MATH 136 - Calculus of a Single Variable 2

Number of Credits: 4
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, hyperbolic, parametric, and polar functions. Integration techniques, such as integration by parts, partial fractions, and trigonometric substitution, are covered in detail. Infinite sequences and series, including convergence tests, power series and Taylor and Maclaurin series, are studied. Students will be required to use mathematical software such as Mathematica, Maple, or MATLAB throughout the course. Advanced Placement (Calculus BC with a score of 3) (Fall, Spring & Summer Only) Five hours lecture each week. Four Credits. Four billable hours.

Pre-requisite(s): MATH 135 with a minimum grade of C or better.
Course Objectives: Upon successful completion of this course, students will be able to:

Solve limits (including L’Hopitals Rule), differentiation, and integration problems using logarithmic properties in addition to all rules learned in Calculus 1 on all types of functions. (PG1)
Integrate functions using the following techniques: (PG1) -Integration by Parts -Partial Fraction -Trigonometric Integration -Trigonometric Substitution
Evaluate improper integrals. (PG1)
Analyze the convergence/divergence of infinite series using the following tests: (PG1) -Geometric -Divergence -Integral -P-Series -Ratio and Root -Comparison (Direct and Limit) -Alternating Series
Determine conditional/absolute convergence of series. (PG1)
Determine the Interval of Convergence of a Series. (PG1)
Represent functions using Taylor and Maclaurin series. (PG1)
Set-up and solve application problems using mathematical software. (PG1, PG3)