Course Description: First course in calculus and analytic geometry with applications in the sciences and engineering. Includes basic techniques of differentiation and integration with applications including rates of change, optimization problems, and curve sketching; includes exponential, logarithmic and trigonometric functions. Calculus is the mathematical language used to describe and analyze change. The course emphasizes how this abstract language and its associated techniques provide a unified way of approaching problems originating in disparate areas of science, technology, and society, highlighting how questions arising in different fields are connected to the same fundamental mathematical ideas. No credit for both MATH 2301 and 1350 (always keep 2301).
Prerequisites: (B or better in MATH 1350) or (C or better in 1300 or 1322) or (Math placement level 3)
Meeting Times and Locations:
Lecture Section 100 meets Mon Wed, Fri 8:35am – 9:30pm in Morton Hall 127.
Associated to Lecture Section 100 are three Recitation Sections, led by Alexander Pahlow
Special Needs: If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let Mark Barsamian know as soon as possible so that your learning needs may be appropriately met. You should also register with the
Office of Student Accessibility Services
to obtain written documentation and to learn about the resources they have available.
Final Exam Date: All MATH 2301 Sections will have a Common Final Exam on Thu Dec 10, 2026, from 4:40pm – 6:40pm in Morton Hall Rooms to be announced later.
Attendance Policy:
Attendance is required for all class meetings, and your attendance (or absence) will be recorded, but attendance is not used in the calculation of your course grade.
Missing Class: If you miss a class for any reason, it is your responsibility to learn the stuff that you missed. You can do this by studying a classmate's notes, watching the videos that Mark Barsamian posts online, and by reading the textbook. Your Instructors will not use office hours to teach topics discussed in class meetings 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 do these three things:
Send Mark Barsamian an e-mail before the quiz/exam, telling him that you are going to miss it because of illness. He will arrange for a date and time for a Make-Up quiz/exam. (Generally, the Make-up for a Friday quiz/exam needs to take place on the following Monday or Tuesday. Therefore, it is important to communicate with him right away.)
Go to the Hudson Student Health Center (or some other Medical Professional) to get examined.
Later, you will need to bring Mark Barsamian your documentation from the Hudson Student Health Center (or a Medical Professional) showing that you were treated there.
Without those three things, you will not be given a make-up. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)
(Observe that self-diagnosis of an illness is not a valid documentation of an illness. In other words, you can't just tell Mark Barsamian that you did not come to a Quiz or Exam because you were not feeling well, and expect to get a Make-Up Quiz or Exam. If you are too sick to come to a Quiz or Exam, then you should be sick enough to go to a medical professional to get diagnosed and treated.)
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 Mark Barsamian well before the quiz or exam to discuss arrangements for a make-up. They will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying Mark Barsamian in advance, you will not be given a make-up.
Missing Quizzes or Exams Because of Religious Observation: The Ohio University Faculty Handbook states the following:
Students may be absent for up to three days each academic semester to take time off for reasons of faith or religious or spiritual belief system or participate in organized activities conducted under the auspices of a religious denomination, church, or other religious or spiritual organization. Faculty shall not impose an academic penalty because of a student being absent nor shall faculty question the sincerity of a student's religious or spiritual belief systems. Students are expected to notify faculty in writing of specific dates requested for alternative accommodations no later than fourteen days after the first day of instruction.
For MATH 2301, this means that if you will be missing any Fall 2026 Quizzes or Exams for religious reasons, and if you want to have a Make-Up Quiz/Exam, you will need to notify your Professor no later than Monday, Sep 7, 2026. You and Mark Barsamian will work out the dates/times of your Make-Up Quiz/Exam. (In general, if you are going to miss a Friday Quiz/Exam, your Professor will schedule you for a Make-Up on the following Monday or Tuesday.)
Missing Presentations, Quizzes, or Exams Because of Personal Travel: This course meets on Mondays, Tuesdays, Wednesdays and Fridays, and attendance is required. Your Personal Travel (to home for the weekend, or out of town for vacations, etc) should be scheduled to not conflict with those class meetings. If you miss a Recitation, Quiz, or Exam because of Personal Travel (not an Offical University Activity), you will not be given a make-up. (When you miss a Quiz or Exam and are not given a Make-Up, the missed Quiz or Exam will be considered your one Quiz or Exam score that gets dropped.)
Electronic Communication Policy (For both Students and Instructors):
Policy for Electronic communication between MATH 2301 Students and Instructors
Electronic communication between MATH 2301 Students and Instructors should be done using one of these two methods:
The Official Ohio University e-mail system. That is, communications should use email addresses ending in @ohio.edu. In other words, send your emails from your OU e-mail account, and address them to a recipient's OU e-mail address. (Students: If you use the Canvas system to send an email to your Instructor, this is automatically taken care of.)
The Teams program. (Teams can be used for chat, voice calling, video calling, and video meetings. It is remarkably powerful.
Do not use a personal email address (such as a gmail address) when sending an email.
Students and Instructors should not communicate via text messages.
Students and Instructors: It is your reponsibility to check your OU e-mail every day. (Students: If you are communicating with your Instructor about a time-sensitive issue, such as trying to schedule a Make-Up Quiz or Exam after an illness, your e-mail replies need to be swift. It is not acceptable to let days pass before replying to an important e-mail message, with your excuse being that you had not checked your OU email. If you do this, you will lose the opportunity to have a Make-Up Quiz or Exam.)
It is a good practice to use a descriptive Subject line such as Regarding MATH 2301 Section XXX on your email messages. That way, the recipient will know to give the email message high priority.
It is also a good practice to use a greeting such as
Hi Elon,
on your email messages, and to identify yourself in your message. And use a closing such as
Thanks, Jeff Bezos
Policy on Cheating:
If cheat on a quiz or exam, you will receive a zero on that quiz or exam and your Instructor will submit a report to the Office of Community Standards and Student Responsibility (CSSR).
If you cheat on another quiz or exam, you will receive a grade of F in the course and your Instructor will again submit a report to the CSSR.
A Basic Skills Diagnostic Test will be given on the first day of class.
20 Minutes at the end of class, taken on paper.
No books, notes, calculators, or phones
Ten problems involving some basic Algebra skills that are needed in MATH 2301.
Each problem is worth 1 point, for a total of 10 points possible.
The Diagnostic Test is scored, but your score is not used in computing your MATH 2301 grade.
Your graded Diagnostic Test is not returned to you. See your score in the Canvas Gradebook.
If you score 7 or less on the Diagnostic Test, you are likely to have difficulty succeeding in MATH 2301. It is strongly recommended that you add the 1 credit course MATH D301 to your current fall semester. (That is, take MATH D301 while simultaneously taking MATH 2301.) (See information about MATH D301 below)
Suggested Supplemental Course: MATH D301:
Information about MATH D301
At most universities around the country, students struggle in Calculus courses. Ohio University MATH 2301 is no exception.
Instructors observe that students who struggle in Calculus generally have very weak Algebra skills. It is impossible to succeed in Calculus without good Algebra skills.
Ohio University MATH D301 Learning Laboratory for Calculus 1 is a one – credit course in which students will work on algebra skills that are needed in MATH 2301. The course meets for 80 minutes each week and is designed to be taken concurrently with MATH 2301.
Syllabus: This web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook Information, Exercises, Grading, Calendar) and then print this web page.
Textbook and WebAssign Information:
click to enlarge
Required Online Course Materials: Through a program called Inclusive Access, the University has negotiated with the publisher a special price for this course's Required Online Course Materials. On the first day of class, you will receive access to an an online system called WebAssign. The WebAssign system includes an eText version of the textbook and an online homework system. The cost of the Online Course Materials is a discounted Inclusive Access Price of $50. That cost will be automatically billed to your Ohio University Student Account. If you drop the course before the drop deadline (Fri, Sep 4), your student account will be credited for any amount billed. After you register, you will receive more information about the Inclusive Access program, including an option to "Opt Out" of participation in the program. To "Opt Out" means that your payment for the Online Course Materials is not handled by the Inclusive Access program. If you do that, you can still use the Online Course Materials, but in order to access them, you will be asked to make a credit card payment for the Retail Price of the materials. (Note that the Retail Price is significantly higher than the Inclusive Access Price.)
Information about the Textbook
Title: Essential Calculus, Early Transcendentals, Second Edition
Author: James Stewart
Publisher: Cengage (2012)
ISBN-13: 978-1133112280
Exercises:
Exercises for 2026 – 2027 Fall Semester MATH 2301 Section 100 (Barsamian) (from Stewart Essential Calculus Early Transcendentals 2nd Edition)
Your goal should be to write solutions to all 405 exercises in this list.
Suggestion: WebAssign does not require that you write stuff down, but you will learn a lot by focusing on your writing. Furthermore, having good writing skills will help you succeed on Quizzes and Exams. Study by writing a complete solution to each problem before typing the answer into WebAssign. Focus on the clarity of your written solution. Keep your written solutions in a notebook. Compare your written solutions to your Instructors’ written solutions in Lectures and Recitations. Find another student, a tutor, the Recitation Instructor, or your Professor to look over your written solutions with you.
Grading:
Grading System for 2026 – 2027 Fall Semester MATH 2301 Section 100 (Barsamian)
During the course, you will accumulate a Points Total of up to 1031 possible points.
Recitation: Best 14 of 15 Tuesday Recitation Activities @ 5 points each = 70 points possible
Quizzes: Best 8 of 9 Quizzes @ 30 points each = 240 points possible
Exams: Best 2 of 3 Exams @ 220 points each = 440 points possible
Final Exam: 250 points possible
WebAssign: 31 Assignments @ 1 point each = 31 points possible
At the end of the semester, your Points Total will be divided by \(1000\) to get a percentage, and then converted into your Course Letter Grade using the 90%, 80%, 70%, 60% Grading Scale described below.
Observe that the Total Possible Points is \(1031\), but your points total is divided by \(1000\) to get the percentage that is used in computing your course grade. This is because the \(31\) points that can be earned by doing WebAssign Homework are considered Extra Credit Points.
The 90%, 80%, 70%, 60% Grading Scale is used on all graded items in this course, and is used in computing your Course Letter Grade.
A grade of A, A- means that you mastered all concepts, with no significant gaps.
If \(93\% \leq score \), then letter grade is A.
If \(90\% \leq score \lt 93\%\), then letter grade is A-.
A grade of B+, B, B- means that you mastered all essential concepts and many advanced concepts, but have some significant gap.
If \(87\% \leq score \lt 90\%\), then letter grade is B+.
If \(83\% \leq score \lt 87\% \), then letter grade is B.
If \(80\% \leq score \lt 83\%\), then letter grade is B-.
A grade of C+, C, C- means that you mastered most essential concepts and some advanced concepts, but have many significant gaps.
If \(77\% \leq score \lt 80\%\), then letter grade is C+.
If \(73\% \leq score \lt 77\%\), then letter grade is C.
If \(70\% \leq score \lt 73\%\), then letter grade is C-.
A grade of D+, D, D- means that you mastered some essential concepts.
If \(67\% \leq score \lt 70\%\), then letter grade is D+.
If \(63\% \leq score \lt 67\% \), then letter grade is D.
If \(60\% \leq score \lt 63\%\), then letter grade is D-.
A grade of F means that you did not master essential concepts.
If \(0\% \leq score \lt 60\%\), then letter grade is F.
There is no grade curving in this course.
Two things that are not part of your Course Grade
Attendance: Attendance is recorded but is not part of your course grade
Written Solutions to Homework Exercises: There is a list of Homework Exercises on this web page. To succeed in the course, you will need to do lots of them (preferrably all of them), writing the solutions on paper. Those written solutions are not graded and are not part of your course grade. (Your scores on the online WebAssign homework will be part of your course grade.)
Mon Aug 24 Lecture L01:
Course Intro; Section 1.3: The Limit of a Function
(First Day Handout)(video)
(Basic Skills Diagnostic Test)
Information about the Basic Skills Diagnostic Test
20 Minutes at the end of class
No books, notes, calculators, or phones
Ten problems involving some basic Algebra skills that are needed in MATH 2301.
Each problem is worth 1 point, for a total of 10 points possible.
The Diagnostic Test is scored, but your score is not used in computing your MATH 2301 grade.
If you score 7 or less on the Diagnostic Test, you are likely to have difficulty succeeding in MATH 2301. It is strongly recommended that you add the 1 credit course MATH D301 to your current fall semester. (That is, take MATH D301 while simultaneously taking MATH 2301.) (See information about MATH D301 above on this web page.)
Tue Aug 25: Recitation R01
Instructions for Recitation R01, Tue Aug 26, 2026
Students will work on the problems in the packet called Recitation R01 Problems. (The Recitation Instructor will hand out printed copies at the beginning of the Recitation session.)
Students should work in groups of two or three.
There should be no students working alone.
There should be no groups with more than three students.
The Recitation Instructor will hand out one copy of the packet to each group.
All the students in the group should print their names on the packet.
Students should complete as much of the packet as they can, and then hand the packet to the Recitation Instructor at the end of the Recitation period.
Six Problems to Be Done in Recitation R02 for MATH 2301 (Barsamian)
Instructions
Students work on the chalkboard in groups of two or three students.
Work on a problem for 5 minutes
Then the Instructor discusses the work of some of the groups for 5 minutes
Then move on to the next problem
[1] A limit that is an Indeterminate Form and that require no trick, just messy work
(This problem is similar to book exercise 1.4#15, which is not assigned. It is also similar to Book Section 1.4 Example 2)
Find the limit
$$\lim_{t\rightarrow -2}\frac{t^2-t-6}{2t^2+5t+2}$$
Show valid steps that lead to your answer.
[2] A limit that Involves Rationalizing
(This problem is similar to homework exercise 1.4#21 and Book Section 1.4 Example 5)
Find the limit
$$\lim_{h\rightarrow 0}\frac{\sqrt{49+h}-7}{h}$$
Show valid steps that lead to your answer.
[3] A Limit that involves the Absolute Value
(This problem is similar to homework exercise 1.4#38, and similar to Book Section 1.4 Example 7)
Find the limit
$$\lim_{x\rightarrow -4}\frac{3x+12}{|x+4|}$$
Show valid steps that lead to your answer.
[4] A Limit involving the Squeeze Theorem
(This problem is similar to homework exercise 1.4#35 and Book Section 1.4 Example 9.)
Prove that that
$$\lim_{x\rightarrow 0}\left[x^2\cos{\left(\frac{3}{x}\right)}\right]=0$$
Show valid steps that lead to your answer.
Hint: Use the Worksheet entitled Using the Squeeze Theorem to organize your work.
[5] A limit that uses the famous fact that \(\lim_{x\rightarrow 0}\frac{\sin{(x)}}{x}=1\)
(This problem is similar to homework exercises 1.4#51 and is related to book Section 1.4 Example 10)
Find the limit
$$\lim_{t\rightarrow 0}\frac{\tan{(12t)}}{\sin{(3t)}}$$
Show valid steps that lead to your answer.
Warning: Don’t be tempted to replace
\(\tan{(12t)}\) with \(12\tan{(t)}\) because \(\tan{(12t)} \neq 12\tan{(t)}\)
Hint: Replace \(tan{(12t)}\) with \(\frac{\sin{(12t)}}{\cos{(12t)}}\)
[6] Problem involving the Intermediate Value Theorem
(a) Let \(f(x)=x+\sqrt[3]{x}-1\).
Use the Intermediate Value Theorem to show that \(f(x)\) has a root
on the interval \((0,1)\). That is, show that there exists an \(x\) value, with \(0 \lt x \lt 1\), such that \(f(x)=0\).
Explain clearly.
Hint: Use the Worksheet entitled Using the Intermediate Value Theorem to organize your work.
(b) (This problem is book exercise 1.5#40, which is similar to homework exercise 1.5#39) Use the Intermediate Value Theorem to show that there is a solution of the equation
$$\sqrt[3]{x}=1-x$$
on the interval (0,1).
Explain clearly.
Fri Oct 23 Lecture L23:
Section 4.3: Derivatives and the Shapes of Graphs
(video)
(Quiz Q5)
Quiz Q5 Information
20 Minutes at the end of class
No books, notes, calculators, or phones
Three Problems, 10 points each, printed on front & back of one sheet of paper
A problem about L’Hospital’s Rule (concepts from 3.7)
A problem about L’Hospital’s Rule (concepts from 3.7)
A problem about finding the critical numbers of a function (concepts from Section 4.1)
Mon Oct 26 Lecture L24:
Section 4.3: Derivatives and the Shapes of Graphs
(video)
Reference Material: Terminology and Tests about Increasing/Decreasing Behavior and Concavity Behavior from Section 4.3.
Definition of Increasing Function (Section 1.1)
Words: Function \(f\) is increasing on the open interval \((a,b)\).
Meaning: If \(a \lt x_1 \lt x_2 \lt b\) and \(x_1 \lt x_2\), then \(f(x_1) \lt f(x_2)\).
Definition of Decreasing Function (Section 1.1)
Words: Function \(f\) is decreasing on the open interval \((a,b)\).
Meaning: If \(a \lt x_1 \lt x_2 \lt b\) and \(x_1 \lt x_2\), then \(f(x_1) \gt f(x_2)\).
Increasing/Decreasing Test (Section 4.3)
If \(f'(x)\) is positive on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be increasing on (at least) the whole interval \((a,b)\).
If \(f'(x)\) is negative on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be decreasing on (at least) the whole interval \((a,b)\).
If \(f'(x)\) is zero on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be constant on (at least) the whole interval \((a,b)\).
Remark: If the Increasing/Decreasing Test guarantees that some function \(f\) is increasing on a whole interval \((a,b)\), then \(f\) could actually be increasing on some larger interval containing \((a,b)\).
But the information about the behavior on the larger interval might not come from the Increasing/Decreasing Test. It might have to come from some careful consideration of the particular situation.
The First Derivative Test for Local Extrema (Section 4.3) Suppose that \(x=c\) is a critical number of a function \(f\), and that \(f\) is continuous near \(c\). That is, there exist real numbers \(a,b\) such that \(a \lt c \lt b\) such that \(f\) is continuous on the whole interval \((a,b)\) and \(f'(c)=0\) or \(f'(c) \ DNE\).
If \(f'(x)\) changes from positive to negative at \(c\). then \(x=c\) is the location of a local maximum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local max value.
If \(f'(x)\) changes from negative to positive at \(c\). then \(x=c\) is the location of a local minimum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local min value.
Definition of Concavity (Section 4.3)
Words: Function \(f\) is concave upward the open interval \((a,b)\).
Meaning: The graph of \(f\) lies above all of its tangents on the open interval \((a,b)\).
Remark: There is analogous definition for concave down.
Related terminology: An inflection point is a point on the graph of a function where the
function is continuous and the concavity changes (from up to down or from down to up).
Concavity Test (Section 4.3)
If \(f''(x)\) is positive on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be concave up on (at least) the whole interval \((a,b)\).
If \(f''(x)\) is negative on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be concave down on (at least) the whole interval \((a,b)\).
If \(f''(x)\) is zero on a whole open interval \((a,b)\), then \(f(x)\) is guaranteed to be a straight-line function, not concave on (at least) the whole interval \((a,b)\).
Second Derivative Test for Local Extrema Suppose that a function \(f\) is continuous near \(x=c\). That is, there exist real numbers \(a,b\) such that \(a \lt c \lt b\) such that \(f\) is continuous on the whole interval \((a,b)\).
If \(f'(c)=0\) and \(f’'(c) \gt 0\). then \(x=c\) is the location of a local minimum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local min value.
If \(f'(c)=0\) and \(f’'(c) \lt 0\). then \(x=c\) is the location of a local maximum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local max value.
Remark: If \(f'(c)=0\) and \(f’'(c) = 0\). then the Second Derivative Test gives no information about possible local max or local min behavior. In that situation, the First Derivative Test for Local Extrema would have to be used instead.
The First Derivative Test for Local Extrema (Section 4.3) Suppose that \(x=c\) is a critical number of a function \(f\), and that \(f\) is continuous near \(c\). That is, there exist real numbers \(a,b\) such that \(a \lt c \lt b\) such that \(f\) is continuous on the whole interval \((a,b)\) and \(f'(c)=0\) or \(f'(c) \ DNE\).
If \(f'(x)\) changes from positive to negative at \(c\). then \(x=c\) is the location of a local maximum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local max value.
If \(f'(x)\) changes from negative to positive at \(c\). then \(x=c\) is the location of a local minimum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local min value.
Second Derivative Test for Local Extrema (Section 4.3) Suppose that a function \(f\) is continuous near \(x=c\). That is, there exist real numbers \(a,b\) such that \(a \lt c \lt b\) such that \(f\) is continuous on the whole interval \((a,b)\).
If \(f'(c)=0\) and \(f’'(c) \gt 0\). then \(x=c\) is the location of a local minimum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local min value.
If \(f'(c)=0\) and \(f’'(c) \lt 0\). then \(x=c\) is the location of a local maximum of \(f(x)\). The corresponding \(y\) value, \(y=f(c)\), is the local max value.
Remark: If \(f'(c)=0\) and \(f’'(c) = 0\). then the Second Derivative Test gives no information about possible local max or local min behavior. In that situation, the First Derivative Test for Local Extrema would have to be used instead.
Review of Notation and Definitions from Previous Lecture, L32
Expressions for Computation of Left and Right Sums (Called Riemann Sums)
Width of Rectangles is
$$\Delta x = \frac{b-a}{n}$$
Important \(x\) values are
$$x_0=a, \ \ x_1=a+\Delta x, \ \ x_2=a+2\Delta x, \ \ \dots \ \ , x_n=a+n\Delta x = b$$
Using these symbols, the formulas for the left and right Riemann sums are
$$L_n=f(x_0 )\Delta x+f(x_1 )\Delta x+\dots+f(x_{n-1} )\Delta x=\sum_{i=0}^{i=n-1}f(x_i )\Delta x$$
$$R_n=f(x_1 )\Delta x+f(x_2 )\Delta x+\dots+f(x_n )\Delta x=\sum_{i=1}^{i=n}f(x_i )\Delta x$$
Expression for Computation of Signed Area
We defined signed area, abbreviated \(SA\), to be limit of the Riemann Sums. That is,
$$SA=\lim_{n\rightarrow \infty}L_n = \lim_{n\rightarrow \infty}R_n$$
Recall that it doesn’t matter whether you take the limit of the left sum, \(L_n\), or the right sum, \(R_n\). The resulting limit will be the same.
Using the limit notation in front of the above expression for \(R_n\), we obtain
$$SA= \lim_{n\rightarrow \infty}R_n= \lim_{n\rightarrow \infty}\left[f(x_1 )\Delta x+f(x_2 )\Delta x+\dots+f(x_n )\Delta x\right]= \lim_{n\rightarrow \infty}\sum_{i=1}^{i=n}f(x_i )\Delta x$$
