Course Abstract Details

MATH-135, Calculus of a Single Variable 1

Credits: 4

This is a General Education Course

Course Description

MATH-135, Calculus of a Single Variable 1, introduces the initial concepts of both differential and integral calculus. The concept of limits will be introduced both informally and through the formal epsilon- delta process. Derivatives and integrals of polynomial, power and trigonometric functions will be developed as well as general differentiation techniques (such as the chain rule and implicit differentiation). Evaluation of definite integrals will be covered through limits of Riemann Sums, numerical integration techniques, and the Fundamental Theorems of Calculus. Applications of calculus to graphing and to physical situations will be extensively developed. Prerequisite: exemption/completion of READ-099 and MATH-129 or MATH-130 with a "C" grade or better, or a satisfactory score on the placement exam. Credit by exam available. Graphing calculator required. See Mathematics Department web site for details. Five hours lecture each week. Four credits. Four billable hours. GENERAL EDUCATION

Course Objectives and Grading Information

MAJOR COURSE OBJECTIVES: Upon completion of this course, the student should be able to:

1. Diagram and describe formal limits using the € - ? process. (GE1, GE2, GE3, PG1, PG2, PG3)

2. Determine limits for rational and trigonometric functions. (GE1, GE3, PG1, PG2)

3. Use the limit process to formulate differentiation rules for polynomial functions. (GE3, PG1, PG2)

4. Calculate derivatives for polynomial, rational, and trigonometric functions using the product, quotient, chain and implicit rules. (GE2, GE3, PG1, PG2, PG3)

5. Determine the asymptotic behavior of functions. (GE1, GE2, GE3, GE4, PG1, PG2, PG3, PG4)

6. Sketch curves based on analysis of functions and the derivative tests. (GE1, GE2, GE3, GE4, PG1, PG2, PG3, PG4)

7. Apply differentiation techniques to optimization and related-rate problems. (GE1, GE2, GE3, GE4, PG1, PG2, PG3, PG4)

8. Explain indefinite integration using the limit of Riemann Sums. (GE1, GE2, GE3, PG1, PG2, PG3)

9. Solve for definite and indefinite integrals directly and using substitution techniques. (GE2, GE3, GE4, PG1, PG2, PG3, PG4)

10. Approximate definite integrals using numerical techniques. (GE3, PG1, PG2)

11. Apply integration techniques to solve problems in area, volume and curve-length applications. (GE2, GE3, GE4, PG1, PG2, PG3, PG4)

12. Apply integration techniques to solve applied problems such as analysis of work, fluid pressure and center-of-mass applications. (GE2, GE3, GE4, PG1, PG2, PG3, PG4)

REQUIRED TEXTBOOK(S)
Larson, R. and Farber, B. Calculus, 9th edition. Brooks/Cole, Cengage Learning, 2010. [ISBN-13: 978-0-547-16702-2]

Learning Goals

The abbreviations in parentheses represent Learning Goals which have been identified for this course and program of study:

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