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Course Materials:
Course Description, Lecture Plan
(Week 1 Handout)
Office Hours: (B.H.) M/W 1:00-1:50
(TA) TBA
Math Help Center:
Drop in tutoring in Mathematics Rm 107/110,
starting Jan. 28.
Exam calculator/index card policy: On exams, each student may
bring in a calculator. PROHIBITED are calculators with built-in computer
algebra systems.
In particular, the following calculators and their upgrades, are
NOT permitted:
TI-89,
TI-92,
TI Voyage 200,
HP-48,
HP-49,
Casio FX2.0,
Casio CFX 9970G.
Also prohibited are laptop, netbook, tablet or handheld computers
including PDAs, electronic writing pads or devices with pen-input,
calculators built into cell phones or any other electronic communication devices.
Preparedness:
Outcomes:
Students will be literate in the language and notation of integral calculus, sequences,
series and power series.
Students should strive for personal mastery of the skills described in
http://www.mtsu.edu/math/forms/Learning_Outcomes_MATH_1920.pdf
and will be well prepared for the sequels, Calculus III MTH 241
and Differential Equations MTH 306.
Preview of what you should be able to do on completing this course:
History/Philosophy/Topics:
wiki Calculus
Discussion:
see me in Mathematics Rm 322 and we will relocate the 2nd floor lounge
area
On exams, each students may bring in one index card
written both sides, with any information.
Are you ready for Calculus II online quiz/review 3 quizzes, each 10 questions)
Are you ready for calculus 2- Marta Hidegkuti
solutions page
Review materials from Publisher website
Are you ready for Calculus III online quiz/reviews (6 quizzes, each 10 questions)
MTH142 Motherhen Notes (A. Piech)
The webwork link for this course is
ww2.math.buffalo.edu/webwork2/2013_1_MTH142_Hassard
Your username is your usual UBIT username, and
your initial password is your UB person #, see the
bottom left of your UB Card (something like 59265358)
When you see the page that lists the homework sets,
there will be numbers 1, 2, 3, 4 .. in blue.
Click on the (blue) 1. This gives HW set 1, a new page listing problems 1, 2, .., 15 in blue.
Click on (blue) Problem 1.
After filling in the answer boxes for a problem, you click on "Check Answers".
If a problem is at all difficult you should work on paper. Be sure to bring partial solutions with you when seeking help. However, you do not hand in the problem solutions on paper, rather you complete each question online and click on "Check Answers"
The webwork system can generate pdf files for entire HW assignments.
Webwork due dates:
Lec. 1 1/14: Sec. 5.5 The Substitution Rule
Lec. 2 1/16: 6.1 Area Between Curves
Lec. 3 1/18: 6.2 Volumes
Quiz 1 on material from sections 5.5, 6.1, 6.2 in recitations on 1/23, 1/25, 1/28
Lec. 4 1/23 6.3 Volumes by Cylindrical Shells
Lec. 5 1/25: 6.4 Work
Lec. 6 1/28: 6.5 Average Value of a Function
Quiz 2 on material from sections 6.3, 6.4, 6.5 in recitations on 1/30, 2/1, 2/4
Lec. 7 1/30: 7.1 Integration by Parts
The following use Integration by Parts twice:
Lec. 8 2/1: 7.2 Trigonometric Integrals
The following are all patrickJMT videos:
Lec. 9 2/4: 7.3 Trigonometric Substitution
Quiz 3 on material from sections 7.1, 7.2 in recitations on 2/6, 2/8, 2/11
Lec. 10 2/6 - a review before the test
Test 1 on Fri. Feb. 8 covers sections 5.5, 6.1-6.5 and 7.1
Lec. 11 2/8 - this period used for test 1
Lec. 12 2/11: 7.4 Integration of Rational Functions by Partial Fractions
long
division x4+0x3-1x2+1x-4 divided by
x2-2x+5 Note HW 12 problem 4 requires long division
before partial fraction decomposition
Quiz 4 on material from sections 7.3, 7.4 in recitations on 2/13, 2/15, 2/18
Lec. 13 2/13: 7.5 Strategy for Integration
Lec. 14 2/15: 7.6 Integration Using Tables and CASs
Lec. 15 02/18: 7.7 Approximate Integration
Quiz 5 on material from sections 7.5, 7.6, 7.7 in recitations on 2/20, 2/22, 2/25
Lec. 16 2/20: 7.8 Improper Integrals
Lec. 17 2/22: 8.1 Arc Length
Lec. 18 2/25: 8.2 Area of a Surface of Revolution
Quiz 6 on material from sections 7.8, 8.1, 8.2 in recitations on 2/27, 3/1, 3/4
Lec. 19 2/27: 8.3 Applications to Physics and Engineering
Lec. 20 3/1 - a review before test 2
Lec. 21 3/4: This period used for test 2
Quiz 7 on material from section 8.3 in recitations on 3/6, 3/8, 3/18
Lec. 22 3/6:
8.4 Applications to Economics and Biology
Lec. 23 3/8:
8.5 Probability
Spring Recess March 11-16
Lec. 24 3/18:
9.4 Models for Population Growth,
Quiz 8 on material from sections 8.4, 8.5, 9.4 in recitations on 3/20, 3/22, 3/25
Lec. 25 3/20:
10.1 Curves Defined by Parametric Equations
Lec. 26 3/22:
10.2 Calculus with Parametric Curves
area enclosed by y=2.5 and curve x = t - 1/t; y = t + 1/t (patrickJMT)
Lec. 27 3/25:
11.1 Sequences
Quiz 9 on material from sections 10.1, 10.2, 11.1 in recitations on 3/27, 3/29, 4/1
Lec. 28 3/27:
11.2 Series
(sum k=1 to 5) 2(-3)k-1 (bullcleo1)
Lec. 29 3/29:
11.3 The Integral Test and Estimates of Sums
Lec. 30 4/1 - a review before test 3. The test covers covers
8.3-8.5, 9.4, 10.1-10.2, 11.1-11.2. There will be 5 questions;
142s13t3_sample_discuss_20130401.pdf
Quiz 10 on material from sections 11.2, 11.3 in recitations on 4/3, 4/5, 4/8
Lec. 31 4/3: This period used for test 3
Lec. 32 4/5:
11.4 Comparison Tests
Lec. 33 4/8:
11.5 Alternating Series
Quiz 11 on material from sections 11.4, 11.5 in recitations on 4/10, 4/12, 4/15
Lec. 34 4/10:
11.6 Absolute Convergence and the Ratio Test
Lec. 35 4/12:
11.7 Strategy for Testing Series
Lec. 36 4/15:
11.8 Power Series
Quiz 12 on material from sections 11.6, 11.7, 11.8 in recitations on 4/17, 4/19,
4/22
Lec. 37 4/17:
11.9 Representation of Functions as Power Series
Lec. 38 4/19:
11.10 Taylor and McLaurin Series
Lec. 39 4/22:
11.11 Applications of Taylor Polynomials
Quiz 13 on material from sections 11.9, 11.10, 11.11 in recitations on 4/24, 4/26,
4/29
Lec. 40 4/24:
10.3 Polar Coordinates
Lec. 41 4/26
10.4 Areas and Lengths in Polar Coordinates
142s13t4_samplefinal.pdf Sample Final
142s13t4_samplefinal_partAsolutions.pdf Sample Final solutions to
Part A
Lec. 42 4/29 Last day of class- Review for the Final
The final will have parts A and B. Part A is on material from 11.3-11.11, 10.3-10.4 and
part B is on the course as a whole.
Final Exam: 5/6/2013, Monday 8:00AM - 11:00AM Room NSC 205
Starting with HW 6 (relating to the lecture on Jan. 25)
the full-credit HW due date will be 4 class periods after the
lecture when the related material was covered.
After the full-credit due date, there is a two-week
period during which HW will be counted at reduced credit of 80%.
Since the HW6 lecture was Fri. Feb. 25, the full credit due date is
Mon. Feb. 4 and the reduced-credit due date is Mon. Feb. 18.
HW: sets 1 and 2 of
course webwork
(Integral) 2x(x2+4)100 dx (patrickJMT)
(Integral) (1+x^3)^9 3
x^2 dx by substitution (brightstorm)
(Integral 3 to 5) x
sqrt(x^2-9) dx by substitution (brightstorm)
(Integral x from pi/2 to pi) -(cos(x))^2 sin(x) dx by substitution (khanacademy)
(Integral) 1/(3-2 x^2)^(1/2) dx by trig substitution (khanacademy)
(Integral) 1/(36 + x^2) dx by trig substitution (khanacademy)
HW: set 3 of
course webwork
y=9-x2 and y=x+3 (wlmui)
(to following are all patrickJMT)
y=x2-4x and y=2x
y=8-x2 and y=x2, for x from -3 to 3
y=cos(x) and y=-sin(x), for x from 0 to pi/2
y=2-x2 and y=-x
two curves, one left, one right
x=y2 and y=x-2
y=2/(1+x2) and y=|x|
HW: set 4 of
course webwork
volume of square-based pyramid (integrationbyawesome)
region bounded by y=x3 and y=x, rotated about x-axis
(patrickJMT)
HW: set 5 of
course webwork
region bounded by y=-x2+x and y=0 rotated about y-axis (patrickJMT)
HW: set 6 of
course webwork
Determine amount of work required to:
pull 60 ft rope weighing 2 lb/ft hanging over edge, to top of building (also, work to pull half-way up) (patrickJMT)
pull 5 m rope weighing 1kg/m with attached object weighing 70kg, to point of suspension
Intro to springs and Hooke's Law (khanacademy)
stretch spring obeying Hooke's Law f(x)=kx from 35cm to 40cm (spring has natural length 30cm;
to stretch spring from 30cm to 42 cm required 2 Newton-meters of work)
(patrickJMT)
stretch spring obeying Hooke's Law f(x)=kx from natural length to 6in beyond natural length (spring requires 10lb force to hold stretched 4 in beyond natural length)
(patrickJMT)
pump out a tank in the shape of a trough with triangular cross-section (patrickJMT)
HW: set 7 of
course webwork
Average value of a Function: derivation (rootmath)
Find the average value of:
f(x)=x2 over the interval [-1,1] (TheIntegralCALC)
f(x)=3x2 - 2 x over the interval [1,4] (rootmath)
g(x)=cos(x) over the interval [0,pi/2] (TheIntegralCALC)
f(x)=(cos(x))4 sin(x) over the interval [0,pi] (TheIntegralCALC)
f(x)=sqrt(4-x2) over the interval [-2,2] (DrChrisTisdell)
The Mean Value Theorem for Integrals (DrChrisTisdell)
HW: set 8 of
course webwork
Rule of thumb in choosing u of (Integral) u dv
(Integral 1 to 2) ln(x)/x^2 dx (patrickJMT)
(Integral) x sin(2x) dx (ExamSolutions)
(Integral) x2 ex dx (khanacademy)
(Integral) (ln(x))2 dx (patrickJMT)
(Integral) e2x sin(x) dx "Loopy Example" (patrickJMT)
HW: set 9 of
course webwork on sections 7.2-7.3 will be due after test
(Integral) (sin(x))3 (cos(x))2 dx
(Integral) (sin(x))3 (cos(x))3 dx
(Integral) (sin(x))2 (cos(x))2 dx
(Integral) (tan(x))2 (sec(x))4 dx
(Integral) (sec(x))4 dx
(Integral) (tan(x))5(sec(x))3 dx
(Integral) (tan(x))5 dx
(Integral) sin(2x) cos(3x) dx
(Integral) sin(2x) sin(2x) dx
(Integral) (cos(x))2 (tan(x))3 dx
(Integral) csc(x) dx
(Integral) (cos(x)+sin(x))/(sin(2x)) dx
HW: set 10 of
course webwork
(Integral) 1/(36 + x2) dx
(khanacademy)
(Integral 0 to 1) 1/(1+x2) dx
(Integral) x3/sqrt(x2+9) dx (patrickJMT)
(Integral) x3/sqrt(16-x2) dx by trig subs. (patrickJMT)
(Integral) 1/sqrt(9 x2 + 4) dx
(Integral) sqrt(6x-x2-5) dx
(khanacademy)
(Integral) 1/(5-4x-x2)5/2) dx
(continued)
and will be similar to questions 1,4,5,6,7,8,9 of midterm 1 Fall 2006 of
www.math.rochester.edu/courses/162/home/old%20exams.html
UR MTH 162 Past Exams
See also questions 1,2,4 and 5 from
B.H. Test 1 from 142 Spring 2000
Test 1 with answers
HW: set 11 of
course webwork
HW: set 12 of
course webwork
HW: set 13 of
course webwork
HW: set 14 of
course webwork
HW: set 15 of
course webwork
(integral -1 to 0)x-2 dx
(patrickJMT)
HW: set 16 of
course webwork
Find the arclength of the curve:
y = (2/3)(x2+1)3/2 for x from 0 to 2 (TheIntegralCALC)
y = x3/2 for x from 0 to 4 (MIT, Lewis; incorrectly titled x2/3)
y = (1/3)(x2+2)3/2 for x from 0 to 1 (patrickJMT)
y = (1/2)x2 - (1/4) ln(x) for x from 2 to 4 (patrickJMT)
HW: set 17 of
course webwork
area of surface of revolution, curve y = x3 for x from 1 to 2, revolving around x-axis
(fordummies)
area of surface of revolution, curve y = x2
(TheIntegralCalc)
area of surface of revolution, curve y = (4 - x2)1/2 for x from -1 to 1, revolving around x-axis
(TheIntegralCalc)
area of surface of revolution, curve y = x1/2 for x from 4 to 9, revolving around x-axis,
same example but with x=g(y)=y2 for y from 2 to 3, and ds in terms of dy
(patrickJMT)
HW: set 18 of
course webwork
hydrostatic force on triangular plate 4m high, 5m wide at top, submerged
so top is at depth of 3m in water (partickJMT)
The effect of hydrostatic pressure on a styrofoam cup
center of mass of region bounded by f=4-x2 and g=x+2, -3
≤ x &le 1
(youtube.com)
The test covers covers 7.2-8.2 and will be similar to
questions 2, 3, 10 and 11 of
UR Midterm 1 from Fall 2006
together with
questions 14 of
UR Final exam from Fall 2006
See
142s13t2_samplesolutions from class
See also solutions at
www.math.rochester.edu/courses/162/home/old%20exams.html
UR MTH 162 Past Exams
Test 2 with answers
HW: set 19
course webwork
HW: set 20 of
course webwork
find probability that your call is answered in first two minutes if probability density function for waiting time is f(t)=0 if t<0, f(t)=(1/6)e-t/6 if t ≥ 0
probability that the amount of rain tomorrow is between 1.9 and 2.1 inches
is the area under the graph of the probability density function for Y from 1.9 to 2.1 (khanacademy)
HW: set 21 of
course webwork
Lake now has 500 fish, carrying capacity is 10000, population triples in
first year. Find population after t years (PatrickJMT)
HW: set 22 of
course webwork
Parametric
curves, graphing x(t)=1+t1/2, y(t) = t2-4t, 0
≤ t ≤ 5 (PatrickJMT)
Car going 5m/s drives off 50m cliff: graphing x(t)=5t+10,
y(t)=50-5t (Khan academy)
HW: set 23 of
course webwork
equation of tangent line to curve x = 3 t2 - t; y = t1/2 at t = 4 (patrickJMT)
arclength of curve x = 1 + 3 t2, y = 4 + 2 t3 for t from 0 to 1 (patrickJMT)
arclength of curve x = et + e-t; y = 5 - 2 t for t from 0 to 3 (patrickJMT)
HW: set 24 of
course webwork
Sequences:
1,2,3,...
0.1, 0.01, 0.001 ...
an=3(-1)n/n!
an=n(n-1)
an=2n/(3n+1)
(teacherspayteachers.com)
HW: set 25 of
course
webwork
Infinite sums of geometric series:
0.21212121... as a geometric series, summed to a fraction
(TheIntegralCALC)
(sum k=0 to ∞) (2/3)k, summed to a fraction
(TheIntegralCALC)
1 + e-1 + e-2 + e-3 + ..., summed
(TheIntegralCALC)
HW: set 26 of course webwork
Show (sum n=1 to ∞) n/(n2+1) C or D
(PatrickJMT)
Show (sum n=1 to ∞) 1/(n2-4n+5) C or D
(PatrickJMT)
Show (sum n=0 to ∞) n
e-n2 C or D
(PatrickJMT)
Q1 a centroid/center of mass problem similar to section 8.3 examples 4 and 5
Q2 a probability density problem like section 8.5 example 1,
(perhaps using a solution of the logistic equation section 9.4 as the probability density f)
Q3 a parametric curve problem, like section 10.2 examples 2 and 5,
or UR Fall 2007 Final question 11/UR Fall 2006 Final question 15
Q4 a limit of sequence problem like section 11.1 examples 7 and 13 or UR Fall 2006 Midterm 2 question 9
Q5 a gemetric series problem like section 11.2 examples 4 and 5 or UR Fall 2009 Midterm 2 question 5
www.math.rochester.edu/courses/162/home/old%20exams.html
UR MTH 162 Past Exams
Test 3 with answers
HW: set 27 of course webwork
(sum n=1 to ∞)1/(n2+3) C or D?
(sum n=3 to ∞)1/sqrt(n-2) C or D?
(sum n=1 to ∞)1/n! C or D?
(bullcleo1)
HW: set 28 of course webwork
(sum n=1 to ∞) (-1)n+1/n C or D?
(sum n=1 to ∞) (-1)n2n/(5n-3) C or D?
(sum n=1 to ∞) (-1)n/(3 ln n) C or D?
(bullcleo1)
HW: set 29 of course webwork
(sum n=1 to ∞)(-1)n+1/(n+2) C or D?
If C, conditionally or absolutely?
(sum n=1 to ∞)(-1)n+1/n(4/3) C or D?
If C, conditionally or absolutely?
(sum n=1 to ∞)(-1)n/5n/(9n-2)C or D?
If C, conditionally or absolutely?
(bullcleo1)
HW: set 30 of course webwork
14 series practice problems worked (PatrickJMT)
HW: set 31 of course webwork
Radius of Convergence for
(sum n=0 to ∞)xn,
(sum n=0 to ∞)(x/2)n,
(sum n=0 to ∞)xn/n!,
(sum n=0 to ∞)xn/(n 2n),
(sum n=0 to ∞)x2n/(2n)! (MIT, Breiner)
HW: set 32 of course webwork
What functions do each of the following represent?
a) (sum n=0 to ∞) xn+2/n!,
b) (sum n=2 to ∞) xn,
c) (sum n=0 to ∞) (xn/n! + xn),
d) (sum n=1 to ∞) xn+1
(MIT, Breiner)
Series for functions
1/(1-x), 1/(1+x), 1/(1-x3),
1/(1+9x2), x/(4x+1), x/(9+x2)
all based on 1/(1-x)
= 1 + x + x2 + x3 + ... (PatrickJMT)
HW: set 33 of course webwork
first few terms of Taylor series for sec(x) (MIT, Lewis)
cosh(x)
2 sin(x) cos(x)
x ln(1-x3) (MIT, Lewis)
HW: set 34 of course webwork
Approximate (integral 0 to 1) x cos(x3 dx to within 3 decimal
places (PatrickJMT)
HW: set 35 of course webwork
write polar form of rectangular equations
x2 + y2 = 1,
y = 2x + 1,
y = 3/x (patrickJMT)
graph
r = 7 sin(theta),
r = 6 + 4 sin(theta) (TheIntegralCALC)
r = 2,
r = tan(theta) sec(theta),
theta = -pi/6,
r2 - 3 r + 2 = 0 (patrickJMT)
graphing a polar curve: r = 3 cos(2 theta),
continued (patrickJMT)
HW: set 36 of course webwork
find area enclosed by one loop of r = sin(4 theta) (partickJMT)
find area of rightmost region bounded by r = 2 and r = 4 cos(theta) (bullcleo1)
find area of middle region bounded by r = 2 and r = 4 sin(theta) (bullcleo1)
find area of inner loop bounded by r = 1 + 1 cos(theta) (bullcleo1)
arclength of curve r = (sin(theta/2))2 for theta from 0 to pi (TheIntegralCalc)
arclength of curve r = 1 - sin(theta) for theta from 0 to 2 pi (bullcleao1)