M 172M - Calculus II

Credit(s): 5

Prerequisite(s): appropriate placement test score, a grade of “C” or better in M 171, or Math Department consent.
This is the second of three standard courses in calculus. The course includes transcendental functions, applications and techniques of integration, infinite series, parametrized curves, and polar curves. (Fall and Spring Semesters)

Course Learning Outcomes: Upon completion of the course, students will be able to

Solve problems using mathematical techniques.
Use integrals to find areas between two curves, volumes, volumes of revolution, work and the average value of a function.
Use integrals to calculate probabilities, arc lengths, surface areas, moments, centers of mass and hydrostatic pressure and force.
Evaluate integrals using direct substitution, integration by parts, trigonometric forms, trigonometric substitution and partial fractions.
Use numerical techniques to approximate definite integrals.
Evaluate improper integrals and use the comparison test to determine whether improper integrals converge or diverge.
Analyze infinite sequences of real numbers, their monotonicity and boundedness.
Analyze series of real numbers (including geometric series and telescoping series), apply the divergence test, integral test, direct comparison test, limit comparison test, alternating series test, ratio test and root test and determine whether a series is absolutely convergent, conditionally convergent or divergent.
Find power series representations for functions, calculate the radius of convergence of a power series, integrate and differentiate power series and find Taylor series representations and Taylor polynomial approximations of functions.
Analyze and graph parametrized curves in rectangular and polar coordinates and find derivatives, arc lengths, surface areas and enclosed areas for these curves.