This course covers advanced topics in Calculus, including sequences, series, tests for convergence, power series, conic sections, parametric equations, polar coordinates, vectors, vector-valued functions, and motion in space. The course aims to teach students how to apply these concepts to solve complex mathematical problems. The teaching method involves lectures, examples, and practice exercises. This course is intended for students who have a strong foundation in Calculus and are looking to deepen their understanding of the subject.
Overview
Syllabus
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.
Taught by
Tyler Wallace
