MATH 136 - Calculus of a Single Variable 2

Number of Credits: 4
Examine limits, derivatives, and integrals of transcendental functions. Apply analytical techniques for integration and extend the concepts of calculus to parametric and polar forms. Use Taylor polynomials to approximate functions and determine the convergence or divergence of improper integrals, infinite sequences, and infinite series. (Fall, Spring & Summer Only) Five hours lecture each week. Four Credits. Four billable hours.

Pre-requisite(s): completion of MATH 135 with a minimum grade of C or a satisfactory MATH placement measure.
Course Topics:

Limits (including by applying L’Hopital’s Rule), derivatives, and integrals of inverse trigonometric, hyperbolic, exponential, logarithmic, polar, and parametric functions
Integration techniques:
1. Integration by Parts
2. Partial Fractions
3. Trigonometric Integration
4. Trigonometric Substitution
Convergence/divergence of improper integrals
Convergence/divergence tests of infinite series
Interval of convergence of a series
Taylor and Maclaurin series

Course Objectives: Upon successful completion of this course, students will be able to:

Evaluate limits (including by applying L’Hopital’s Rule), derivatives, and integrals of inverse trigonometric, hyperbolic, exponential, logarithmic, polar, and parametric functions using logarithmic properties in addition to all rules learned in Calculus of a Single Variable I.
Evaluate integrals using the following techniques including integration by parts, partial fractions, trigonometric integration, and trigonometric substitution.
Evaluate and determine the convergence/divergence of improper integrals.
Analyze the convergence/divergence of infinite series using a variety of tests.
Determine conditional/absolute convergence of series.
Determine the interval of convergence of a series.
Represent functions using Taylor and Maclaurin series.