## Department of Mathematics - RHIT Topics Outline for MA112 - Calculus II - 2010-11

last posted to site: 08/19/10

Note: The Fall quarter class is predominantly Advanced Placement Freshman. However, some time will be spent reviewing some topics and getting up to speed in Maple. Students taking a course later in the year will have already been instructed in Maple in a prior course.

### Text and Text Materials

Text: Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.
DE Problem supplement: 2004-05 version from Angel

### Approximate Timing and Pace

There should be 3 or 4 tests, perhaps a final review day or two. This is integrated into the timing below.
For pedagogical reasons the series material may be taught earlier and the DE material shifted to the final week.
Please note that some additional time needs to be spent teaching Maple MA111 topics for fall sections.
Optional topics in italics

 Fall AP Sections Winter and Spring Sections Chapter Sections Time and Notes Chapter Sections Time and Notes Review 5.1, 5.2, 5.3 Maple review sheet: Maple for Calculus I and other review materials 0.5 weeks approx Some formal review of material from 5.1-5.3 as needed, in addition students should read/review 5.1-5.3 as needed. Some focused instruction on Maple in addition to informal Maple instruction as needed in context of the course. 5.4, 5.5, 5.6 1 week 5.4, 5.5, 5.6 1 week 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7 2 weeks on applications 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7 2 weeks 7.1, 7.3, 7.4 0.5 week (7.2 is taught in the DE material below) 7.1, 7.3, 7.4 0.5 week (7.2 is taught in the DE material below) 8.1, 8.2, 8.3, 8.4, 8.5, 8.7 4.6 l'Hopital's rule as needed Integral Tables 8.5 if needed 2 weeks 8.1, 8.2, 8.3, 8.4, 8.5, 8.7 4.6 l'Hopital's rule as needed Integral Tables 8.5 if needed 2 weeks 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 10.10 3 weeks 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 10.10 3 weeks 7.2, 9.1, Supplementary DE material 1 week 7.2, 9.1, Supplementary DE material 1 week

### Text Topics - Optional or partial section topics in italics, Review topics in bold italics,

5. Integration

5.1 Estimating with Finite Sums (optional review)

5.2 Sigma Notation and Limits of Finite Sums (optional review)

5.3 The Definite Integral (optional review)

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Method

5.6 Substitution and Area Between Curves

6. Applications of Definite Integrals

6.1 Volumes Using Cross-Sections

6.2 Volumes by Cylindrical Shells (lightly)

6.3 Arc Length

6.4 Areas of Surfaces of Revolution (optional)

6.6 Work and Fluid Forces

6.7 Moments and Centers of Mass (optional)

7. Transcendental Functions

7.1 The Logarithm Defined as an Integral

7.2 Exponential Growth and Decay (this material should be combined with the DE supplement)

7.3 Hyperbolic Functions (inverse hyperbolic functions optional)

7.4 Relative Rates of Growth (optional)

8. Techniques of Integration

8.1 Integration by Parts

8.2 Trigonometric Integrals (lightly or optional)

8.3 Trigonometric Substitutions (lightly or optional)

8.4 Integration of Rational Functions by Partial Fractions

8.5 Integral Tables and Computer Algebra Systems (optional)

8.6 Numerical Integration (may be shifted to the introductory material in Chapter 5, Simpson's rule optional)

8.7 Improper Integrals ( review l'Hopital's Rule 4.5 if needed)

10. Infinite Sequences and Series

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 The Ratio and Root Tests (Root Test optional)

10.6 Alternating Series, Absolute and Conditional Convergence (focus on absolute convergence, alternating series test lightly) (optional)

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Convergence of Taylor Series (specific examples) (Error Estimates optional)

10.10 The Binomial Series and Applications of Taylor Series (optional)

DE Material

The material from 7.2 might be taught here

The smaller version of the DE supplement from 2004-05

9.1 Solutions, Slope Fields, and Euler's Method