1352-11 Final Exam Review Information

Chapter: Sections to review for final

Chapter 6 6.1: area between curves
6.2: volumes (washer, disk, cylindrical shell methods)
6.3: polar (graphing (review Table 6.2), area, etc.)
6.4: arc length and surface area (in rectangular coordinates; you can skip the ones in polar)
6.5: work by a variable force, Hooke's law (that's as far as we covered)
[6.6 - skip]

Chapter 7 7.1: u-substitutions and integration tables
7.2: integration by parts
7.3: trig methods (powers of sine and cosine, powers of secant and tangent, trig substitutions as in Table 7.1)
7.4: partial fractions (all except Weierstrass substitution)
7.5: summary of integration (I highly recommend this section as a review of 7.1 - 7.4)
[7.6 - you can skip 7.6 (differential equations)]
7.7: improper integrals
[7.8 - you can skip 7.8 (hyperbolic functions)]

Chapter 8 8.1: sequences
8.2: infinite series (partial sums, convergence and divergence, properties, geometric series)
8.3: divergence test, integral test, p-series
8.4: comparison tests (direct comparison, limit comparison, zero-infinity limit comparison, q-log series)
8.5: ratio and root tests
8.6: alternating series, alternating series test, alternating p-series, error estimates, absolute and conditional convergence, generalized ratio and root tests
8.7: power series, interval of convergence, convergence set
8.8: Taylor and Maclaurin series (note: you do not need to memorize the Taylor and Maclaurin series in Table 8.2, but I will assume that you could calculate any of them if asked) (Can skip binomial series since I didn't cover it.)

Chapter 9 9.1: vectors in 2 dimensions
9.2: vectors in 3 dimensions
9.3: dot product (properties, angle between vectors, orthogonality) (We skipped projections and work.)
9.4: cross product (calculation, properties, orthogonality, magnitude of cross product) (I won't assume you have memorized Lagrange's identity or the cab-bac formula; we also skipped applications and triple product.)
[That's it for Ch. 9. I started to cover 9.6 in class, but did not get far enough to be useful. So you are only responsible for 9.1 through 9.4.]

Integrals and derivatives In addition to the chapter specific topics above, I will assume that you know the integrals and derivatives on the back cover pages of the textbook (all but the hyperbolic and inverse hyperbolic ones). These include trig and inverse trig integrals and derivatives.

Trig identities (appendix E) Don't forget to review your trig identities (see Appendix E). In particular, if they are needed I would assume you know:
Definitions (p. A-31)
Basic identities (1 - 7, 12 - 14)
Double angle identities (21, 22)
Half angle identities (24, 25)

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Last updated: December 3, 2008
Copyright © 2008, Victoria Howle and Department of Mathematics & Statistics, Texas Tech University All rights reserved.
Comments: Victoria E. Howle (victoria.howle@ttu.edu)

Chapter:	Sections to review for final
Chapter 6	6.1: area between curves 6.2: volumes (washer, disk, cylindrical shell methods) 6.3: polar (graphing (review Table 6.2), area, etc.) 6.4: arc length and surface area (in rectangular coordinates; you can skip the ones in polar) 6.5: work by a variable force, Hooke's law (that's as far as we covered) [6.6 - skip]
Chapter 7	7.1: u-substitutions and integration tables 7.2: integration by parts 7.3: trig methods (powers of sine and cosine, powers of secant and tangent, trig substitutions as in Table 7.1) 7.4: partial fractions (all except Weierstrass substitution) 7.5: summary of integration (I highly recommend this section as a review of 7.1 - 7.4) [7.6 - you can skip 7.6 (differential equations)] 7.7: improper integrals [7.8 - you can skip 7.8 (hyperbolic functions)]
Chapter 8	8.1: sequences 8.2: infinite series (partial sums, convergence and divergence, properties, geometric series) 8.3: divergence test, integral test, p-series 8.4: comparison tests (direct comparison, limit comparison, zero-infinity limit comparison, q-log series) 8.5: ratio and root tests 8.6: alternating series, alternating series test, alternating p-series, error estimates, absolute and conditional convergence, generalized ratio and root tests 8.7: power series, interval of convergence, convergence set 8.8: Taylor and Maclaurin series (note: you do not need to memorize the Taylor and Maclaurin series in Table 8.2, but I will assume that you could calculate any of them if asked) (Can skip binomial series since I didn't cover it.)
Chapter 9	9.1: vectors in 2 dimensions 9.2: vectors in 3 dimensions 9.3: dot product (properties, angle between vectors, orthogonality) (We skipped projections and work.) 9.4: cross product (calculation, properties, orthogonality, magnitude of cross product) (I won't assume you have memorized Lagrange's identity or the cab-bac formula; we also skipped applications and triple product.) [That's it for Ch. 9. I started to cover 9.6 in class, but did not get far enough to be useful. So you are only responsible for 9.1 through 9.4.]
Integrals and derivatives	In addition to the chapter specific topics above, I will assume that you know the integrals and derivatives on the back cover pages of the textbook (all but the hyperbolic and inverse hyperbolic ones). These include trig and inverse trig integrals and derivatives.
Trig identities (appendix E)	Don't forget to review your trig identities (see Appendix E). In particular, if they are needed I would assume you know: Definitions (p. A-31) Basic identities (1 - 7, 12 - 14) Double angle identities (21, 22) Half angle identities (24, 25)