MATH 2254   CALCULUS II    4 CREDIT HOURS

Prerequisite: MATH 2253

 

A continuation of MATH 2253. Topics include differentiation and integration of transcendental functions,

integration techniques, indeterminate forms, L'Hopital's rule, improper integrals,  infinite sequences and series,

Maclaurin and Taylor series, conic sections, and polar coordinates.

 

Text: Thomas' Calculus, by Thomas, Weir, Hass, Giordano,  11th edition  (Pearson/Addison-Wesley)

Calculator: TI-89 (including its "Titanium" variant)

 

CODES:  NC = do not use any calculator, with the exception noted below;  C = use the calculator without restriction

 

NOTE: For some problems marked NC, it is allowable (and useful) to use the calculator for graphing ONLY.

 

 

DAY

TOPICS

SECTION(S)

HOMEWORK ASSIGNMENTS

1 & 2

Inverse Functions

7.1

(p473) NC: 1-8,10,11,13,15,18,19,21,22,24, 25,27,31,36,41             C:  53,54

3 & 4

Natural Logarithm

7.2

(p484)  NC:  1,3,4, odd 5-29, 33, odd 37-51, 57,65,69,72,73,74     C:  85,86,88

5 & 6

Exponential Function

7.3

(p493)  NC: 1,3, odd 5-33,  odd 37-61, 52, 67,69,71               C:  70,77

7

Bases other than e

7.4

(p500)  NC:  1,2,7, odd 11-25, 31,33,39,41,43, odd 47-53, 57,61,65,71,75

C:  77,79,80,83, 87(a-d)

8 & 9

Inverse Trig Functions

7.7

(p530) NC: 1,3,5,7,13,17,18,19,29,31,33, 34,41,43,49-53, 61,62,65,69,70, 71-74,77, 79,81,85,89,91,93,95,99,101,107,125,133, 139              C:  127,137,151,153

 

(optional) Hyperbolic Functions

7.8

(p542)  NC: 1,5,13,17,25,35,41,84

10

REVIEW

 

 

11

TEST 1

 

 

12 & 13

Basic Integration Rules

8.1

(p558)  NC:  1-7, 12,13, 17-21, 25-29, 33, 37-41, 43,47,48,51,53,55,57

14 & 15

Integration by Parts

8.2

(p568)  NC:  1-9, 11,13,21,23,31, 34(a), 39,40,41

16,17,18

Partial Fractions

8.3

(p579)  NC:  1-8, odd 9-25, odd 29-37

C:  45,46

19 & 20

Trigonometric Integrals

8.4

(p585)  NC:  odd 1-11, 15,17,19, odd 23-29, 30,33,34,36             C: 43

21,22,23

Trig Substitution

8.5

(p591)  NC:  odd 1-23, 29,35

C: 41,42

24

Integration by Calculator

8.6

(p600)  C: 5,11,19,21,31,33,43,51,77

[SIMPLIFY all answers ]    ( NOT tables )

25 & 26

Indeterminate Forms

and L'Hopital's Rule

4.6

(p298)  NC: 1,3,4, 7-13, 16,19,23,24,26, 27,29         C: 35,36

27 & 28

Improper Integrals

8.8

(p631)  NC:  1-5, 7-11, 15,21,22,24, 25,27,67,69,70       C:  89,90

29

REVIEW

 

 

30

TEST 2

 

 

31

Sequences

11.1

(p757)  NC: 1-5, 13-16, odd 23-45, 44,56,60,97,98

C:  121,129,133,135

32 & 33

Infinite Series

11.2

(p769)  NC: 1,2,3,7,9,11, 23-33, 41,43,45,51,52,77

34 & 35

Integral Test and p-series

11.3

(p775)  NC:  odd 1-19, 6,22,28

C:  33

36

Comparison Tests

11.4

(p781)  NC: 2,3,4,5,8,11,17,27

37 & 38

Ratio and Root Tests

11.5

(p786)  NC: 2-9, 15-19, 21,45

39

REVIEW

 

 

40

TEST 3

 

 

41

Alternating Series,

Absolute Convergence

11.6

(p792)  NC:  1-6, odd 11-21, odd 25-33, 45,49,51

C: 59

42 & 43

Power Series

11.7

(p804)  NC: odd 1-19, 10,12,24,33,34,39,40

44 & 45

Maclaurin and Taylor Series

11.8

(p810)  NC:  1-7, 9-13, 17,19,27,33

(also graph using calculator)

46 & 47

Convergence and Error Estimates

11.9

(p819)  NC: odd 1-23, 22,35,49

C:  29,57

48

Applications of Power Series

(SKIP differential equation part)

11.10

(p831)  NC:  1,2,3,11,47

C:  odd 33-43, 59,67

49

REVIEW

 

 

50

TEST 4

 

 

51

Conic Sections

10.1

(p693)  NC:  1-8, odd 9-43,  odd 57-67, 83

52 & 53

Parametric Equations

10.4

(p712)  NC: 1-7, 9,17

C:  19-25

54

Polar Coordinates

10.5

(p718)  NC:  odd 1-19, odd 23-35, 43,45, 49-57

55

Graphing in Polar Coordinates

10.6

(p724)  NC:  odd 1-9, 13,17,19,25,27, 31,33,35              C:  43,45,49

56

Area in Polar Coordinates

10.7

(p730)  NC: 1-10

(also graph using calculator)

57

REVIEW

 

 

58

TEST 5

 

 

59

REVIEW

 

 

60

REVIEW