As a courtesy to my students, I have scanned my personal lecture notes. These
are meant to complement your own lecture notes, because during class I amplify
on the contents of these lecture notes extensively. These lecture notes are
*not* a replacement for attending the course lectures. If you miss class,
in addition to reading my own lecture notes, you should also obtain the notes
from one or more of your peers.

**Chapter 1: A Library of Functions
**1.1
Functions & change

1.2 Exponential functions

Handout from Prof. Hwang clarifying difference between forms of exponential functions.

1.3 New functions from old

1.4 Logarithmic functions

1.5 Trigonometric functions

1.6 Powers, polynomials, and rational functions

1.7 Introduction to continuity

**Chapter 2: Key Concept: The Derivative
**2.1
How do we measure speed?

2.2 Limits

Activity for 2.2

2.3 The derivative at a point

Activity for 2.3

2.4 The derivative function

Activity for 2.4

2.5 Interpretations of the derivative

Activity for 2.5

2.6 The second derivative

2.7 Continuity & differentiability

**Chapter 3: Short-cuts to Differentiation
**3.1
Powers and polynomials

3.2 The exponential function

3.3 The product and quotient rules

3.4 The chain rule

3.5 The trigonometric functions

3.6 Applications of the chain rule

3.7 Implicit functions

<3.8 skipped>

3.9 Local linearity

3.10 L'Hopital's Rule

Prof. Hwang's Worksheet on L'Hopital's Rule

**Chapter 4: Using the Derivative
**4.1
Using first and second derivatives

4.2 Families of curves

4.3 Optimization

Prof. Hwang's worksheet on Optimization

4.5 Optimization and modeling

4.6 Hyperbolic functions

4.7 Theorems about continuous and differentiable functions

Template for practice examining y=f(x)

**Chapter 5: Key Concept: The Definite Integral
**5.1
How do we measure distance traveled?

5.2 The definite integral

5.3 Interpretations of the definite integral

5.4 Theorems about the definite integral

Professor Hwang's worksheet on the definite integral

Professor Hwang's review questions
for the final exam

Solutions to Professor
Hwang's review questions

**Chapter 6: Constructing Antiderivatives
**6.1 Antiderivatives Graphically
and Numerically

Using your Graphing Calculator to estimate definite integrals

6.2 Constructing Antiderivatives Analytically

6.3 Differential Equations and 6.5 Equations of Motion

6.4 Second Fundamental Theorem of Calculus

**Chapter 7: Integration
**7.1 Substitution

7.2 Integration by Parts

7.3 Tables (handout will be provided in class)

Review Completing the Square

Review Polynomial Division

7.4 Algebraic Identities and Trigonometric Substitution

Professor Little's handout on Partial Fractions

Professor Little's handout on Trigonometric Substitution

7.5 Approximating Definite Integrals (no lecture notes available at this time)

Numerical Integration Program for a TI-81

Numerical Integration Program for a TI-82

Numerical Integration Program for a TI-85

7.6 Approximation Errors and Simpson's Rule

7.7 Improper Integrals

7.8 Comparison of Improper Integrals

**Chapter 8: Using the Definite Integral
**8.1 Areas and Volumes

8.2 Applications to Geometry

8.3 Density and Center of Mass

8.4 Applications to Physics

8.5 <skipped>

8.6 <skipped>

8.7 <skipped>

**Chapter 9: Series
**9.1 Geometric Series

9.2 Convergence of Sequences and Series

9.3 <skipped>

9.4 <skipped>

Practice Problems for Chapter 9

Quinine Activity

10.1 Taylor Polynomials

10.2 Taylor Series

10.3 Finding and Using Taylor Series

10.4 The Error in Taylor Polynomial Approximations

10.5 <skipped>

Practice Problems for Chapter 10

**Chapter 11: Differential Equations**

11.1 What is a Differential Equation?

11.2 Slope Fields (I can email you these notes, for some reason they won't post!)

** Graphing Calculators can sketch Slope Fields!**

Go onto a search engine, such as google.com, to find instructions
to program your graphing calculator. Enter your model number (e.g. TI-81) and
the words "slope field" into the search box. You will find multiple
versions of programs. Note that the TI-89 already has this capability, so there's
no need to program anything (you need to go to MODE and
change from FUNCTION to DIFFERENTIAL EQUATIONS.
Then, put any function into the y1 slot and graph it). A favorite link from
2003-2004 was http://math.arizona.edu/~krawczyk/calcul.html#83
, but there are many other choices.

Hint: The expression **IS>** in many programs is a built-in
function.

To test your program, enter in y1=sin(x) and then call the program. You should
see a

screen filled with little lines that look like y(x) = cos(x) +C for a bunch
of values of C. Next,

try a function like y1=x+y. You can enter in the variable "y" by using
the alpha-key.

**Graphing Calculators can use Euler's Method!**

Go to a search engine, such as google.com,
to find instructions to program your graphing calculator. Enter in your calculator
model, plus the word Euler. You will find multiple versions of the program.
It's best to find one that both graphs your answer and also gives you a table
of (x,y) points on the numerically estimated solution. A favorite link from
2003-2004 was http://math.arizona.edu/~krawczyk/calcul.html
, but there are many other choices.

*To test your program, enter in y1=y and call the program. Start at the point
(0,1) and use
a step size of 0.1. Your answer should look like Figure 11.25 on page 489 of
your text book.*

11.4 Separation of Variables

11.5 Growth and Decay

We probably won't make it to these last few sections, although I include lecture
notes here for your interest:

11.6 & 11.7 Handout

11.6 Applications and Modeling

11.7 Models of Population Growth