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. This course is available to take individually or as part of a degree or certificate program. To enroll, speak with an Enrollment Representative.

Double Integrals

  • Determine limits of integration for intersecting curves.
  • Model surface area using polar coordinates.
  • Evaluate iterated integrals.
  • Perform double integration after reversing the order of integration (Fubini's theorem).
  • Perform double integrals over general regions.

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.
  • Calculate the volume of a solid using triple integrals.

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

  • 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.

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