MAT 112E - Mathematics II

Course Objectives

1. To provide the evaluation of integrals by using integral techniques.
2. To give the basic concepts of analytic geometry.
3. To give a broad knowledge and basic understanding of sequences and series.

Course Description

Techniques of Integration: Integration by Parts, Partial Fractions, Trigonometric Substitution, Numerical Integration, Improper Integrals.
Conic Sections and Polar Coordinates: Conic Sections and Quadratic Equations, Polar Coordinates, Areas and Lengths in Polar Coordinates.
Infinite Sequences and Series: Sequences, Infinite Series, The Integral Tests, Comparison Tests, The Ratio and Root Tests, Alternating Series, Power Series, Taylor and Maclaurin Series, Fourier Series.
Vectors and the Geometry Space: Vectors, Dot Product, The Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces.
Vector-Valued Functions: Vector Functions, Limits and Continuity and Integrals of Vector Functions.