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.