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.
Integration in Vector Fields
- 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.
- Evaluate vector fields using line integrals.
- Apply Green’s Theorem.
- Evaluate shapes using surface integrals.
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.
- 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.
- 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.
- 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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