MAC 2313 : Calculus with Analytic Geometry III
Multivariable calculus: vectors and alternative coordinate systems, differentiation and integration of functions of several variables, vector fields, and the classical integral theorems of vector calculus.
Instructor: Abel Okojunu
Term: Fall 2025
Role
Instructor of record, Fall 2025, responsible for classroom instruction, student mentoring, and assessment feedback. The course was coordinated across multiple sections, with a common departmental syllabus and shared assessments.
Course Overview
A five-credit course in multivariable calculus and the third in the calculus sequence. It extends single-variable calculus to functions of several variables and to vector fields, closing with the classical integral theorems that connect differentiation and integration in higher dimensions.
Topics
- Functions of several variables and their graphical representations
- Vectors and alternative coordinate systems
- Partial derivatives, gradients, and local linearization
- Optimization, including constrained optimization
- Multiple integration in polar, cylindrical, and spherical coordinates
- Parameterized curves and vector fields
- Line integrals, flux integrals, and divergence
- Curl, Stokes’ theorem, and the divergence theorem
Prerequisites
Calculus II (MAC 2312) with a grade of C− or better.
Grading
| Component | Weight |
|---|---|
| Midterm Exams | 50% |
| Final Exam | 20% |
| Homework | 20% |
| Quizzes | 10% |
Course Materials
Hughes-Hallett, D., Gleason, A. M., & McCallum, W. G. (2021). Calculus: Single and multivariable (8th ed.). Wiley.
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Aug 25 – Aug 28 | Course introduction and orientation Start of term | |
| 2–3 | Sep 2 – Sep 11 | Functions of Several Variables Sections 12.1, 12.2, 12.3, 12.4, 12.5, 12.6 | |
| 4 | Sep 15 – Sep 18 | Vectors Sections 13.1, 13.2, 13.3 | |
| 5 | Sep 22 – Sep 25 | Vectors; Differentiating Functions of Several Variables Sections 13.4, 14.1 | |
| 6–7 | Sep 29 – Oct 9 | Differentiating Functions of Several Variables Sections 14.2, 14.3, 14.4, 14.5, 14.6, 14.7, 14.8 | |
| 8 | Oct 13 – Oct 16 | Optimization Sections 15.1, 15.2 | |
| 9 | Oct 21 – Oct 23 | Optimization; Integrating Functions of Several Variables Sections 15.3, 16.1, 16.2 | |
| 10 | Oct 27 – Oct 30 | Integrating Functions of Several Variables; Parameterization and Vector Fields Sections 16.3, 16.4, 16.5, 17.1 | |
| 11 | Nov 3 – Nov 6 | Parameterization and Vector Fields Sections 17.2, 17.3, 17.4 | |
| 12 | Nov 10 – Nov 13 | Parameterization and Vector Fields; Line Integrals Sections 17.4, 18.1, 18.2 | |
| 13 | Nov 17 – Nov 20 | Line Integrals; Flux Integrals and Divergence Sections 18.3, 18.4, 19.1 | |
| 14 | Nov 24 – Nov 27 | Flux Integrals and Divergence Sections 19.2 | |
| 15 | Dec 1 – Dec 4 | Flux Integrals and Divergence; Curl and Stokes’ Theorem Sections 19.3, 19.4, 20.1 | |
| 16 | Dec 10 – Dec 11 | Functions of Several Variables; Curl and Stokes’ Theorem; Coordinates and Parameterized Surfaces Sections 12.2, 20.2, 20.3, 21.1, 21.2, 21.3 |