Calculus III

Explore advanced calculus concepts in this 10-hour course covering sequences, infinite series, power series, conic sections, parametric equations, polar coordinates, vectors, and vector-valued functions. Delve into topics such as divergence and integral tests, comparison tests, Taylor and Maclaurin series, calculus of parametric curves, dot and cross products, equations of lines and planes in space, quadric surfaces, cylindrical and spherical coordinates, arc length, curvature, and motion in space.

5.1 Sequences.
5.2 Infinite Series.
5.3 The Divergence and Integral Tests.
5.4 Comparison Tests.
5.5 Alternating Series.
5.6 Ratio and Root Tests.
6.1 Power Series and Functions.
6.2 Properties of Power Series.
6.3 Taylor and Maclaurin Series.
7.5 Conic Sections.
7.1 Parametric Equations.
7.2 Calculus of Parametric Curves.
7.3 Polar Coordinates.
7.4 Area in Polar Coordinates.
2.1 Vectors in the Plane.
2.2 Vectors in Three Dimensions.
2.3 The Dot Product.
2.4 The Cross Product.
2.5 Equations of Lines and Planes in Space.
2.6 Quadric Surfaces.
2.7 Cylindrical and Spherical Coordinates.
3.1 Vector-Valued Functions and Space Curves.
3.2 Calculus of Vector-Valued Functions.
3.3 Arc Length and Curvature.
3.4 Motion in Space.