MATH 3300 Calculus III section 100 (6547), Spring 2025-26

Catalog Entry (2025-26)

Description:
Third course in calculus and analytic geometry with applications in the sciences and engineering. Includes partial differentiation, multiple integrals, line and surface integrals, and the integral theorems of vector calculus.
Requisites:
C or better in MATH 2302
Credit Hours:
4
Repeat/Retake Information:
May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours:
3.0 lecture; 1.0 recitation
Grades:
Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Course Transferability:
TAG course: OMT018 Calculus III
College Credit Plus:
Level 1
Learning Outcomes:
New Learning Outcomes (official but not yet in the catalog):
  1. Students will be able to perform and apply vector operations, including the dot and cross product of vectors, in the plane and space.
  2. Students will be able to graph and find equations of lines, planes, cylinders and quadratic surfaces.
  3. Students will be able to differentiate and integrate vector-valued functions.
  4. Students will be able to interpret position vectors that are a function of time as velocity and acceleration.
  5. Students will be able to evaluate limits and determine the continuity and differentiability of functions of several variables.
  6. Students will be able to describe graphs, level curves and level surfaces of functions of several variables.
  7. Students will be able to find partial derivatives, directional derivatives, and gradients and use them to solve applied problems.
  8. Students will be able to find equations of tangent planes and normal lines to surfaces that are given implicitly or parametrically.
  9. Students will be able to use the chain rule for functions of several variables (including implicit differentiation).
  10. Students will be able to find critical points using first partials and interpret them as relative extrema/saddle points using the second partials test.
  11. Students will be able to find absolute extrema on a closed region.
  12. Students will be able to solve to optimization problems for functions of several variables.
  13. Students will be able to use Lagrange multipliers to solve constrained optimization problems.
  14. Students will be able to evaluate multiple integrals in appropriate coordinate systems such as rectangular, polar, cylindrical and spherical coordinates.
  15. Students will be able to apply integration techniques to solve problems involving volume, surface area, density, moments and centroids.
  16. Students will be able to use Jacobians to change variables in multiple integrals.
  17. Students will be able to use evaluate line and surface integrals.
  18. Students will be able to identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals to solve applied problems.
  19. Students will be able to identify conservative and inverse square fields.
  20. Students will be able to find the curl and divergence of a vector field.
  21. Students will be able to solve applied problems by finding the work done on an object moving in a vector field.
  22. Students will be able to solve applied problems by finding the flux of a field through a surface.
  23. Students will be able to solve problems using Green's Theorem, the Divergence Theorem and Stokes's Theorem.

Syllabus

Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, Morton Hall 555. Office hours (tentatively) Mondays 3:05-4:00pm, Wednesdays 2:00-2:55pm, and Fridays 10:45-11:40am. Do not hesitate to contact me with questions or to make an appointment to meet at another time.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/2265/3300/.
Text:
APEX Calculus (5th edition, online) by Gregory Hartman, with other contributors. This free online text works well on phones, tablets, and computers, and has some interactive content and auto-corrected exercises.
Lecture Component:
Recitation Component:
You are also enrolled in one of the recitation sections: All recitations are led by Nutifafa Akpeleasi.

On weeks of tests, the recitation will consist of test review and open time for questions. In the remaining 10 weeks, recitations will typically consist of:

If you miss the recitation, then you may turn in the groupwork as an individual by class on the following Monday, but it will have a 25% late penalty.

Tests:
There will be 4 mid-term tests. Your best 3 scores count toward your grade. Calculators are not permitted. Bring your student ID to the tests. The tests are cumulative.

Missed tests:
Tests missed due to university excused absences for illness, death in the immediate family, religious observance, jury duty, or involvement in University-sponsored activities can be made up if
  • you let me know in advance and I approve the absence, and
  • you are able to take the test before the class meets on the following Wednesday.
Otherwise, the first missed test is automatically dropped since only your best 3 out of 4 count in your grade. A second missed test will be replaced by your final exam score. Further missed tests count as 0.

Final Exam:
The final exam is on Wednesday April 29, 10:10am-12:10pm in our regular classroom.
Text exercises:
Exercises are recommended for each section of the text. These are not collected or graded, but doing them is the foundation for your learning. This textbook has only a moderate number of exercises, so for many sections all the exercises are recommended. In the html text, many of them will check your answer and others have answers in the back of the book.
Grades:
Your final average is composed of An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
Academic Misconduct:
Recitation Groupwork:
  • You may use your book, Wikipedia, other Calculus books, general websites about Calculus, etc. without special acknowledgment.
  • If your group receives any help specifically on the problem you are trying to solve (such as assistance from another group or software that solves the problem), you must acknowledge in writing what help you received and from whom or what source (including internet links and AI). (You do not need to acknowledge your recitation leader.)
A minor, first-time violation will receive a warning and discussion and clarification of the rules.
Tests, final exam:
You may not give or receive any assistance during a test or the exam, including but not limited to using notes, phones, calculators, computers, or another student's solutions. (You may ask me questions.) A minor, first-time violation will result in a zero grade on that test.
Serious or second violations will result in failure in the class and be reported to the Office of Community Standards and Student Responsibility, which may impose additional sanctions. You may appeal any sanctions through the grade appeal process.
Religious Accommodations
In accordance with the university's policy 40.003: Reasonable Accommodations of Sincerely Held Religious Beliefs and Practices:

You may be absent for up to three (3) days each academic semester, without penalty, to take time off for reasons of faith or religious or spiritual belief system or to participate in organized activities conducted under the auspices of a religious denomination, church, or other religious or spiritual organization. You are required to notify me in writing of specific dates requested for alternative accommodations no later than fourteen (14) days after the first day of instruction. These requests will remain confidential. For more information about this policy, contact the office of Civil Rights Compliance.

Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met. You should also register with Student Accessibility Services to obtain written documentation and to learn about the resources they have available.
Responsible Employee Reporting Obligation:
If I learn of any instances of sexual harassment, sexual violence, and/or other forms of prohibited discrimination, I am required to report them. If you wish to share such information in confidence, then use the Office of Equity and Civil Rights Compliance.
Advice:
How to be successful at CalculusHow to be unsuccessful at Calculus
Have a growth mindset: believe that through effort you can improve your mathematical skills. Have a fixed mindset: believe that your mathematical skills are set, so effort is either unneccessary or futile.
Show up and do the work.Skip stuff. Start with an occasional class, then a recitation, then some homework, ...
Figure out the solutions to activities and exercises. Find the solutions to activities and exercises by copying from classmates, looking at posted answers, searching the internet, asking AI, etc.
Be active in class: think, write, talk, do, ...Be passive (or distracted) in class, waiting for learning to somehow happen.
Read the book. Carefully. Multiple times. Don't read the book. Make excuses like "It is too confusing.", "I learn better from videos.", or "The instructor should tell me everything I need to know in class."
Do the exercises in the text. Ignore the exercises in the text. Convince yourself that since it is not collected it must not be important.
Strive for mastery. Mastery is when you can solve the problem confidently by yourself. Settle for familiarity rather than mastery. Familiarity is when you recognize a problem and can follow along when someone else, a video, or the book solves it.
Sparingly use videos like Khan Academy. When you do, pay attention and work along with the video. Use videos a lot and as a replacement for reading. Count it as studying when you let them play in the background while you do something else.
Make sure all members of your group (including yourself) understand the recitation groupwork before submitting it.Do the recitation groupwork by splitting up the problems and working on them separately. That way you only have to learn a third of it.
When you are struggling, get help.When you are struggling, hide.
Learning resources:
People:
  • Your classmates.
  • Your recitation leader.
  • Your instructor.
The Academic Achievement Center
has a STEM Academy in Morton 415 that offers Small Group Tutoring, Drop-in Tutoring, and Study Groups.
Software:
Other Textbooks:
openstax has many free online Mathematics textbooks, including a Calculus Volume 3 book that has many of the topics we cover. (We will use this book for two topics missing from our book.)

MATH 5300 (12612) Modifications

For student enrolled in the MATH 5300 graduate version of this course, the above syllabus is modified as follows.

Additional Learning Outcome:
Students will be able to apply vector calculus methods to solve advanced theoretical and applied problems.
Recitation:
You are also enrolled in MATH 5300-101 (12733), which is listed as arranged. You may choose which of the MATH 3300 recitations listed above to attend.
Graduate Assignments:
You will do two assignments to give you the opportunity to demonstrate that you can apply vector calculus methods to solve advanced theoretical and applied problems in your field. The first is due around Spring break and must use a method from chapters 11, 12, or 13. The second is due at the final exam and must use a method from chapters 14 or 15.
Grades:
Your final average is composed of
  • 15% for the graduate assignments,
  • 20% for your best 8 (out of 10) recitation scores,
  • 40% for your best 3 (out of 4) tests, and
  • 25% for the final exam.
An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.

Schedule (Subject to change)

Week Date Section/Topic Text Exercises Information/Resources
1
Chapter 11 Vectors
Mon Jan 12 11.1 Introduction to Cartesian Coordinates in Space 1-32 [23-26]
Wed Jan 14 11.2 An Introduction to Vectors 1-36 [11, 18, 24] sage vectors
Thu Jan 15Recitation: Groupwork: 11.1 #8, 11, 16, 26, 32 ; 11.2 #12, 34
Fri Jan 16 11.3 The Dot Product 1-39 [7, 13, 25] sage dot product
2
Mon Jan 19 Martin Luther King, Jr. Day holiday, no class
Wed Jan 21 11.4 The Cross Product 1-44 [7, 27, 33] sage cross product
Thu Jan 22 Recitation: Groupwork: TBA
Fri Jan 23 11.5 Lines 1-31 [5, 27] (drop deadline) desmos parametric line
3
Mon Jan 26 11.6 Planes 1-32 [9, 11, 13, 15, 17, 19, 27]
Chapter 12 Vector Valued Functions
Wed Jan 28 12.1 Vector-Valued Functions 1-34 [7, 19, 22] desmos circular motion
Thu Jan 29 Recitation: Test preparation
Fri Jan 30 Test through 11.6
4
Mon Feb 2 12.2 Calculus and Vector-Valued Functions 1-45 [7, 12, 24, 33, 36, 39, 41]
Wed Feb 4 12.3 The Calculus of Motion 1-42 [7, 29]
Thu Feb 5Recitation: Groupwork: TBA
Fri Feb 6 12.4 Unit Tangent and Normal Vectors but skip 12.4.3; also skip 12.5 1, 2, 5-24 [5, 21]
5
Chapter 13 Functions of Several Variables
Mon Feb 9 13.1 Introduction to Multivariable Functions 1-31 [19, 23] desmos level curves
Wed Feb 11 13.2 Limits and Continuity of Multivariable Functions 1-20 [13, 17] desmos 2D limits
Thu Feb 12 Recitation: Groupwork: TBA
Fri Feb 13 13.3 Partial Derivatives 1-34 [26, 31] desmos partial derivatives
Definitions of differentiability from 13.4 Differentiability and the Total Differential 1, 2
6
Mon Feb 16 13.5 The Multivariable Chain Rule 1-30 [17, 19, 23, 30] desmos chain rule
Wed Feb 18 13.6 Directional Derivatives 1-28 [7, 13, 19, 25] desmos gradient vector; desmos gradient and level curves
Thu Feb 19 Recitation: Test preparation
Fri Feb 20 Test through 13.5
7
Mon Feb 23 13.7 Tangent Lines, Normal Lines, and Tangent Planes 1-24 [17, 21]
Wed Feb 25 13.8 Extreme Values 1-18 [12, 15]
Thu Feb 26Recitation: Groupwork: TBA
Fri Feb 27 openstax 4.8 Lagrange Multipliers 359-379 odd [367] desmos Lagrange Multipliers, 2D example, 3D example
8
Chapter 14 Multiple Integration
Mon Mar 2 14.1 Iterated Integrals and Area 1-22 [15, 19] desmos bounds of integration I, bounds on integration II
Wed Mar 4 14.2 Double Integration and Volume 1-26 [7, 23] desmos double integral
Thu Mar 5 Recitation: Groupwork: TBA
Fri Mar 6 14.3 Double Integration with Polar Coordinates 1-16 [13]
Spring Break
9
Mon Mar 16 14.4 Center of Mass 1-30 [20]
Wed Mar 18 14.5 Surface Area 1-19 [7, 11]
Thu Mar 19 Recitation: Test preparation
Fri Mar 20 Test through 14.4
10
Mon Mar 23 14.6 Volume Between Surfaces and Triple Integration 1-24 [7, 17] desmos triple integral
Wed Mar 25 14.7 Triple Integration with Cylindrical and Spherical Coordinates 1-44 [25, 33, 41] desmos spherical coordinate volume
Thu Mar 26Recitation: Groupwork: TBA
Fri Mar 27 openstax 5.7 Change of Variables in Multiple Integrals 357-401 odd [385, 389, 393] (drop deadline with WP/WF)
11
Chapter 15 Vector Analysis
Mon Mar 30 15.1 Introduction to Line Integrals 1-20 [15, 19]
Wed Apr 1 15.2 Vector Fields 1-18 [13] 3blue1brown video: Divergence and curl
Thu Apr 2 Recitation: Groupwork: TBA
Fri Apr 3 15.3 Line Integrals over Vector Fields 1-21 [11, 17]
12
Mon Apr 6 15.4 Flow, Flux, Green’s Theorem and the Divergence Theorem 1-24 [13, 17]
Wed Apr 8 15.5 Parametrized Surfaces and Surface Area 1-24 [7, 17]
Thu Apr 9 Recitation: Test preparation
Fri Apr 10 Test through 15.4
13
Mon Apr 13 15.6 Surface Integrals 1-14 [5, 7]
Wed Apr 15 15.7 The Divergence Theorem and Stokes’ Theorem 1-24 [13, 17]
Thu Apr 16Recitation: Groupwork: TBA
Fri Apr 17 Catch up
14
Mon Apr 20 Catch up
Wed Apr 22 Catch up
Thu Apr 23 Recitation: Groupwork: TBA
Fri Apr 24 Recap/ Review/ Exam preparation
15
Wed Apr 29 Final Exam 10:10am-12:10pm in our regular classroom.
Martin J. Mohlenkamp

Last modified: Wed Dec 17 15:49:41 UTC 2025