Topics Covered:
Chapter 5 – Integrals
5.2 The definite integral (very quick review)
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite integrals and the Net Change Theorem
5.5 The Substitution Rule
Chapter 6 – Applications of Integration
6.1 Area between curves
6.2 Volumes
Chapter 7 – Techniques of Integration
7.1 Integration by parts
7.2 Trigonometric integrals
7.3 Trigonometric substitution
7.4 Integration of rational functions by partial fractions
7.5 Strategy for integration (for review)
7.8 Improper integrals
Chapter 11 – Infinite Sequences and Series
11.1 Sequences
11.2 Series
11.3 The Integral Test and estimates of sums
11.4 The comparison tests
11.5 Alternating series
11.6 Absolute convergence; the Ratio and Root Tests—except subsection Rearrangements
11.7 Strategy for testing series (for review)
11.8 Power series
11.9 Representation of functions as power series
11.10 Taylor and Maclaurin series—except subsection Multiplication
and Division of Power Series and Binomial Series
Chapter 10 – Parametric Equations and Polar Coordinates
10.1 Curves defined by parametric equations
10.2 Calculus with parametric curves—only subsections Tangents and Arc Length (not subsections Area and Surface Area)
10.3 Polar coordinates
10.4 Areas and length in polar coordinates
Notice that some of these sections will be covered for the most part, but not in their entirety. Students will only be responsible for the covered material.