MATH 21200: Calculus II
Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 20100
Hours/Credits: 4 HR/WK; 4 CR
Date Effective: Fall 2024
Course Supervisor: Niel Shell
Catalog Description
Techniques of integration, improper integrals, infinite sequences and series, Taylor series, geometry of space, and quadric surfaces.
Text
Calculus: Early Transcendentals by Stewart, Clegg, and Watson, 9th Edition, Pearson.
Syllabus, Suggested Schedule
| Class | Topics | Section |
|---|---|---|
| 1 | Exponential Growth, Hyperbolic Functions | 3.8, 3.11, Appendix G |
| 2 | Fundamental Theorem, Substitution | 5.3, 5.5 |
| 3 | The Substitution Rule, Integration by Parts | 5.5, 7.1 |
| 4 | Integration by Parts | 7.1 |
| 5 | Trig Integrals | 7.2 |
| 6 | Trig Substitution | 7.3 |
| 7 | Rational Functions and Partial Fractions | 7.4 |
| 8 | Exam 1 | |
| 9 | Strategies and Approximate Integrals | 7.5, 7.7 |
| 10 | Improper Integrals | 7.8 |
| 11 | Sequences | 11.1 |
| 12 | Series | 11.2 |
| 13 | Integral Test | 11.3 |
| 14 | Comparison Test | 11.4 |
| 15 | Alternating Series, Absolute Convergence | 11.5 |
| 16 | The Ration and Root tests | 11.6 |
| 17 | Exam 2 | |
| 18 | Strategies for Testing Series, Power Series | 11.7, 11.8 |
| 19 | Representing Functions as Power Series | 11.9 |
| 20 | Taylor and Maclaurin Series | 11.10 |
| 21 | Taylor and Maclaurin Series (part 2) | 11.10 |
| 22 | Seperable Differential Equation | 9.3 |
| 23 | Polar Coordinates | 10.3 |
| 24 | Exam 3 | |
| 25 | Areas and Lengths in Polar Coordinates (skip Lengths) | 10.4 |
| 26 | Conic Sections | Appendix C |
| 27 | Three Dimensional Coordinate Systems | 12.1 |
| 28 | Cylinders and Quadratic Surfaces | 12.6 |
Course Learning Outcomes
After taking this course, the student should be able to:
- Solve exponential growth and decay problems. a, c, d
- Solve separable differential equations. a
- Use standard integration techniques. a, g
- Determine convergence or divergence of improper integrals. a, b
- Determine absolute or conditional convergence of series. a, e
- Work with and represent functions as power series. a, b
- Graph and compute areas using polar coordinates. a, b
- Sketch three-dimensional graphs. b
- Classify and graph quadratic surfaces. a, b
Departmental Learning Outcomes
The mathematics department, in its varied courses, aims to teach students to:
a. Perform numeric and symbolic
computations.
b. Construct and apply symbolic and graphical
representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical
problems.
e. State (e1) and apply (e2) mathematical definitions and
theorems.
