MATH 162: Calculus IIA

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Prerequisites

MATH 161

Most science programs require between one and two years of calculus. See Comparing the Calculus Sequences.

Description

• A continuation of MATH 161 with a treatment of integral calculus and applications, calculus with parametric curves and polar coordiantes, and sequences and series.

• Reinforces algebraic manipulation and trig techniques learned in high school.

• Provides tools for use in other disciplines, although most examples come from geometry, graphs and the simple physics of motion.

• Rigorous proofs, providing guarantees that the techniques always work if certain criteria are met, are left to later courses in analysis such as MATH 265.

Topics covered

Applications of integration including areas, volumes, work, and arc length. Techniques of integration including integration by parts, trigonometric substitution, partial fractions. Improper integrals. Calculus with parametric curves and polar coordinates. Sequences, series, tests for convergence including comparison tests, integral test, alternating series test, ratio test, root test. Taylor and Maclaurin series.