MATH 275 Calculus 3*

This is the final course in the calculus sequence. Topics include vectors, functions of several variables, multiple integration, parametric surfaces, vector fields and three-dimensional vector algebra. Applications involve the Fundamental Theorem of Line Integrals, Green’s Theorem, Divergence Theorem, and Stoke’s Theorem.

Credits

4 Credits

Semester Contact Hours Lecture

60

Prerequisite

MATH 175

MATH 275Calculus 3*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

I. General Information

Department

Mathematics & Engineering

II. Course Specification

Course Type

Program Requirement

Credit Hours Narrative

4 Credits

Semester Contact Hours Lecture

60

Prerequisite Narrative

MATH 175

Grading Method

Letter grade

Repeatable

N

III. Catalog Course Description

This is the final course in the calculus sequence. Topics include vectors, functions of several variables, multiple integration, parametric surfaces, vector fields and three-dimensional vector algebra. Applications involve the Fundamental Theorem of Line Integrals, Green’s Theorem, Divergence Theorem, and Stoke’s Theorem.

IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

• Apply the techniques of calculus to multi-dimensional space.
• Apply that knowledge to skill-based and real-world problems.
• Communicate the solutions to the questions.

V. Topical Outline (Course Content)

Vectors, including the Dot Product and the Cross Product Equations of Lines and Planes Cylinders and Quadric Surfaces Vector Functions and Space Curves Derivatives and Integrals of Vector Functions Arc Length and Curvature Motion in Space: Velocity and Acceleration Functions of Several Variables Limits and Continuity Partial Derivatives Tangent Planes and Linear Approximations The Chain Rule Directional Derivatives and the Gradient Vector Maximum and Minimum Values Lagrange Multipliers Double Integrals over Rectangles Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Application of Double Integrals Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Change of Variables in Multiple Integrals Vector Fields Line Integrals The Fundamental Theorem for Line Integrals Green’s Theorem Curl and Divergence Parametric Surfaces and Their Areas Surface Integrals Stokes’ Theorem The Divergence Theorem

VI. Delivery Methodologies