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# MT 182 - Calculus and Analytic Geometry II

Credit Hours: 4

Second course in a four-semester sequence. Topics include techniques of integration, applications of integration, infinite sequence and series, polar coordinates and parametric equations.

Course Outcomes
Upon completion of this course, the student will be able to:

• evaluate definite and indefinite integrals by the method of substitution;
• use the integral as the limit of a Riemann sum to solve applied problems involving areas, volumes, arc length, work, surface area and if time permits, liquid pressure and force;
• compute indefinite integrals by "u" substitution, integration by parts, trigonometric and inverse trigonometric substitutions, partial fractions and by use of tables;
• estimate the value of a definite integral by using numeric approximation techniques consisting of: trapezoidal and Simpson's Rule;
• ascertain whether an integral is improper and determine its convergence or divergence;
• apply appropriate tests to determine the convergence or divergence of sequences and series;
• compute Taylor, Maclaurin, and Power series expansion of certain functions, and where applicable, the derivatives and integrals of these series;
• convert rectangular to polar coordinates and vice versa and sketch graphs in both coordinate systems;
• compute the area under the curve using polar methods;
• convert equations in rectangular and polar form to parametric form and vice versa;
• use a hand held graphing calculator as a tool to reduce computational work and concentrate on the analytic aspects of a variety of problems;
• compute tangent lines and arc lengths using polar coordinates;
• demonstrate the skill to solve growth decay problems and separable differential equations;
• present the derivatives and integrals of the hyperbolic and inverse hyperbolic functions

Prerequisites: MT 181 or equivalent and appropriate mathematics level code.*
F/S (C, N, S)

*Level code is determined by Mathematics Department placement test and/or successful completion of math courses.