Math 141 - Calculus II

Credits: 4

Course Description: Continuation of MATH 140. Topics include transcendental functions, techniques of integration, applications of the integral, improper integrals, l'Hospital's rule, sequences, and series.

Pre-Requisites: MATH 140 or equivalent.

Note: Because MATH 141 is the second part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 140.

Frequency:

Current Textbook: Single Variable Calculus. 6th Edition, by James Stewart, published by Brooks/Cole, 2008. ISBN: 0495011614 Check with your instructor to make sure this is the textbook used for your section.

Chapter 6:

6.1 Areas between Curves. (Review)
6.2 Volumes. (Review)
6.3 Volumes by Cylindrical Shells.

Chapter 7:

7.2 Exponential Functions and Their Derivatives. (Review)
7.3 Logarithmic Functions. (Review)
7.4 Derivatives of Logarithmic Functions. (Review)
7.5 Inverse Trigonometric Functions.
7.7 Indeterminate Forms and L'Hospital's Rule.

Chapter 8:

8.1 Integration by Parts.
8.2 Trigonometric Integrals.
8.3 Trigonometric Substitution.
8.4 Integration of Rational Functions by Partial Fractions.
8.8 Improper Integrals.

Chapter 9:

9.1 Arc Length.

Chapter 10:

10.1 Modeling with Differential Equations.
10.2 Direction Fields and Euler's Method.
10.3 Separable Equations.
10.4 Exponential Growth and Decay.

Chapter 11:

11.1 Curves Defined by Parametric Equations.
11.2 Calculus with Parametric Curves.
11.3 Polar Coordinates.
11.4 Areas and Lengths in Polar Coordinates.

Chapter 12:

12.1 Sequences.
12.2 Series.
12.3 The Integral Test and Estimates of Sums.
12.4 The Comparison Tests.
12.5 Alternating Series.
12.6 Absolute Convergence and the Ratio and Root Tests.
12.8 Power Series.
12.9 Representation of Functions as Power Series.
12.10 Taylor and Maclaurin Series.
12.11 The Binomial Series.
12.12 Applications of Taylor Polynomials. (Optional)

Appendix G:

Complex Numbers.