Math 231. Calculus II
Lecture Syllabus

Textbook: Smith and Minton, Calculus: Early Transcendental Functions, 3rd edition, McGraw Hill.

This syllabus assumes MW lectures and Tuesday-Thursday discussion sections, with 28 lecture hours in the semester. It includes 25 lectures, leaving 3 exam hours.

It is assumed that the Teaching Assistants in this course will do some lecturing in their discussion sections so as to keep the timeline for the syllabus on track. Instructors should plan on this when planning their course plan.

Recommended lecture schedule:

Chapter 6 : Techniques of Integration (6 lectures)

0 lectures 6.1 Review of formulas and techniques
1 lecture 6.2 Integration by parts
2 lectures 6.3 Powers of trig functions; trig substitution
1 lecture 6.4 Rational functions; partial fraction decomposition
0 lectures 6.5 Integration tables and computer algebra systems
2 lectures 6.6 Improper integrals; comparison test

Note: portions of 6.1, 6.5 can be covered in discussion sections

Chapter 7 : First-Order Differential Equations (1 lecture)

1 lecture 7.1 Exponential growth and decay

Chapter 8 : Infinite Series (12 lectures)

2 lectures 8.1 Sequences
1.5 lectures 8.2 Infinite series
1.5 lectures 8.3 Integral test; comparison tests
1 lecture 8.4 Alternating series
1 lecture 8.5 Absolute convergence; ratio test
1.5 lectures 8.6 Power series
2 lectures 8.7 Taylor series
1.5 lectures 8.8 Applications of Taylor series
(optional) 8.9 Fourier series

Chapter 9 : Parametric equations and polar coordinates (6 lectures)

1 lecture 9.1 Plane curves and parametric equations
1 lecture 9.2 Calculus and parametric equations
1 lecture 9.3 Arc length and surface area in parametric equations
1 lecture 9.4 Polar coordinates
1 lecture 9.5 Calculus and polar coordinates
1 lecture 9.6 Conic sections
(optional) 9.7 Conic sections in polar coordinates

Recommended exam schedule

It is impractical to give one hour exam covering the whole of chapter 8, and a natural break point is between sections 8.5 and 8.6.

Exam #1. Cover sections 6.2, 6.3, 6.4, 6.6, 7.1
Exam #2. Cover sections 8.1-8.5.
Exam #3. Cover sections 8.6-8.8, 9.1-9.3 (optional 9.4, 9.5)

General notes

Ch. 6: This is a "warm-up" chapter. Some techniques, particularly integration by parts and the method of partial fractions, have important applications aside from evaluating integrals. The goal here is to have students understand the basics, not to be able to work by hand difficult integrals. In 6.2, one may also teach the "tabular" method of repeated integration by parts. Spend a lot of time with 6.6, as it gives students a lot of good practice working with limits, useful skills needed in Ch. 8. Cover also the comparison test for improper integrals, a good preview of one of the tests for infinite series.

Ch. 8: This is the most difficult, and most important, component of the course. It is very important to proceedslowly and thoroughly. Invariably many students will struggle with basics such as the difference between a sequence and a series. Do not rush the material, and emphasize the "trial and error" method to analyzing series for convergence. The students are expected to be able to justify with words why a sequence or series converges/diverges, citing appropriate tests and theorems. They are not expected to write formal proofs.

Ch. 9: A "cool-down" chapter that gives the students a breather after the heavy chapter on series. 9.3 provides a generalization of the formulas learned in Calculus I (section 5.4) for arc length and area of a surface of revolution. Sections 9.1-9.6 will be needed in Calculus III, so make sure to leave enough time to cover all of them.

Revised by Kevin Ford 08/15/07; approved by R. Muncaster