Aug 11, 2020
MT 177 - Mathematical Analysis for Management
Credit Hours: 4
MT177 is a one-semester terminal course for Business majors. MT177 fulfills the MT175/MT176 mathematics requirement for Business majors. This course incorporates most of the topics from MT175, basic differentiation and applications, exponential and log functions, and introduction to integration. This course also includes some material which was previously encountered in MT176 i.e. functions of two variables and optimization thereof and more integral calculus (e.g. integration techniques of substitution and integration by parts).
Upon completion of this course, the student will be able to:
- define a function and relate this concept to graphing and modeling;
- perform the fundamental operations with functions, including composites;
- define a derivative using the limit concept and apply this definition to simple functions;
- differentiate functions using rules and techniques of differentiation;
- determine the continuity and differentiability of functions;
- calculate the second derivative and apply it to a variety of problems;
- interpret derivative information and apply to graphing simple polynomial and rational functions;
- analyze and solve word problems involving derivatives and integrals;
- interpret, graph and differentiate natural log and exponential functions;
- relate exponential functions to problems in business, biology, psychology;
- calculate, interpret and relate anti-derivative of a function to the indefinite integral; and
- calculate and interpret the definite integral.
- analyze and interpret the following based on a graphing calculator:
- finding limits of functions;
- using the calculator as a check in describing graphs of functions; and
- finding areas of a region between two curves.
- using the graphing calculator in applications – e.g. exponential decay, compound interest, etc.;
- 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 p.
Prerequisites: MT 126 or equivalent and appropriate mathematics level code. Level code is determined by Mathematics Department placement test and/or successful completion of mathematics courses.
F/S (C, N, S)