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