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MAT137 - Calculus for Business
Catalog Description: Covers the principal concepts of differential and integral calculus as they relate to business applications. Students will study functions (including exponential and logarithmic), limits, differentiation, and integration. Emphasis will be placed upon the use of calculus in solving problems from the fields of business & economics. Prerequisite: MAT 136 or MAT 140 with a grade of ‘C’ or higher or by placement or instructor permission.
Lecture: 4 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of the course, the student will be able to:
1.Evaluate and graph linear, quadratic, exponential, and logarithmic functions.
2.Write intuitive definitions for the concepts of limit and continuity.
3.Evaluate limits of basic functions, using algebraic, numerical, and/or graphical methods.
4.Determine whether or not a function is continuous at a point.
5.Find the derivative (using the formal limit definition of derivative) of a polynomial or rational function.
6.Find the derivative of a polynomial, exponential, or logarithmic function.
7.Apply the various rules of differentiation (product rule, quotient rule, chain rule) as appropriate.
8.Use derivatives to find marginal cost, profit, and revenue functions.
9.Use derivatives to investigate features of simple functions such as:
a.Absolute extreme values
b.Relative extreme values
c.Intervals of increase/decrease
d.Intervals of upward/downward concavity
10.Use derivatives to solve optimization applications.*
11.Solve growth and decay applications using logarithmic and exponential functions.
12.Determine general antiderivatives using basic integration formulas and rules.
13.Evaluate definite integrals.
14.Evaluate integrals using several methods such as:
a.Method of parts
b.Using integral tables.
15.Apply integration techniques to find the area under the curve of a given function.
16.Find the average value of a function using a definite integral.
17.Determine consumer's and producer's surplus using definite integrals.*
18.Determine the value of continuous cash flow using definite integrals.
19.Evaluate functions of several variables.
20.Determine partial derivatives and second order partial derivatives and apply these concepts to various applications (i.e. Cobb-Douglas model, optimization problems).
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
a. Solve application problems involving profit, cost, revenue, demand, and supply functions.
b. Use compound interest formula to solve problems.
c. Review graphing quadratic, exponential, logarithmic, and piecewise functions.
d. Obtain linear and quadratic functions using modeling.
II. Limits and Continuity
a. Write an intuitive, precise English definition of a limit
b. Write an intuitive, precise English definition of continuity
c. Evaluate limits of functions numerically and graphically
d. Evaluate limits of functions algebraically using algebraic rules.
e. Determine whether a function is continuous at a point c.
a. Explain the average rate of change and instantaneous rate of change.
b. Compute the average rate of change (slope of secant line) using a simplified difference.
c. Write the definition of the derivative of a function and find the derivative of a polynomial function using the definition
d. Differentiate polynomial functions
e. Differentiate sums and differences, products and quotients, and composite functions.
f. Determine higher order derivatives.
IV. Applications of Derivatives
a. Find slopes and equations of tangent lines at a given point.
b. Find points where the tangent line is horizontal or has slope equal to a specified value.
c. Determine marginal cost, revenue, and profit functions.
d. Find relative extrema and points of inflection of a function.
e. Use first and second derivative information to sketch the graph of polynomial functions.
f. Determine the absolute extrema of a function.
g. Solve optimization problems from areas of business and economics.
V. Exponential and Logarithmic Functions
a. Review the properties of exponential and logarithmic functions.
b. Differentiate exponential & logarithmic functions and related products, quotients, and compositions.
c. Solve growth and decay application problems.
a. Write and apply the definition of an indefinite integral.
b. Determine general antiderivatives using basic integration formulas and rules.
c. Use an initial condition to solve initial value problems and corresponding applications.
a. Write and apply the definition of a definite integral.
b. Evaluate both definite and indefinite integrals of appropriate polynomial, exponential, and logarithmic functions, making use of a variety of techniques such as u-substitutions, integration by parts, and integration tables.
VIII. Applications of Integration
a. Apply integration techniques to finding the area under a curve and the area between two curves.
b. Solve problems involving average value of a function over a closed interval.
c. Determine consumer's and producer's surplus at the supply/demand equilibrium point.
d. Solve applications using the Net Change Theorem.
IX. Functions of Two or More Variables
a. Evaluate functions of several variables.
b. Determine partial derivatives and second order partial derivatives.
c. Optimization of functions of two or more variables
Effective Term: Fall 2012