Suggested Syllabus for Math 2B – CALCULUS (for Winter 2010) (rev. 12/28/2009)

Textbook – “Calculus” by J. Stewart (6th edition) (Check below for more textbook info)

NOTE: This is only a suggested syllabus. The actual syllabus used by an individual instructor -- and especially, the lectures during which the midterms take place -- may be different. Do not post this syllabus on your course website unless you plan to follow it exactly.

Lecture # / Chapter/Section /

Topics

1 * / 5.1 / Areas and Distances (See Comment #1 below)
2 / 5.2 / The Definite Integral
3 / 5.3 / Fundamental Theorem of Calculus
4 / 5.4 / Indefinite Integral and the Net Change Theorem
5 / 5.5 / The Substitution Rule
6 / 6.1 / Area Between Two Curves
7 / 6.2 / Volume by Slices (start)
8 / 6.2, 6.5 / Volume by Slices (end); Average Value
9 / 7.1 / Inverse Functions
10 / 7.2 ("gray") / The Natural Logarithmic Function (See Comment #2 below)
11 / --- / REVIEW FOR MIDTERM #1
12 / MIDTERM #1 / NOTE: Lect 12 = Monday of Week # 5 (See Comment #3 below)
13 / 7.3 ("gray") / The Natural Exponential Function
14 / 7.4 ("gray") / General Logarithmic and Exponential Functions
15 / 7.5 / Exponential Growth and Decay
16 / 7.6 / Inverse Trigonometric Functions
17 / 7.8 / L’Hospital’s Rule (See Comment #4 below)
18 / 8.1 / Integration by Parts
19 / 8.2 / Trigonometric Integrals
20 / --- / REVIEW FOR MIDTERM #2
21 / MIDTERM #2 / NOTE: Lect 21 = Wed of Week # 8 (See Comment # 5 below)
22 / 8.3; 9.1 / Trig Substitutions; Arclength (See Comment # 6 below)
23 / 8.4 / Method of Partial Fractions (See Comment # 7 below)
24 / 8.8 / Improper Integrals
25 / 11.1 / Curves Defined by Parametric Equations
26 / 11.2 (Part I) / Calculus with Parametric Curves-Tangents and Arc Length
27 / 11.3 / Polar Coordinates (See Comment # 8 below)
28 / --- / REVIEW FOR FINAL EXAM
29 / --- / NO LECTURE # 29 in WINTER 2010

*The lecture numbers correspond to the standard schedule of three MWF lectures, each 50 minutes long, per week. This usually comes to 29 lectures. WARNING: In Winter 2010 there are only 28 MWF lectures.

TEXTBOOKS: Stewart’s “Single Variable Calculus” (6th edition) is also acceptable, as long as the student will NOT take Math 2D-2E. There is also a paperback "custom version" that has "UC Irvine" on the cover. WARNING – Stewart sells several other calculus texts which are NOT suitable for Math 2B. In particular, avoid any Stewart book with the words “Early Transcendentals” or “Concepts and Contexts” in the title.

COMMENTS:

(1) Some students will have studied the first sections of Chapter 5 in Math 2A. Other students will have studied the alternate version provided by the Department (see: Supplementary Notes on Antiderivatives on the Department website.). Regardless, past experience has demonstrated that a review of 5.1-5.3 will be of value for all students. Indeed, a quick review of Section 4.9 (Antiderivatives) might also be useful -- perhaps in the first discussion meeting?

(2) The Stewart text offers two approaches to exp and log, in Sections 7.2, 7.3, 7.4, and in Sections 7.2, 7.3, 7.4; the pages in the  sections are tinted gray. We shall follow Sections 7.2, 7.3, 7.4 ("Logarithms via the are under y = 1/x") to aid in the goal of making Math 2B uniform across the lectures.

(3) The timing of the Midterm #1 is somewhat flexible, but also crucial: You need to cover enough material for meaty exam problems, but you cannot postpone this exam too long—students should receive the graded exams by Tuesday of the 6th week (for sections with a Tuesday discussion) or by Thursday of the 5th week (for Thursday discussions). If you are willing use lecture time to hand them back, you should do so by Monday of the 6th week. (Remember that students need to decide before Friday of the 6th week whether to drop your course, and making this decision may require that they have enough time to see their graded exam and then discuss their options with their academic counselor.)

(4) The limits of ex/xn and xn ln x, as x approaches infinity and 0+, respectively, are mentioned only for special cases of n=1 and n=2 in Section 7.8. You may wish to mention the cases for general n.

(5) As was the case with Midterm #1, you have a little flexibility in the timing of Midterm #2. Probably the main issue will be whether your discussions meet on Tuesdays or on Thursdays.

(6) Because there are only 28 lectures in Winter 2010, you may wish to simply state the formula for the length of an arc of the graph y = f(x), without deriving it; and then use it as an excuse for interesting integrals.

(7) Reports from those who have taught Math 2B indicate that one lecture is not enough time for doing "Partial Fractions". The same may be true for "Trig Integrals", "Trig Substitutions", "Improper Integrals", etc.

(8) The topic of "polar coordinates" is mentioned explicitly in the UCI Calalogue's official description of the contents of Math 2B, so we do have to cover it. What is described above is the bare minimum to keep us legal; it does not include, for example, arelength or area in polar coordinates,.