**5.4 The Definite Integral as a Limit of Sums**(Quiz 9)****Topic:**The Definite Integral as a Limit of Sums**Book Section:**5.4 The Definite Integral**Lecture Notes:**Lecture Notes Day 46**Homework:**- H85: Using Properties of Definite Integral (33,41,45,49,51,53)
- H86: Conceptual Problems (55,56)

**>>> Quiz 9 <<<**

**Tue Nov 20 is an Optional Class Meeting****Wed Nov 21 - Fri Nov 23 is Thanksgiving Break No Class**

**Day #47:**5.5 Fundamental Theorem of Calculus**Topic:**The Fundamental Theorem of Calculus**Book Section:**5.5 The Fundamental Theorem of Calculus**Class Drills:**Class Drill 32: The Fundamental Theorem of Calculus**Lecture Notes:**Lecture Notes Day 47**Homework:**H87: Basic Definite Integrals (11,13,15,17,19,21,23,25,27,31)

**Day #48:**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 48**Homework:**- H88: Harder Definite Integrals (35,36,38,39,41,45)
- H89: Total Change Problems (69,71,89)

**Day #49:**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 49**Homework:**H90: Average Value of a Function Over an Interval (49,51,55,92)

**Day #50:****In-Class Exam 4 on Chapter 5**

**Day #51:**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 Drills:**Class Drill 33: Finding Area Bounded by Curves Using Two Different Methods**Lecture Notes:**Lecture Notes Day 51**Homework:**- H91: Area between curve and x-axis (9,11,17,21,23,25,57)
- H92: Area between two curves (3,5,37,47,53,55,63)

**Day #52:**6.1 Applications of the Area Between Two Curves**Topic:**Applications of the Area Between Two Curves**Book Section:**6.1 Area Between Curves**Handout:**Handout on the Gini Index**Lecture Notes:**Lecture Notes Day 52**Homework:**H93: Applications of the Area Between Two Curves (83,85,89)

**Day #53:**6.2 Total Income & Future Value for Continuous Income Stream**(Quiz 10)****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 53**Homework:**- H94: Total Income from a Continuous Income Stream (37,39,41,43)
- H95: Future Value of Continuous Income Stream (9,13,45,47,49,51,53,67)

**>>> Quiz 10 <<<**

**Day #54:**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 54**Homework:**H96: Consumers’ Surplus; Consumers’ Surplus (69,71,73,75,77)

**Mon Dec 10 Section 105 has its Final Exam from 10:10am - 12:10pm in Morton 115 (Exam Info)****Wed Dec 12 Section 109 has its Final Exam from 10:10am - 12:10pm in Morton 215 (Exam Info)**

page maintained by Mark Barsamian, last updated Jan 7, 2019