MAT 182 - Calculus II
Exponential and logarithmic functions from an integral viewpoint, the calculus of inverse functions. Techniques of integration including integration by parts, partial fractions and trigonometric substitution. Improper integrals. Sequences, detecting convergence, and L'Hospital's rule. Infinite series, tests for convergence, power series, Maclaurin series and Taylor series. Polar curves, parametric equations and conics in calculus.
Prerequisite: MAT 181 Calculus I
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Define a sequence and a series.
2. Test series for convergence.
3. Test alternating series for absolute or conditional convergence.
4. Perform operations with power series.
5. Find the radius of convergence of a power series.
6. Develop Taylor and Maclaurin series expansions for a function.
7. Employ various integration techniques including integration by parts, trigonometric substitution and partial fractions.
8. Evaluate improper integrals.
9. Solve elementary differential equations.
10. Compute limits using L'Hopital's Rule.
11. Transform from rectangular to polar coordinates and from polar to rectangular.
12. Graph in polar coordinates.
13. Compute area in polar coordinates.
14. Compute arc length in polar coordinates.
15. Perform applications of integration.
16. Use Calculus with parametric equations.
17. Recognize graphs and perform calculus on various conics.
This course prepares students to meet the Mathematics General Education requirement.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recongnize the limitations of mathematical and statistical methods.
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