For students in business, life science, and the social sciences but not engineering, mathematics, or physical science majors. Introduces differential and integral calculus of algebraic, logarithmic, and exponential functions of one variable. Covers graphical, numerical, and algebraic determination of derivatives and definite integrals, applications of the derivative including minima and maxima, and integration and its applications. Includes applications throughout the course. Credit cannot be earned for both MATH 153 and 180. Includes the use of technology for business-related applications. Requires a graphing calculator with the TI-84 Plus series recommended.
Goals, Topics, and Objectives
- To introduce and develop the essential concepts of calculus from graphical, numerical, and algebraic points of view.
- To develop manipulation and approximation techniques for elementary differentiation and integration.
- To develop a sense for the power of calculus as a problem-solving tool through a variety of applications in business and economics.
- Algebra review
- Add, subtract, and multiply polynomials.
- Factor polynomials.
- Add, subtract, and multiply rational expressions.
- Solve linear equations.
- Solve quadratic equations algebraically using factoring, the square root property, and the quadratic formula.
- Solve linear, quadratic, and rational inequalities.
- Simplify expressions using the Properties of Exponents involving both integer and rational exponents.
- Solve radical equations algebraically.
- Rationalize the numerator and the denominator of a fraction.
- Find the limits of algebraic functions using numerical, algebraic, and graphical means, with and without calculator support.
- Determine if an algebraic function is continuous using algebraic and graphical means.
- Evaluate derivatives of algebraic functions using numerical, algebraic, and graphical means, with and without calculator support.
- Evaluate derivatives of algebraic functions using (a) the definition of derivative and (b) the derivative rules.
- Applications of Differentiation
- Identify that the solution to a problem requires using a derivative, describe what the derivative represents, and solve the problem.
- Determine the key characteristics of a function using the derivative and second derivative of the function.
- Solve business-related application problems such as maximizing profit, minimizing average cost, customer/producer surplus, and analysis of income stream as well as related applications from selected areas of the life and social sciences.
- Exponential and Logarithmic Functions
- Solve equations involving exponential and logarithmic functions.
- Evaluate derivatives of exponential and logarithmic functions using the derivative rules.
- Solve business-related application problems that are modeled with exponential and logarithmic functions.
- Evaluate integrals using numerical, algebraic and graphical means, with and without calculator support.
- Evaluate integrals using the rules for antiderivatives and the Fundamental Theorem of Calculus.
- Evaluate integrals using the techniques of integration by substitution and integration by parts.
- Applications of Integration
- Identify that the solution to a problem requires using an integral, describe what the integral represents, and solve the problem.
- Solve business-related application problems such as average value and continuous money flow.
Assessment and Requirements
- A comprehensive final examination, weighted in a manner that is worth at least fifteen percent (15%) of the final course grade, is required for all sections. In selected semesters this exam may be a common exam administered to all sections of Math 153.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.
A graphing calculator is required of each student. The Mathematics Department recommends and uses the TI-84 Series.
Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.