M408S
Integral Calculus and Series
Fall 2010
MWF 8:00 to 9:00 in ECJ 1.202
(55115, 55120, 55125)
INSTRUCTOR: Dr. Gary Berg
Office: RLM 13.164 phone: 471-6410
email: [email protected]
Office Hours:
Calculus II-Stewart
5.1
Dr. Berg
Spring 2010
Areas and Distances
Integral calculus arose from the need to calculate areas and volumes of complex
shapes.
The Area Problem
Before the Fundamental Theorem
Calculus II-Stewart
5.4
Dr. Berg
Spring 2010
Indefinite Integrals and the Net Change Theorem
Antiderivatives play such an important role in integration that integral notation is
commonly used to repre
Calculus II-Stewart
6.2
Dr. Berg
Spring 2010
Volume
Volume by Cross Section
A right cylinder has congruent cross sections and side(s) at right angles to the
base. A prism, for example, is a right tria
Calculus II-Stewart
6.1
Dr. Berg
Spring 2010
Area Between Curves
To approximate the area between two curves, we can use rectangles as we did
before. Suppose that f ( x ) g( x ) on the interval [ a, b]
Calculus II-Stewart
5.5
Dr. Berg
Spring 2010
The Substitution Rule
The substitution rule reverses the chain rule. Recall that, by the chain rule,
[ f (g( x )] = f ( g( x ) g( x ) . Reversing this yiel
Calculus II-Stewart
7.4
Dr. Berg
Spring 2010
Logarithmic Functions
Derivatives
Theorem
d
dx
1
1
d
(ln x ) = x and dx (ln g( x ) ) = g( x ) g( x ) .
Example A
d
dx
1
(ln (tan x ) = tan x sec 2 x .
Exam
Calculus II-Stewart
7.2
Dr. Berg
Spring 2010
Calculus with Exponential Functions
The Exponential Function
Bacteria double their population at regular intervals through cell division. We
speak of the h
Calculus II-Stewart
7.6
Dr. Berg
Spring 2010
Inverse Trig Functions
Inverses
The inverses of the trig functions are an important addition to our toolbox. Recall
that f 1 ( x ) = y if and only if f ( y