Course Abstract Details

MATH-136, Calculus of a Single Variable 2

Credits: 4

Course Description

MATH-136, Calculus of a Single Variable 2, expands the group of functions whose derivatives and integrals are studied in MATH-135. Functions added are the exponential, logarithmic, inverse trigonometric and hyperbolic functions. Infinite sequences and series, including convergence tests, power series and Taylor and Maclaurin series, are studied. An introduction is given for conic sections, and derivatives and integrals in parametric and polar coordinates are covered. Students will be required to use a graphing calculator and significant mathematical software such as Mathematica, Maple, or MATLAB throughout the course. See Mathematics Department web site for details. Prerequisite: MATH-135 with a "C" grade or better. Five hours lecture each week. Four credits. Four billable hours. GENERAL EDUCATION

Course Objectives and Grading Information

MAJOR COURSE OBJECTIVES: Upon completing this course the student should be able to:

1. Solve integration problems involving logarithmic, exponential, inverse trigonometric and hyperbolic functions and powers of trigonometric functions. (GE3, PG 1, PG4)

2. Integrate functions using the following techniques: (GE3, PG 1) - Integration by parts - Integration by partial fractions - Integration by trigonometric substitution

3. Analyze indeterminate forms and use L'Hopital's Rule to find their limits. (GE3, PG 1)

4. Evaluate improper integrals. (GE3, PG 1, PG4)

5. Analyze the convergence/divergence of infinite series using appropriate tests. (GE2, GE3, PG 1, PG3)

6. Represent functions using Taylor and Maclaurin series. (GE2, GE3, PG 1, PG3, PG4)

7. Develop equations and graphs of conic sections. (GE2, GE3, PG 1, PG3, PG4)

8. Differentiate and integrate parametric and polar functions. (GE2, GE3, PG 1, PG3, PG4)

9. Set-up and solve application problems using technology, such as graphing calculators and mathematical software. (GE1, GE2, GE3, PG 1, PG2, PG3, PG4)

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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