| |
Jul 06, 2025
|
|
|
|
|
MAT 250 - Calculus 3
Credits: 4
4 Lecture Hours
Prerequisites: MAT 202
Description
In this course, students continue to explore mathematical concepts introduced in MAT 202 . Students learn several examples of quadric surfaces, as well as the calculus of vector-valued and multivariate functions. Additionally, students learn to solve problems using 3-dimensional analytic geometry and vector analysis.
Learning Outcomes
Upon successful completion of the course, the student will:
- Analyze vector-valued functions describing curves in two and three dimensional space.
- Produce graphs in three dimensional Cartesian, cylindrical and spherical coordinate systems.
- Determine equations of lines and planes in three dimensional space, including tangent planes and normal lines to surfaces.
- Compute partial derivatives, total differentials, directional derivatives and gradients.
- Identify extreme values of multi-variable functions under given conditions.
- Apply double and triple integrals to determine areas of regions and volumes of solids in various coordinate systems.
- Evaluate line integrals and surface integrals using appropriate theorems.
- Solve selected application problems.
Listed Topics
- Three dimensional analytic geometry: three dimensional coordinate systems, lines, planes and quadric surfaces
- Vector-valued functions, parametric equations and curves in two and three dimensional space
- Arc length and curvature
- Differential calculus of functions of more than one variable: limits, continuity, partial derivatives differentials, tangent planes, the chain rule, directional derivatives and gradients
- Extreme values, including Lagrange multipliers
- Integral change of variables
- Multiple integration in various coordinate systems
- Line integrals
- Surface integrals
- Curl
- Divergence
- The Fundamental Theorem of Line Integrals
- Green’s Theorem
- Stokes’ Theorem
- The Divergence Theorem
Reference Materials
Each student is required to have a textbook/e-book/homework system adopted by the Mathematics Department at the specific campus.
Students who successfully complete this course acquire general knowledge, skills and abilities that align with CCAC’s definition of an educated person. Specifically, this course fulfills these General Education Goals: - Critical Thinking & Problem Solving
- Quantitative & Scientific Reasoning
Approved By: Dr. Quintin B. Bullock Date Approved: 5/8/2023
Last Reviewed: 5/8/2023
Course and Section Search
Add to Portfolio (opens a new window)
|
|