Winter 08 116 Schedule
1/4 Friday
1. Syllabus
a. Point system:
Each problem in team homework and quiz has 3 points.
1 point will be given when student attempted to solve individual homework
problem in class.
2 extra points will be given when the student solve the problem correctly.
b. Weekly quiz: 2 problems, Wednesday, after reviewing individual homework.
c. Reading next chapter before come to the class.
2. Student Info Sheet
a. Include an easy problem to check students’ understandings.
3. Wide summary
Chapter 5: Definite Integrals
How do we calculate
1

 12
ln( 1  x 2 )dx numerically?
Chapter 6: Antiderivatives
d x 2
How to solve  e t dt ?
dx 0
Chapter 7: Integration
How to solve  sin( x)e  x dx ?
Chapter 8: Using Definite Integrals
Find the volume of the sphere of radius R.
Chapter 9: Sequence and Series

1
Does the series  sin( 2 ) converge?
n
n 1
Chapter 10: Taylor Series

2n
Where does 
converge to?
n 1 n!
Chapter 11: Differential Equations
Find a function y  f (x) satisfying y   2 y (1  y ) .
4. First chapter
5.1 How do we measure distance traveled?
Distance = (average velocity) * (time traveled)
constant velocity
→
uniformly increasing velocity
varying velocity
area under the curve
Left and Right sum
5. Homework
5.1:5, 15, 21, 23, 25
1/7 Monday
1. Team arrangement – did in 1/4
Area of Living – North campus, East Quad, South Quad, Central Campus, etc
1st team homework due 1/11
1st team homework: chp5rev:36, 38, 40, 46
1.1 Online student information / Student guide on web
1.2 Assigning students to teams who missed the last class
1.3 Brief review of last class
n
left/right sum approximation of distance
 f ( x )x
i 1
i
definite integral – definition, area under the curve lim
n 
n
 f ( x )x
i 1
2. Homework Review
5.1:15, 5.1:23
3. Chapter 5.2 and 5.3, 5.4
5.2 The definite integral – covered in 1/4
notation
definition – Large sigma
definite integral as an area (positive or negative f(x))
general Riemann sum
5.2:5, 5.2:20
5.3 Fundamental theorem of calculus
statement
average value of f from a to b
5.3: 4, 5.3: 28
5.4 Theorems about definite integrals

b
a
a
f ( x)dx   f ( x)dx
b
i
b
c
c

 f ( x)  g ( x)dx   f ( x)dx   g ( x)dx
 cf ( x)dx  c f ( x)dx
Area between f(x) and g(x)  f ( x)  g ( x)dx
If f is even,  f ( x)dx  2 f ( x)dx . If f is odd,  f ( x)dx  0
If m  f ( x)  M , then m(b  a)   f ( x)dx  M (b  a)
If f ( x)  g ( x) , then  f ( x)dx   g ( x)dx
a
b
f ( x)dx   f ( x)dx   f ( x)dx
b
a
a
b
b
a
a
b
b
a
a
b
a
a
a
a
0
a
a
b
a
b
b
a
a
5.4: 21-24, 36-39
4. Quiz about student guide on Wednesday
5. Homework
5.2: 7, 27, 29, 31
5.3: 13, 17, 23, 25, 34
5.4: 3, 9, 13, 15
Read 6.1 and 6.2
1/9 Wednesday
0.1 Brief Review
b
Fundamental Theorem of Calculus F (b)  F (a)   f ( x)dx
a
Algebra of definite integrals
Question: Find approximate value of
ln(x)
x
-0.5
0.223
-0.1
0.01
1

 12
ln( 1  x 2 )dx by using
0.3
0.086
0.2 Office hours on Wednesday change to 10:30pm-11:30am
0.3 Entrance Gateway Test
0.4 Online student information
1. Homework Review
5.2: 29, 5.3: 34
2. Quiz and Quiz Review
0.75
0.446
3. Chapter 6.1
6.1 Antiderivatives
Graph of f(x)
positive/negative slope
critical point
inflection point
F(x)+C
→
→
→
Graph of f’(x)
positive/negative value
crossing x-axis
critical point
6.1: 10, 17
6.2 Constructing antiderivatives
 kdx  kx  C
x n 1
 x dx  n  1  C , n  1
1
 x dx  ln x  C
n
 e dx  e  C
 cos xdx  sin x  C
 sin xdx   cos x  C
x
x
6.2: 16, 54, 58, 80, 86
4. Homework
5.4: 17, 19, 31, 40
6.1: 7, 15, 19, 23, 25
6.2: 9, 17, 19, 31, 55
1/11 Friday
0.1 Assign a team: Jeremy and Kyle
0.2 Brief review of 6.1 and 6.2
antiderivatives: graphs, formulas
remaining 6.2: 80, 86
1. Homework Review
5.4: 17, 6.1: 23
2. Chapter 6.4 (6.3 is not included)
x
Second Fundamental Theorem of Calculus F ( x)   f (t )dt
a
6.4: 8, 16, 18, 22, 24 bold ones left to do on 1/14
3. 1st team homework due
4. Homework
6.2: 59, 67, 71, 75, 77, 82
6.4: 3, 9, 11, 13, 19, 21, 23, 25, 27 (were not assigned)
5. Quiz on Chapter 5 on Wednesday
1/14 Monday
1. Homework Review
6.2: 71, 82
2. Review on Chapter 6 – problem unsolved.
3. Chapter 7.1, 7.2
7.1 Integration by substitution
d
( f ( g ( x)))  f ( g ( x))  g ( x) inside function and outside function
dx
 f ( g ( x))  g ( x)dx  f ( g ( x))  C choosing inside and outside function
7.1: 38, 50, 54, 76
4. Homework
6.4: 3, 9, 11, 13, 19, 21, 23, 25, 27
2nd team homework: 5.3: 36, Chp5Rev: 44, 6.1: 24, Chp6Proj2
5. Quiz on chapter 5 on Wednesday
1/16 Wednesday
0.1 Deadlines
1/25 Exam 1 conflict
1/28 Gateway test deadline
1. Homework review
6.4: 9, 21, 27
2. Quiz and Quiz Review – on chapter 5
2.1 Chapter 7.1 #76(b)
explain why w does not / does change sometime
integral of cos(x^2)
3. Chapter 7.2 (did not cover in 1/16)
7.2 Integration by parts
d
(uv)  u v  uv 
 u v  uvdx  uv
dx
u
→
v
log - polynomial - cos/sin - exp
 uvdx  uv   u vdx
7.2: 8, 12, 18, 30, 42
5. Homework
7.1: 11, 25, 27, 31, 33, 37, 49, 57, 75, 77, 83, 87
1/18 Friday
1. Homework review
7.1: 57, 87
2. Chapter 7.4
7.2 Integration by parts
d
(uv)  u v  uv 
 u v  uvdx  uv
dx
u
→
v
log - polynomial - cos/sin - exp
 uvdx  uv   u vdx
7.2: 8, 12, 18, 30, 42
7.3 Table of integrals
Focus on how to transform the given integral formula into the given integral
expression
7.3: 2, 6, 8, 12, 14, 20, 26, 34, 48
3. 2nd Team homework due today
4. Quiz on Chapter 6 on Wednesday 1/23
5. Homework
7.2: 3, 9, 15, 19, 23, 27, 37, 38, 51, 53
7.3: 1-39 odd, 47
1/21 Monday (no class)
1/23 Wednesday
0.1 Deadlines
1/23 Drop
1/25 Exam 1 conflict
1/28 Gateway test deadline
0.2 Review
7.2:  (ln x) 2 dx
7.3: 12, 20, 26
1. Homework review (didn’t do)
7.2: 37, 51, 53
7.3: 9, 37, 47
2. Quiz and quiz review – on chapter 6
3. Chapter 7.4
7.4 Method of partial fraction (Omitting the trigonometric substitution)
P( x)
Calculating integral such as 
dx
Q( x)
P( x)
: use long division if degree of P(x) ≥ degree of Q(x) and then,
Q( x)
An
A
A2
P( x)
 1 

n
m
2
x  a ( x  a)
( x  a ) ( x  b)
( x  a) n
Bm
B
B2
 1 

2
x  b ( x  b)
( x  b) m
example:
x 5  3x  1
x( x  1) 2
7.4: 2, 16, 18, 24, 26, 32, 34, 36, 38, 40, 50, 64
Introduce sinh/cosh 7.4:39
4. Homework
7.4: 1, 3, 15, 19, 33, 35, 37, 39, 49, 57, 63 (extras: 16, 24, 26, 32, 34, 36, 38, 40)
1/25 Friday
1. Homework Review
7.2: 37, 51, 53
7.3: 9, 37, 47
7.4: 63, 49
2. Chapter 7.5
7.5: Approximating definite integrals
LEFT (n)  RIGHT (n)
MID (n) 
2
b
If f is increasing on [a,b], then LEFT (n)   f ( x)dx  RIGHT (n)
a
b
If f is decreasing on [a,b], then RIGHT (n)   f ( x)dx  LEFT (n)
a
b
If f is concave up on [a,b], then MID (n)   f ( x)dx  TRAP (n)
a
b
If f is concave down on [a,b], then TRAP (n)   f ( x)dx  MID (n)
a
7.5: 4, 10, 12, 16
3. 3rd Team homework due
4. Homework
7.5: 1-23 odd
1/28 Monday
1. Homework Review
7.5: 9, 13, 15, 21
2. Chapter 7.7
7.7: Improper integrals
Type 1 improper integral:

b
 f ( x)dx  lim  f ( x)dx converges, diverges
b
a


c
f ( x)dx 



a

f ( x)dx   f ( x)dx
c
Type 2 improper integral
b

a
c
f ( x)dx  lim
c b 
 f ( x)dx
a
f (x)   when x  b
likewise, x  a and explain the difference between c  b  and c  b
b

c
b
a
c
f ( x)dx   f ( x)dx   f ( x)dx
a
7.7: 10, 12, 14, 24, 30
3. Homework
7.7: 11, 13, 15, 17, 19, 23, 25, 31, 33
1/30 Wednesday
1. Homework Review
2. Quiz and quiz review – on chapter 7
2/1 Friday
Review 1
2/4 Monday
Review 2
2/6 Wednesday