## 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)