Ch 7.1 : Integration by parts
In this section, we study one of the most important theorems in
mathematics, namely the integration by parts.
The Theorem
Theorem (Integration by parts)
If f and g are differentiable functions, then
Z
Z
0
0
f (x)g (x)dx = f (

Ch 6.4 : General Logarithmic and Exponential Functions
In this section, we will
1. define general exponential and logarithmic functions
2. revisit the laws of exponents
3. look at the change of base formula for general logarithmic
function
4. study the di

Ch 6.2? - Page 421
In this section, well
1. define a natural log function
2. investigate the laws of log functions
3. define the natural number e
4. differentiate natural log functions
5. look at the method of logarithmic differentiation
Definition
Defini

Ch 11.2 : Series
In this section, we will
1. define a series (or an infinite series) as the sum of the terms in
an infinite sequence.
2. define convergent and divergent series
3. look at theorems concerning convergent or divergent series.
Ch 11.2 : Series

Ch 7.4 : Integration of Rational Functions by Partial
Fractions
In this section, we will
1. learn how to integrate any rational function
R(x)
P(x)
Q(x) = S(x) + Q(x) , where P, Q, R, and S are polynomials
(and degree of R < degree of Q), using partial fra

Ch 6.8: Indeterminate Forms and lHospitals Rule
In this section, we will investigate indeterminate forms of type
I 0
0
I
and use the lHospitals Rule to find the limit of such forms.
Examples of indeterminate forms
1. limx0
sin x
x
2. limx1
ln x
x1
3. lim

Ch 6.1: Inverse function
In this section, we will
1. define an one-to-one (1-1) function,
2. define an inverse function, f 1 , of f , provided that f is 1-1.
3. look at the domain and the range of the inverse function
4. develop a method of finding the in

Ch 11.1 : Sequences
In this section, we will
1. define a sequence as a list of numbers written in a definite
order
2. define a convergent or divergent sequence
3. define an increasing or decreasing sequence
4. look at theorems concerning convergent sequen

Ch 7.5: Strategy for integration
In this section, we will
1. review basic integration formulas
2. and try the four-step strategy, stated in the textbook
Table of integration formulas
The four-step strategy
1. Simplify the integrand (if possible)
2. Look f

Ch 6.3? : The natural exponential function
In this section, we will
1. define the natural exponential function f (x) = e x in relation
to the natural log function.
2. graph f (x) = e x
3. Some properties/laws of exponents
4. find the derivative of the nat

Ch 11.7: Strategy for testing series (A review section)
1. If the series is a p-series
and diverges if p 1.
P
1
np ,
then it it converges if p > 1
P (n1)
2. If the series is a geometric series
ar
, then it converges
if |r | < 1 and diverges if |r | 1. Som

Ch 11.8 : Power series
In this section, we will
1. define a power series as
constants.
P
n=0 cn (x
a)n , where cn s are
2. define an interval of convergence and the radius of
convergence for the given power series
3. look at a theorem regarding the inter

Ch 11.6: Absolute Convergence and the Ratio and Root
Tests
In this section, we will
1. define an absolutely convergent series
2. look at theorems concerning absolutely convergent theorem
3. use the ratio test to determine whether a given series is
(absolu

Ch 11.5 Alternating Series
In this section, we will
1. study series whose terms are not all or eventually positive.
(e.g., an alternating series)
2. study the convergence test for an alternating series.
Alternating series
An alternating series is a series

Review of Prerequisite Material
Math 2254 Worksheet 1
Important Note: If this is more than a cobweb removal exercise for you - if you are really struggling
with a lot of these questions - come see me ASAP! If your Calc I background is weak, then your
succ

Ch 11.9 : Representation of functions as power series
In this section, we will
1. learn to
types of functions as sums of power
Prepresent certain
n
series
c
(x
a)
n
n=0
2. differentiate/integrate power series.
The base example
Show that
1
1x
=
P
n=0 x
n

Ch 7.2 : Trigonometric integrals
In this sections, we will evaluate trigonometric integrals of the
forms
R
1. sinm x cosn xdx
R
2. tanm x secn xdx
R
R
R
3. sin mx cos nxdx, sin mx sin nxdx, or cos mx cos nxdx
Strategy for
R
sinm x cosn xdx
Example 1
Evalu

Ch 7.3: Trigonometric Substitution
In this section, we will solve integrals whose integrands contain
1. a2 x 2
2. a2 + x 2
3. x 2 a2
by substituting x with appropriate trig functions.
Strategy
Example :
Evaluate
R
a2 x 2
1
dx.
9x 2
Example 1 (from textbo

Sec. 6.6: Inverse Trigonometric Functions
In this section, we will
I
revisit definitions of trig functions - both right triangle and
unit circle definitions
I
define inverse trig functions and their domains and ranges
I
revisit the cancellation laws given