Des Moines Area
Community College
COURSE INFORMATION
Acronym/Number MATH130
Title CALCULUS II
Credit Breakout 5 5 0 0 0
(credit lecture lab practicum work experience)
PREREQUISITE(S):
MATH129
COURSE DESCRIPTION:
Continuation of MATH129. Techniques of integration, hyperbolic functions, polar coordinates, indeterminate forms, improper integrals, infinite series, partial derivatives, multiple integrals.
COURSE COMPETENCIES:
During this course, the student will be expected to:
1. Utilize Inverse Trigonometric and Hyperbolic Functions.
1.1 Define the inverse Trig functions.
1.2 Calculate derivatives and integrals of the inverse Trig functions.
1.3 Define the inverse Hyperbolic functions.
1.4 Calculate derivatives and integrals of the inverse Hyperbolic functions.
2. Use basic techniques of integration.
2.1 Calculate certain integrals by integration by parts.
2.2 Integrate powers of Sine and Cosine.
2.3 Integrate powers of Secant and Tangent.
2.4 Integrate by Trig substitution.
2.5 Integrate by partial fractions.
2.6 Integrate by miscellaneous techniques.
3. Integrate improper integrals.
3.1 Identify the various types of improper integrals.
3.2 Evaluate a given improper integral.
4. Evaluate indeterminate forms.
4.1 Identify the basic 0/0 indeterminate form.
4.2 Use L.'Hopital's rule for the 0/0 form.
4.3 Identify other indeterminate forms.
4.4 Use L.'Hopital's rule for the other forms.
5. Evaluate infinite series.
5.1 Define the limit of an infinite series.
5.2 Determine convergence by the integral test.
5.3 Determine convergence by the comparison test.
5.4 Determine convergence for alternating series.
5.5 Define conditional convergence.
5.6 Define power series.
5.7 Determine the radius of convergence for a power series.
5.8 Determine Taylor and Maclaurin series for certain elementary functions.
5.9 Differentiate and integrate power series.
6. Calculate with polar coordinates.
6.1 Define polar coordinates.
6.2 Write the equations relating polar coordinates and rectangular coordinates.
6.3 Graph functions represented in polar form.
6.4 Determine areas of regions defined by polar form equations.
6.5 Calculate slopes and arc lengths for functions specified in polar form.
7. Differentiate functions of many variables.
7.1 Determine limits for functions of many variables.
7.2 Determine partial derivatives for functions of many variables.
7.3 Use the chain rule for functions of many variables.
7.4 Determine tangent planes for functions of 2 variables.
7.5 Calculate directional derivatives and gradients for functions of 2 variables.
8. Evaluate double and triple integrals.
8.1 Define the double and triple integral.
8.2 Evaluate multiple integrals using Fubini's Theorem.
8.3 Evaluate double integrals in polar coordinates.
8.4 Evaluate triple integrals in cylindrical and spherical coordinates.
INSTRUCTIONAL MATERIALS:
Textbooks: For each text used in this course, identify the minimum chapters to be covered in this course.
None
Study guide
Transparencies
Test banks
Computer hardware/software
Other (example: Laboratory equipment for biology/chemistry class)
Computer Laboratory
Preparation
date 11/93
by: Mark Alberts
Campus: A B C U OC
extension: 6627
verified by: WB
Competencies are reviewed annually.