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Calculus for the Managerial Science
I. Course Description: This course deals with functions and mathematics of finance, and concentrates on calculus techniques used to solve business and managerial related problems.
II. Purpose of the Course: This course is designed for students who have completed MTH 122 or earned an equivalent placement test score. The course will concentrate on developing a thorough understanding of real-valued functions as well as the mechanics of differential and integral calculus of one variable. The presentation of the topics will focus on problem solving skills involving applications from business and the social sciences.
III. College Learning Outcomes and Objectives: This course is designed to help students fulfill the Quantitative Competence Learning Outcome through achievement of the following learning objectives:
(9a) Students can formulate specific questions from vague
problems, select effective problem-solving strategies, and know which
mathematical operations are appropriate in particular contexts.
(9c) Students can use a calculator correctly , confidently, and appropriately and/or use computer software for mathematical tasks.
(9d) Students can use tables, graphs, spreadsheets and statistical techniques to organize, interpret and present numerical information .
IV. Course Objectives:
1. Students should be able to perform operations with functions and identify the domain, range and inverse of a function. (LO 9a, c, d)
2. Students should be able to analyze and graph polynomial , rational, exponential and logarithmic functions by plotting critical points and identifying roots and by making use of transformations and properties of symmetry. (LO 9a, c, d)
3. Students should be able to complete problems which demonstrate both an understanding of the mechanics of the topic as well as an understanding of its various applications in the managerial, social and life sciences. (LO 9a, c, d)
4. Students should be able to explain in general terms the concepts of limit and continuity of functions. (LO 9a)
5. Students should be able to evaluate the limit of polynomial, exponential & trigonometric functions and analyze limits graphically. (LO 9a, c, d)
6. Students should be able to distinguish between the average rate of change and the derivative of a function. (LO 9a)
7. Students should be able to find the derivative of a function by applying the sum , product, quotient and chain rules . (LO 9a)
8. Students should be able to make use of the properties of derivatives to sketch the graphs of functions. (LO 9a, c)
9. Students should be able to apply the mechanics of differentiation to solving maxima-minima and related rates problems. (LO 9a, c)
11. Students should be able to find antiderivatives of functions using the methods of substitution and integration by parts. (LO 9a)
12. Students should be able to explain in broad terms the relationship between the antiderivative and area under curve. (LO 9a)
13. Students should be able to use the definite integral to solve applications from the fields of business and economics. (LO 9a, b, c)
14. Students should be able to analyze functions with electronic graphing tools. (LO 9c, d)
15. Students should be able to utilize written communication forms that are appropriate to the mathematical sciences .
V. Topical Outline
A. Background Information and Concepts
1. Functions and relations
2. Exponential and logarithmic functions
3. Terms and notation
B. Differential Calculus
1. Rates of change and slope
2. The notion of the derivative
3. The mechanics of differentiation of polynomial and rational functions
4. Marginal analysis in business and economics
5. The use of the derivative in curve sketching
6. Maxima and minima applications
7. Related rates applications
8. Differentiation of trigonometric functions
C. Integral Calculus
1. The notion of antiderivatives and indefinite integrals
2. Integration by substitution
3. Differential equations involving natural growth and decay
4. Area under a curve and the definite integral
5. Area between two curves
6. Applications to business and economics
7. Integration methods and integration tables
8. Integration of trigonometric functions