# Calculus IV

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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 This course is available to take individually or To enroll, speak with an Enrollment Representative.

#### Course details:

Credits: 3
Continuing education units: XX
Professional development units: XX
Duration: 5 weeks

#### Vector-Valued Functions

• 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.

• Graph vector functions.
• Integrate vector functions to describe projectile 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.

#### 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.

#### 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.
Tuition for individual courses varies. For more information, please call or chat live with an Enrollment Representative.