Course Description
Integration techniques, indeterminate forms, improper integrals, and power series expansions are the principal topics of the course. Specific topics include integration (by parts, substitutions, partial fractions, and inverse circular and hyperbolic functions), L'Hopital's rule, convergences tests for infinite series, and Taylor polynomials. IAI: MTH 902 Mathematics. IAI: M1 900-2.
Prerequisite(s)
MATH 2515 with a grade of C or better or appropriate advanced placement exam score - Must be completed prior to taking this course. Appropriate assessment score or ENGL 1422 with a grade of C or better - Must be taken either prior to or at the same time as this course.
At the end of this course, students will be able to:
- Apply integration by parts, partial fractions, and trigonometric substitutions to solve integral problems.
- Solve indeterminate forms of limit problems using l’Hopital’s Rule.
- Identify and evaluate simple improper integrals
- Identify infinite series as convergent or divergent using the basic tests presented.
- Expand simple analytic functions in a Taylor series.
- Find the derivatives of parabolas, ellipses, and hyperbolas using implicit differentiation.
- Solve simple vector problems involving magnitude, unit vectors, dot, and cross products
Topical Outline
1. Logarithmic and Exponential Functions Revisited
2. Exponential Models
3. L'Hopital's Rule
4. Hyperbolic Functions
5. Basic Approaches
6. Integration by Parts
2. Exponential Models
3. L'Hopital's Rule
4. Hyperbolic Functions
5. Basic Approaches
6. Integration by Parts
7. Trigonometric Integrals
8. Trigonometric Substitutions
9. Partial Fractions
10. Other Integration Strategies
11. Numerical Integration
12. Improper Integrals
13. An Overview
14. Sequences
15. Infinite Series
16. The Divergence and Integral Tests
17. Comparison Tests
18. Alternating Series Test
19. The Ratio and Root Tests
20. Choosing a Convergence Test
21. Approximating Functions with Polynomials
22. Properties of Power Series
23. Taylor Series
24. Working with Taylor Series
25. Vectors in the Plane
26. Vectors in Three Dimensions
27. Dot Products
28. Cross Products