MT 177 - Mathematical Analysis for Management

1. define a function and relate this concept to graphing and modeling;
2. perform the fundamental operations with functions, including composites;
3. define a derivative using the limit concept and apply this definition to simple functions;
4. differentiate functions using rules and techniques of differentiation;
5. determine the continuity and differentiability of functions;
6. calculate the second derivative and apply it to a variety of problems;
7. interpret derivative information and apply it to graphing simple polynomial and rational functions;
8. analyze and solve word problems involving derivatives and integrals;
9. interpret, graph, and differentiate natural log and exponential functions;
10. relate exponential functions to problems in business, biology, and psychology;
11. calculate, interpret and relate anti-derivative of a function to the indefinite integral; and
12. calculate and interpret the definite integral.

Technology Objectives:

13. analyze and interpret the following based on a graphing calculator:
    1. finding limits of functions;
    2. using the calculator as a check-in describing graphs of functions; and
    3. finding areas of a region between two curves.
14. using the graphing calculator in applications - e.g. exponential decay, compound interest, etc.;
15. demonstrate skill in performing routine differentiation and integration of elementary functions including the sine, cosine, and tangent;
16. identify, evaluate, and find the partial derivatives of a function of several variables, and apply this knowledge to solve relative extreme problems;
17. apply the method of Lagrange multipliers to the solution of constrained optimization problems;
18. 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;
19. identify and solve certain types of differential equations using separation of variables and, where applicable, find a numerical solution using Euler’s Method;
20. analyze solutions of certain types of differential equations by employing quantitative methods;
21. apply the techniques presented in the above objectives to problems in economics, business, and the social sciences; and
22. 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, an optional topic is selected:
     
23. recognize and construct nth Taylor polynomials for a given function f(x) at x = a. Define, recognize, and give examples of infinite series; and
24. demonstrate skill in constructing Taylor series for simple functions and in their use for computational p.