MATH 101, Winter 2013

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.

• 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
  • §7.1 Integration by Parts (ignore “reduction formulas”)
  • §7.2 Trigonometric Integrals (ignore sin mx cos nx, etc.)
• Week 5
  • §7.3 Trigonometric Substitution (ignore inverse secant and inverse hyperbolic substitutions)
  • §7.4 Integration of Rational Functions by Partial Fractions (ignore “CASE IV: Q(x) contains a repeated irreducible quadratic factor”)
• Week 6
• §7.7 Approximate Integration
• §7.8 Improper Integrals
• Week 7
  • §8.3 Applications to Physics and Engineering (ignore Hydrostatic Pressure and Force and Theorem of Pappus)
  • §9.3 Separable Equations (ignore direction fields and Orthogonal Trajectories)
• Week 8
  • §11.1 Sequences (ignore Definitions 2 and 5, 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)