Name: TA Name: Math 20B. Midterm Exam 1 April 28, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each questio
Math 20B Integral Calculus
Lecture 4
'
1
$
Areas and volumes are computed by integration
Review: Substitution rule.
Slide 1
Areas between curves (Sec. 6.1).
Volumes: (Sec. 6.2)
General solid.
Solids of revolution.
&
%
'
$
Substitution is an inverse f
Math 20B Integral Calculus
Lecture 23
'
1
$
Functions dened using innite series
Slide 1
Power series.
The convergence of power series.
Dierentiation and integration.
&
%
'
$
The geometric series can be used to dene a
function
We have learned how to add
Print Name:
Section Number:
TA Name:
Section Time:
Math 20B.
Final Exam
June 12, 2006
No calculators or any other devices are allowed on this exam.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
Read each questi
Math 20B Integral Calculus
Lecture 15
'
1
$
Integration of rational functions
Slide 1
Review: Decomposition of a polynomial.
Integration of rational functions: Cases I - IV.
Examples.
The three main integrals.
&
%
'
$
A rational function is a quotient
Math 20B Integral Calculus
Lecture 18
'
1
$
Integrals of functions on innite domains
Slide 1
Review: Improper integrals type I.
Type II: Three main possibilities.
Limit of an innite sequence.
&
%
'
$
Generalizations of
b
a
f (x) dx in I = [a, b]
Integr
Math 20B Integral Calculus
Lecture 12
'
1
$
Tricks for trigs
Slide 1
Review: Recursion formulas.
Integral of some trigonometric functions.
integrals of f : I C.
R
&
%
'
$
Reduction formulas are a simple way to write
complicated integrals
In the case of
Math 20B Integral Calculus
Lecture 6
'
1
$
Miscellaneous topics
Slide 1
Average of a function.
Integral form of the Mean Value Theorem.
Polar coordinates.
&
%
'
$
Integration provides a way to dene the average
of a continuous function on a closed inter
Math 20B Integral Calculus
Lecture 20
'
1
$
Criterias for convergence of series
Slide 1
Review: A rough criteria.
Integral test for convergence.
Estimating the remainder.
Comparison test for convergence.
&
%
'
$
Here is a very rough criteria to check
Math 20B Integral Calculus
Lecture 9
'
1
$
z = a + bi, powers, roots, and exponentials
Slide 1
Review: Cartesian and polar representations.
Powers and roots.
Exponential and Euler formula.
&
%
'
$
Complex numbers can be associated with points
in a plan
Math 20B Integral Calculus
Lecture 1
'
1
$
Review on Integration (Secs. 5.1 - 5.3)
Remarks on the course.
Slide 1
Review: Sec. 5.1-5.3
Origins of Calculus.
Riemann Sums.
New functions from old ones.
&
%
'
$
A mathematical description of motion motiva