MATH 101, Winter 2012

COURSE OUTLINE

All lecture sections of MATH 101 cover the topics listed below in the given order. A “Week” represents approximately a week’s worth of lecture time, not necessarily a calendar week.

Section numbers below refer to the text; most of Chapters 5, 6, 7, and 11 are covered, as well as parts of Chapters 8 and 9.

Note: Sections 6.3, 8.1, 8.5, 9.1, 9.2, 9.4, 9.5, 10.3, 10.4, 17.1, 17.2, and 17.3 have been included in MATH 101 in the past but are not covered this year. Also, Chapter 11 was included for the first time last year. In a nutshell, less time is spent on differential equations than in the past, probabilty and polar coordinates are not covered, and sequences and series are covered. Keep these changes in mind when looking at old final exams.

• Week 1
  • §5.1 Areas and Distances
  • §5.2 The Definite Integral
• Week 2
  • §5.3 The Fundamental Theorem of Calculus
  • §5.4 Indefinite Integrals and the Net Change Theorem (ignore sinh and cosh formulas)
  • §5.5 The Substitution Rule
• Week 3
  • §6.1 Areas Between Curves
  • §6.2 Volumes
• Week 4
  • §6.4 Work
  • §6.5 Average Value of a Function
  • §7.1 Integration by Parts (ignore “reduction formulas”)
• Week 5
  • §7.2 Trigonometric Integrals (ignore sin mx cos nx, etc.)
  • §7.3 Trigonometric Substitution (ignore inverse secant and inverse hyperbolic substitutions)
• Week 6
  • §7.4 Integration of Rational Functions by Partial Fractions (ignore “CASE IV: Q(x) contains a repeated irreducible quadratic factor”)
  • §7.5 Strategy for Integration
  • §7.7 Approximate Integration
• Week 7
  • §7.8 Improper Integrals
  • §8.3 Applications to Physics and Engineering (ignore Hydrostatic Pressure and Force and Theorem of Pappus)
  • §9.3 Separable Equations (ignore Orthogonal Trajectories)
• Week 8
  • §11.1 Sequences (ignore Definitions 2 and 5, Example 6, proof of Monotonic Sequence Theorem, Example 14)
  • §11.2 Series
• Week 9
  • §11.3 The Integral Test and Estimates of Sums (ignore Estimating the Sum of a Series and Proof of the Integral Test)
  • §11.4 The Comparison Tests (ignore Estimating Sums)
• Week 10
  • §11.5 Alternating Series
  • §11.6 Absolute Convergence and the Ratio and Root Tests (ignore The Root Test)
• Week 11
  • §11.8 Power Series
  • §11.9 Representations of Functions as Power Series
• Week 12
  • §11.10 Taylor and Maclaurin Series (ignore Binomial Series)
  • Review