mth420 | undergraduate

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 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

topic title goes here

    Integration in Vector Fields

    • Describe the fundamental theorem uniting Green's, Divergence, and Stokes' theorems.
    • 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.

    Taylor and Maclaurin Series

    • Apply different methods to evaluate series for convergence or divergence.
    • Generate terms in Taylor and Maclaurin series.
    • Evaluate functions and integrals using power series.
    • Evaluate sequences for convergence or divergence.

    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.
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