MATH 162: Calculus II
| Course Details | |
|---|---|
| Credit Hours: | 4 |
| Prerequisites: | MATH 161 with a grade of C- or higher |
| Description: A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric functions. Techniques of integration. Applications of integration to topics such as volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's Theorem with remainder. | |
James Stewart. Calculus, Early Transcendentals (WebAssign eBook) 8th ed. Cengage Learning
Note: Starting Fall 2020, MATH 161 will use a different textbook: Calculus Resequenced for Students in STEM by Dwyer and Gruenward, preliminary edition, Wiley. ISBN: 978-1119321590.
Review of prerequisite Material from MATH 161
Chapter 6. Applications of Integration
6.1 Area Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.4 Optional: Work
6.5 Average Value of a Function
Chapter 7: Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.6 Integration Using Tables and Computer Algebra Systems
7.7 Approximate Integration
7.8 Improper Integrals
Chapter 8: Further Applications of Integration
Instructor chooses from among these topics
8.1 Arc Length
8.2 Area of a Surface of Revolution
8.3 Applications to Physics and Engineering
8.4 Applications to Economics and Biology
8.5 Probability
Chapter 11: Infinite Sequences and Series
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclauren Series
11.11 Optional: Applications of Taylor Polynomials
Chapter 10: Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
10.2 Optional: Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Optional: Areas and Lengths in Polar Coordinates
10.5 Optional: Conic Sections
10.6 Optional: Conic Sections in Polar Coordinates
