MAT 217 - Calculus II

Credits: 5
Lecture Hours: 5
Lab Hours: 0
Practicum Hours: 0
Work Experience: 0
Course Type: Core

Continuation of Calculus I. Topics include applications of integration, integration techniques, L’Hopital’s rule, improper integrals, infinite sequences, series, Taylor and Maclaurin series, the calculus of plane curves, parametric equations and polar equations.
Prerequisite: Pre-requisite: MAT 211 with a C- or better.
Competencies

Solve application problems using calculus
1. Use an integral to calculate area between two curves
2. Find volume of a solid of revolution using the disk method
3. Find volume of a solid of revolution using the shell method
4. Calculate arc length using an integral
5. Calculate area of a surface of revolution using an integral
6. Use an integral to calculate work done by a variable force
7. Use integrals to calculate moments and center of mass of a planar lamina
Use basic techniques of integration
1. Calculate certain integrals by integration by parts
2. Integrate powers of Sine and Cosine
3. Integrate powers of Secant and Tangent
4. Integrate by Trig substitution
5. Integrate by partial fractions
6. Integrate by using tables and other miscellaneous techniques
Evaluate indeterminate forms
1. Identify the basic 0/0 indeterminate form
2. Use L.’Hopital’s rule for the 0/0 form
3. Identify other indeterminate forms
4. Use L.’Hopital’s rule for the other forms
Integrate improper integrals
1. Identify the various types of improper integrals
2. Evaluate a given improper integral
Evaluate infinite series
1. Define the limit of an infinite series
2. Determine convergence by the integral test
3. Determine convergence by the comparison test
4. Determine convergence for alternating series
5. Define conditional convergence
Evaluate power series
1. Define power series
2. Determine the radius of convergence for a power series
3. Determine Taylor and Maclaurin series for certain elementary functions
4. Differentiate and integrate power series
Analyze plane curves and 2-D geometry
1. Evaluate derivatives and integrals of parametric equations
2. Calculate arc length for parametric equations using an integral
3. Calculate area of surface of revolution for parametric equations using an integral
4. Define polar coordinates
5. Write the equations relating polar coordinates and rectangular coordinates
6. Graph functions represented in polar form
7. Determine areas of regions defined by polar form equations
8. Calculate slopes and arc lengths for functions specified in polar form