Calculus IV –

mth420

(3 credits)

This course presents students with advanced calculus topics. Students examine line integrals, vector fields, non-elementary functions, as well as Fourier series and the Fourier transform. Students also investigate Green’s Theorem and Stokes’ Theorem.

This undergraduate-level course is 5 weeks. To enroll, speak with an Enrollment Advisor.

Topics and Objectives

Vector-Valued Functions
- Graph vector functions.
- Integrate vector functions to describe projectile motion.
- Determine limits, continuity, smoothness, curvature, and arc length for vector functions.
- Find tangent, normal, and binomial vectors (Frenet or TNB frame) for a given function.
- Describe motion along a curve using rectilinear and polar coordinates.
- Examine velocity and acceleration using Kepler's laws of planetary motion.
Double Integrals
- Evaluate iterated integrals.
- Perform double integration after reversing the order of integration (Fubini's theorem).
- Perform double integrals over general regions.
- Determine limits of integration for intersecting curves.
- Model surface area using polar coordinates.
Triple Integrals
- Calculate the volume of a solid using triple integrals.
- Determine moments and center of mass for solid objects.
- Use integration to model physical properties, such as inertia.
- Perform triple integrals using cylindrical and spherical coordinates.
- Use the Jacobian to facilitate integral substitutions.
Integration in Vector Fields
- Evaluate vector fields using line integrals.
- Apply Green’s Theorem.
- Evaluate shapes using surface integrals.
- Determine the flux of a vector field across a closed curve.
- Use Stokes’ Theorem to evaluate functions and test for conservative fields.
- Describe the fundamental theorem uniting Green's, Divergence, and Stokes' theorems.
Taylor and Maclaurin Series
- Evaluate sequences for convergence or divergence.
- Apply different methods to evaluate series for convergence or divergence.
- Generate terms in Taylor and Maclaurin series.
- Evaluate functions and integrals using power series.

The University of Phoenix reserves the right to modify courses.
While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Advisor.
Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.

Calculus IV –

mth420

Vector-Valued Functions

Double Integrals

Triple Integrals

Integration in Vector Fields

Taylor and Maclaurin Series

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