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'Hospital's rule, improper integrals, infinite sequences and series, Maclaurin and Taylor series, conic sections, and polar coordinates.

Text: Calculus,7E by James Stewart,  7th edition  (Brooks/Cole)

Calculator: TI-83 or TI-84 series

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.

NOTE: Stewart contains two versions of sections 6.2, 6.3, and 6.4 labeled with and without an asterisk. The instructor may choose to cover logarithms followed by exponentials (6.2*, 6.3*, and 6.4*) or exponentials followed by logarithms (6.2, 6.2, and 6.4). Students should consult with their instructor regarding section coverage and homework requirements.

(The following schedule and homework are suggested and will vary with instructor. Students should consult with their instructor regarding exam dates and homework requirements.)

Week

Topic

Section (in Stewart)

Homework

Exam

1

Inverse functions, Natural logarithm

6.1, 6.2*

(pg. 390) NC: 3-13, 21, 23, 25, 27, 33, 35-42

(pg 428) NC: 1-9odd, 11-14, 15, 17-37odd, 49, 65-74

 

2

Natural exponential function, General logarithms and exponentials

6.3*, 6.4*

(pg. 434) NC: 1-14, 21, 23, 27-51odd, 53, 81-92

(pg. 444) NC: 3-10, 25-41odd; C: 11, 15

 

3

Inverse Trigonometric functions, Indeterminate forms & l'Hopital's rule

6.6, 6.8

(pg. 459) NC: 1-11odd, 22, 23-33, 38, 59-70

 

4

Indeterminate forms & l'Hospital's rule

6.8

(pg. 477) NC: 1, 3, 7-25odd, 29-35odd, 41, 49, 55, 57, 59, 61

Exam I

5

Integration by parts, Trigonometric integrals

7.1, 7.2

(pg. 492) NC: 1, 2, 3-23odd, 27-35odd, 37, 39

(pg. 500) NC: 1-39odd

 

6

Trigonometric substitution, Partial fractions, Strategies for Integration

7.3, 7.4, 7.5

(pg. 507) NC: 1, 2, 3, 5-19odd, 23, 25, 27, 29

(pg. 516) NC: 1-4, 7, 9, 11-27odd, 39, 41, 47

 

7

Strategies for Integration, Improper integrals

7.5, 7.8

(pg. 523) NC: 1-51odd

(pg. 551) NC: 1, 2, 5-39odd, 41, 49-54

 

8

Sequences

11.1

(pg. 724) NC: 1, 3, 5, 9, 13, 23-51odd, 73, 75, 77

Exam II

9

Series, Integral test, Comparison tests

11.2, 11.3, 11.4

(pg 735) NC: 1, 5, 7, 16, 17, 27-47odd, 57, 59, 61, 63

(pg. 744) NC: 1, 3-25odd, 27, 29

(pg. 750) NC: 1, 3-31odd

 

10

Alternating series, Absolute convergence and the ratio and root tests

11.5, 11.6

(pg. 755) NC: 1, 3-19odd, 27, 29

(pg. 761) NC: 1, 3-29odd, 31, 35

 

11

Convergence testing strategies, Power series

11.7, 11.8

(pg. 764) NC: 1-27odd, 31-37odd

(pg. 769) NC: 3-19odd, 23, 25, 27

Exam III

12

Representation of functions as power series, Taylor & Maclaurin series,

11.9, 11.10

(pg. 775) NC: 3, 5, 9, 15, 17, 25, 29

(pg. 789) NC: 5, 7, 9, 13, 15, 16,17, 19, 29, 31, 33, 47, 49

 

13

Applications of Taylor Polynomials, Curves defined by parametric equations

11.11, 10.1

(pg. 798) NC: 3, 5, 7, 9; C: 13, 17, 19

(pg. 665) NC: 5, 7, 9, 11, 13, 14

 

14

Calculus with parametric curves, Polar coordinates

10.2, 10.3

(pg. 675) NC: 1, 3, 5, 7, 11, 13, 17

(pg. 686) NC: 1-6, 7-12, 29-43odd

 

15

Areas in polar coordinates, Conic sections

10.4, 10.5

(pg. 692) NC: 1, 2, 6, 9, 17, 19, 23, 27

(pg. 700) NC: 1-7odd, 11, 13, 15, 19, 21, 23, 25, 27, 29

Exam IV

 

 

 ©