Calculus 3
Covers infinite series, curves in parametric and polar forms, vectors, partial differentiation, and multiple integrals. Applications of these topics focus on analysis of functions and surfaces in 3 dimensional space. Fall only. Prerequisite: MAT 142 with a grade of ‘C’ or higher or by placement. May be taken concurrently with MAT 142 with instructor permission.
Subject Code: MAT
Course Number: 245
Credits: 4
Lecture Hours 4
Course Learning Outcomes:
1. Sketch or use a graphing utility to the graph a parametric or polar curve
2. Perform basic vector arithmetic (magnitudes, dot products, cross products, triple-scalar products, orthogonal projections)
3. Evaluate a function of two or more variables at a specific point
4. Determine and sketch the domain of a function of two variables
5. Find and evaluate partial derivatives of functions of two or more variables (including various chain rules)
6. Use partial derivatives to solve application problems (related rates, linear approximation, gradients, optimization problems, Lagrange multipliers)
7. Use a double integral (Cartesian or polar) to find the volume of a solid bounded by surfaces in 3-space
8. Identify the properties of a given vector field (graph, conservativeness, curl, divergence, potential function)
9. Evaluate a line integral
10. Determine the work done by a particle moving through a vector field (Fundamental Theorem, Green’s Theorem)
Effective Term: Fall 2025
Tutoring Services
Tutoring for all GCC students is available free of charge by professional and peer tutors. We are offering tutoring online for: accounting, math, writing, chemistry, physics, general biology, anatomy & physiology, American Sign Language, and success skills.
