Each preliminary exam will have about nine problems, and the final exam will have about fifteen..
REVIEW 1 Integration
Lesson Section Topic
Page Problems
5 5.2 Definite Integral, Ln, Rn
376 2,4
7 5.3 Fundamental Theorem of Calculus,
Part 1 388 8,10;14,18,54
9 5.4 Definite Integral; Change
Theorem
397 38,58
1,2,10 5.5 Substitution in Integrals
406 50,58,62,64
11 5.5 Symmetric Integrals
406 60& pg409#9 explain
12 6.1 Area Between Curves
420 16,22
13 6.2 Volumes by Cross-Sections (Discs
and Washers) 430 4,6,8
14 6.3 Volumes by Shells
436 2,4
15 6.4 Work
441 4,10
16 6.5 Average Value of a Function
445 4
REVIEW 2 Techniques of Integration
Lesson Section Topic
Page Problems
17 7.1 integration by parts
457 6,10,22
18 7.2 trigonometric integration
465 2,6,8?,42
19-20 7.3 trigonometric and hyperbolic substitutions
472 4,6,8,32
21 7.4 partial fractions and integration(Cf
Exer 9,11) 481 10,12,16
22 7.7 trapezoidal and midpoint rules
504 26T4, 26M4
23 7.8 improper integrals: unbdd intervals/integrands
515 10,16; 28,32
25 8.1 arc length
530 2,8
26 8.2 area of a surface of revolution
L20?
537 6,8,12
REVIEW 3 Sequences and Series
Lesson Section Topic
Page Problems
27-28 11.1 sequences
685 16&18,26&28,36&40
29-30 11.2 series
694 6&12,16,18,36,44
31 11.3 integrl test; p-series
703 12
32 11.4 comparison tests
709 12
33 11.5 conv absolutely? conv conditionally?
diverge? 713 2,8,10,24,26
34-35 11.6 conv absolutely? conv conditionally? diverge?
719 4,6,12,14,16,20,30
36 11.7 conv absolutely? conv conditionally?
diverge? 722 4,12,16,18,20,22,24,26
REVIEW 4 Power Series and Ordinary Differential
Equations
Lesson Section Topic
Page Problems
37-38 11.8 radius and interval of convergence
727 4,10,12,16
39 11.9 algebra of power series
733 4,8
40 11.9 differentiation&integration of power
series 733 16,18
41-42 11.10 derive a Taylor series
746 14,16
43 11.12 error in alternating power series
755 26,28
46 9.3 separation of variables
586 2,4
REVIEW for the FINAL EXAM
Lesson Section Topic
Page Problems
7 5.3 Fundamental Theorem of Calculus,
Part 1 388 16,14
10 5.5 Substitution in a Definite Integral
406 12,28
13 6.2 Volumes by Cross-Sections (Discs
& Washers) Rev:447 7
17 7.1 integration by parts
457 4,12,40
19-20 7.3 trigonometric and hyperbolic substitutions
472 10,14,16
22 7.7 trapezoidal and midpoint rules
505 28T6, 28M6
23 7.8 improper integrals: unbdd intervals/integrands
515 12,18; 28,30
36 11.7 conv absolutely? conv conditionally?
diverge? 722 8,14,30
37-38 11.8 radius and interval of convergence
727 18,22
39 11.9 algebra of power series
733 6,10
40 11.9 differentiation&integration of power
series 733 24,26
46 9.3 separation of variables
586 8,10,12
REVIEW 3 Sequences and series
A geometric sequence converges to zero if its ratio r satisfies
|r|<1
An increasing sequence bounded above converges
A series is a pair of sequences: one of terms and one of partial sums.
We say a series converges if and only if its sequence of partial sums
converges.
For a series to converge, it is necessary that its sequence of terms
converge to zero.
(But just because the terms tend to zero, we cannot say the series
converges!!!)
Partial sums of nonnegative terms either converge to a number or diverge
to infinity.
Direct comparison of sums depends on direct comparison of terms.
Limit comparison depends on the limit of a ratio between two sequences
of terms.
p-series behavior is derived using the integral test.
Ratio and root tests are based on comparisons with geometric series.
REVIEW 4
An alternating series converges if its terms have magnitudes which
decrease steadily to zero.
Given an alternating series, distinguish among absolute convergence,
conditional convergence, and divergence.
Constructing a power series for a given function requires finding a
pattern in the derivatives.
Differentiated or integrated power series converge
in the interior of the original interval of convergence.