MATH 142 Spring 2005- Course log and homework

Problems in italics have been discussed in class

1/12 Course policies

Areas by approximation (intro)

5.1: 1, 3, 5

1/14 Upper/lower approximations; definition of definite integral

5.2: 3, 6, 7, 8, 29, 49

Riemann sums- programs for the TI83+

1/18 Properties of definite integrals; integration of polynomials

5.2: 32, 33, 35, 36, 47, 48

1/19 Riemann sums- calculator examples; homework problems (5.2)

1/21 Evaluation theorem, indefinite integrals

5.3: 19, 22, 26, 29, 31, 34, 48

1/24 Homework problems; fund thm of calculus

5.4: 2, 4, 7, 10, 11, 14, 16, 19, 20, 24

1/25 quiz 1: 5.2: 7, 33, 36; 5.3: 26

proof of FTC, example from HW

Policy announcement: the syllabus did not address the relative weights

of quizzes and exams. The policy is this: each problem proposed in a quiz/exam

will have the same weight in the final average. Since quizzes will have 3-4

problems and exams 6-8, it follows that each exam will enter the course grade

with about twice as much weight as each quiz.

1/26 applications of FTC-examples

trapezoidal rule (program has been added to the TI-83+ link above)

5.9: 2, 8, 11 (omit Simpson's rule) , 16, 17 (trapezoidal, midpoint-no Simpson), 29

1/28 error bounds for left/right endpoint sums (with proof); for midpoint, trapezoidal (no proof)

By Monday, you should have the calculator programs for Riemann sums/trapezoidal up and

running (they will be needed for the test!) Note also:

The 7th entry in the MATH menu of the TI-83+ is

fMax( function, argument, lower, upper)

It returns the maximum value of the function, as the argument takes values in the interval [lower, upper].

For example, if I use the Y= key to edit in y2= the function

y2=3x^2/(2 square root (1+x^3))

and then type the command:

fMax( y2, x, 0,1)

I get the maximum value of this function in [0,1] (calculator answer: 1*, essentially, smaller than the

estimate 3/2 found `by hand' in class.) This command fMax can be used to find the constants

M1 and M2 in the error bounds (but of course you have to take first resp. second derivatives `by hand'

and store them as functions in y2= (resp. y3=). Hopefully your calculator can't take derivatives (if it does,

let me know and it will be aprehended.)

( * Incidentally, the correct value is 1.5/sqrt(2), about 1.061, achieved at x=1 (the function is increasing in [0,1], check

it), which goes to show you- don't trust calculators too much.)

1/31 discussion of problems from 5.4, 5.9

2/1 Exam 1 (PDF file)

2/2 techniques of integration: substitution (5.5)

5.5: 9, 24, 28, 32, 45, 46, 49, 50, 51, 56, 62

2/4 integration by parts (5.6)

discussion of exam 1

5.6: 4, 10, 12, 16, 24, 26, 28

2/7 discussion of HW problems

partial fractions

Appendix G: 5, 7, 20, 24, 25, 26

5.7: 24, 31

2/8 quiz 2 5.5: 45, 49, 51, 62; 5.6: 16, 28

use of trigonometric identities

5.7: 1, 2, 5, 6, 31

2/9 trigonometric substitution (3 examples)

integration practice sheet handed out

5.7: 9, 10, 11, 13, 14, 30

2/11 areas

6.1: 8, 12, 13, 14, 15, 16, 22, 27, 28

2/14 discussion of HW problems (integration)

2/15 Exam 2: sections 5.1 to 5.7, 5.9 (Simpson's rule excluded), 6.1 (parametric curves excluded)

(study- HW for above sections, plus: exam 1, quizzes 1 and 2, `integration practice' sheet)

Exam 2 (PDF file)

2/16 parametrized curves (sp. case: polar curves): parametrizing graphs, eliminating parameter

arc length, velocity vector, speed (=length of velocity vector)

6.3: 5, 6, 10, 24, 25 (compute also the velocity vectors and their lengths)

H2: 35, 36, 39 (use a calculator to plot the curves)

2/18 area enclosed by parametrized curves

6.1: 29, 32, 33

H2: 5, 6, 7, 8

2/21 discussion of HW problems

2/22 QUIZ 3: HW for lectures on 2/16, 2/18

solution of quiz 3, solution of exam 2 (conclusion)

2/23 volumes

6.2: 2, 3, 8, 9, 10, 22, 23, 26, 29, 30, 32

2/25 averages (6.4)

6.4: 9, 11, 13

2/28 center of mass: point masses along a line, continuous mass

distributions along a line. Weighted average (discrete, continuous)

discussion of HW problems

3/1 Quiz 4: Hw for 6.2, 6.4

weighted average of continuous functions with respect to a `weight function'.

3/2 center of mass (6.5)- decomposition principle

6.5: 26, 27, 29, 31, 32

3/4 center of mass of homogeneous laminas; handout

3/7 discussion of problems in handout

CM for non-homogeneous laminas

3/8 Quiz 5: Hw for center of mass (problems from handout)

Pappus' theorem and applications

3/9 Continuous random variables: probability density, expectation

Examples: exponential, uniform

6.7: 3, 5, 6, 7

3/11 Normal random variables

6.7: 8, 10, 11, 12

3/14 5.10 improper integrals

HW problems on probability

5.10: 6, 8, 17, 22

3/15 review (driven by student questions)

Review problems (p. 500/501): 3, 7, 11, 15, 22, 28, 29

Important: review also the HW problems for this chapter, including handouts

3/16 (Wednesday) Exam 3: 6.1 to 6.5 (6.5: CM only) 6.7, appendix H

Exam 3(PDF)

3/18 5.10 improper integrals (cont'd)

3/28 5.10: 26, 30, 32, 41, 43, 45, 46, 47, 48

3/29 Discussion of exam 3; sequences (8.1)

3/30 sequences- examples

4/1 series- geometric, telescoping, harmonic

8.2: 5, 14, 16, 19 (telescoping), 21, 20, 23, 25, 26, 28, 30, 36

4/4 discussion of section 5.10 HW (improper integrals)

4/5 Quiz 6: HW on improper integrals (5.10)

solution of quiz; integral test

4/6 Integral test- remainder estimate; (limit) comparison test

discussion of problems from 8.2

8.3: 14, 16, 18, 20, 22, 24, 27, 28, 35

4/8 Exam 4: center of mass, probability, improper integrals, series (up to 4/1 lecture)

Exam 4 (PDF)

4/11 Alternating series (inc. remainder estimate), ratio test

8.4: 5, 6, 9, 12, 13, 17, 23, 25, 26, 27

4/12 solution of exam 4

problems from handout (convergence of series)

4/13 power series/representation of functions (8.5, 8.6)

8.5: 9, 11, 14, 15, 20

4/15 8.6: 5, 8, 10, 13, 14, 16, 22, 24, 26, 28

4/18 Taylor/MacLaurin series

8.7: 4, 6, 13, 17, 19, 23, 29, 37, 39, 47, 48, 54

4/19 Quiz 7: HW from 8.3, 8.4

Taylor/McLaurin series (cont'd)

4/20 Taylor polynomials/ remainder estimate(8.7, 8.9)

8.9: 3, 5, 8, 14, 16, 17, 18, 19

discussion of problems from 8.5, 8.6

4/22 (Friday) Exam 5: ch 8 (8.2 to 8.6, handout on series)

Exam 5 (PDF) (with ANSWERS!)

4/25 Binomial series (8.8)

8.8: 4, 5, 9, 10, 11

4/26, 2/27 Problems from ch. 8

8.7: 32, 34, 38, 48, 50; 8.8: 9; 8.9: 8, 14, 18, 20

Review (p. 641): 31, 33, 35, 42, 43, 44, 45, 46, 47 (a) (c)

5/6 (Friday) Final exam, 10:15-12:15 (8.5 to 8.9)

Please note: the problems on the final will be based on the HW problems

listed above for these sections, and on the problems listed from p.641 (review).

If you know how to do those, you should do fine,

Pay special atttention to those that appeared on quizzes/exams.