MT 177 - Mathematical Analysis for Management

• 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.

Technology Objectives:

• 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.