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: Spring 2025
Role
Instructor of record, Spring 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 | 25% |
| Homework | 20% |
| Quizzes | 5% |
Course Materials
Hughes-Hallett, D., Gleason, A. M., & McCallum, W. G. (2021). Calculus: Single and multivariable (8th ed.). Wiley.
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1–2 | Jan 13 – Jan 21 | Functions of Several Variables Sections 12.1, 12.2, 12.3, 12.4, 12.5, 12.6 | |
| 3–4 | Jan 29 – Feb 5 | Vectors Sections 13.1, 13.2, 13.3, 13.4 | |
| 5–6 | Feb 10 – Feb 20 | Differentiating Functions of Several Variables Sections 14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7 | |
| 7 | Feb 26 – Feb 27 | Differentiating Functions of Several Variables; Optimization Sections 14.8, 15.1 | |
| 8 | Mar 4 – Mar 6 | Optimization; Integrating Functions of Several Variables Sections 15.2, 16.1 | |
| 9 | Mar 17 | Integrating Functions of Several Variables Sections 16.2, 16.3, 16.4 | |
| 10 | Mar 18 – Mar 20 | Optimization; Integrating Functions of Several Variables Sections 15.3, 16.5 | |
| 11–12 | Mar 26 – Apr 7 | Parameterization and Vector Fields; Line Integrals Sections 17.1, 17.2, 17.3, 17.4, 18.1, 18.2, 18.3 | |
| 13 | Apr 8 – Apr 14 | Line Integrals Sections 18.4 | |
| 14 | Apr 15 | Flux Integrals and Divergence Sections 19.1 | |
| 15 | Apr 22 – Apr 28 | Flux Integrals and Divergence; Curl and Stokes’ Theorem; Coordinates and Parameterized Surfaces Sections 19.2, 19.3, 19.4, 20.1, 20.2, 20.3, 21.1, 21.2, 21.3 | |
| 16 | Apr 30 | Final Exam Assessment |