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# MT 176 - Survey of Calculus II

Credit Hours: 4

Continuation of MT 175. Topics include differentiation and integration of trigonometric functions, other techniques of integration, improper integrals, functions of several variables, introduction to differential equations and applications of calculus to the theory of probability. The optional topic involves Taylor polynomials and infinite series.

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

• demonstrate skill in performing routine differentiation and integration of elementary functions including the sine, cosine, and tangent;
• identify, evaluate, and find the partial derivatives of a function of several variables, and apply this knowledge to solve relative extreme problems;
• apply the method of Lagrange multipliers to the solution of constrained optimization problems;
• perform integration by the methods of substitution and by parts, and apply these methods to the evaluation of definite integrals, approximate integration and improper integrals;
• identify and solve certain types of differential equations using separation of variables and, where applicable, find a numerical solution using Euler's Method;
• analyze solutions of certain types of differential equations by employing quantitative methods;
• apply the techniques presented in the above objectives to problems in economics, business and the social sciences; and
• apply techniques of integration to the study of simple probability problems including expected value and variance of a continuous random variable, including examples of exponential, normal and standard normal density functions.

If recommended optional topic is selected:

• recognize and construct nth Taylor polynomials for a given function f (x) at x = a. Define, recognize, and give examples of infinite series; and
• demonstrate skill in constructing Taylor series for simple functions and in their use for computational purposes.

Prerequisites: MT 175 or equivalent and/or 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.