# MTH 241 - Calculus III

## Course Description

The course covers multivariable calculus including three-dimensional analytical geometry, vector valued functions, partial differentiation, and multiple integration (with applications of each), and vector calculus. Group 1 course.

5

5

5

## Required Prerequisites

A grade of 2.0 or better in MTH 142 or equivalent

## Recommended Prerequisites or Skills Competencies

Placement into ENG 111

## General Education Outcomes supported by this course

Quantitative Reasoning

## Course Learning Outcomes

Knowledge:
• Graph both space curves and surfaces in three dimensions in rectangular, cylindrical, or spherical coordinates.
• Demonstrate proper use of vectors and vector valued functions, including dot and cross products, equations of lines, planes and curves in space.
• Compute partial derivatives to find the gradient vector, directional derivatives, and to maximize or minimize a function of multiple variables using both the extreme value theorem and Lagrange multipliers.
• Write and evaluate double and triple integrals to find surface area, volume, length of curve and work.
• Learn the concepts and theorems of vector calculus, including line integrals, divergence, curl and surface integrals.
Application:
• Perform proper operations on functions to find extrema and tangent approximations.
• Determine the most effective coordinate system to use to evaluate an iterated integral.
• Discern the proper order and limits of an iterated integral.
• Appropriately use Stoke's Theorem and the Divergence Theorem.
Integration:
• Represent multidimensional physical relationships and use calculus theory and techniques to solve them.
Human Dimension:
• Identify their mathematical strengths and weakness and recognize they can overcome their weaknesses.
• Collaborate with peers during group work.
Caring - Civic Learning:
• Collaborate with peers during group work.
Learning How to Learn:
• Recognize the impact mathematics plays in civic situations such as politics, education and income.
• Reflect on failure and revise appropriately.