Topics Outline for MA112 - Calculus II - 2010-11

**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:** Thomas' Calculus - Early Transcendentals
Twelfth Edition - Weir, Hass

**Supplement:** Just in Time - bundled with text.

**DE Problem supplement**: 2004-05 version from Angel

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 |
||

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 |

**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