MATH& 264 - Calculus IV

5 Credits

Fourth quarter of the Calculus sequence. Topics include the calculus of polar functions, sequences, infinite series, double and triple integrals in multiple coordinate systems, line and surface integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

Pre-requisite(s) MATH& 153 or MATH& 163 min 2.0
Course Note Graphing Calculator Required; TI-84 recommended
Fees

Quarters Typically Offered
Fall Day
Spring Day

Designed to Serve Transfer students in mathematics, engineering, and the sciences
Active Date 20230328T10:34:15

Grading Basis Decimal Grade
Class Limit 32
Contact Hours: Lecture 55
Total Contact Hours 55
Degree Distributions:
AA

Quantitative Skills
Science

ProfTech Related Instruction

Computation

PLA Eligible Yes

Course Outline

Calculus with polar coordinates
Infinite sequences and series
Double and triple integrals
Line integrals: Green’s Theorem and Stokes’ Theorem
Surface integrals: the Divergence Theorem
Numerical methods: Approximating infinite series
Applications: Area, volume, and surface area
Applications to physics: Moments and centroids, work, and flux

Student Learning Outcomes
Construct graphs and calculate areas and arclengths for polar curves.

Apply convergence tests to determine if infinite series converge.

Construct and evaluate double integrals in the polar coordinate systems.

Construct and evaluate triple integrals in rectangular, cylindrical, and spherical coordinate systems.

Construct and evaluate line and surface integrals.

Apply the Fundamental Theorem of Line Integrals, Green’s, Stokes’, and the Divergence theorems to evaluate line and surface integrals.

Determine if vector fields are conservative and independent of path and interpret what this says about vector fields.

Solve applications, including average value of a function, volumes, areas, centroids, work, and flux.