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.
Prerequisite
MATH 175 with a grade of 'C' or better
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 with a grade of 'C' or better
Grading Method
Letter grade
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