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.
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.
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.
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.
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.
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.
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