- Address each of the three areas (1, 2, 3) below.
- Email your paper (no more than 2 pages) to me by midnight Thursday night with the subject line:
MATH1510-[section] HW0 [last name], [first name]

- Your experience with mathematics. Examples of topics you could write about include:
- Compare the best mathematics teacher you ever had with the worst mathematics teacher you ever had. What makes a good math teacher?
- What was the best experience you ever had with mathematics? What was the worst experience?
- What was the hardest math problem you ever attempted? Were you successful? How did you feel about it?
- What do you find easiest about mathematics, and what gives you the most difficulty, and why?

- The practicality of mathematics. Examples of topics you could write about include:
- Have you ever attempted to solve a math problem just for the fun of it, or do you only do math problems if they are assigned?
- Have you ever done a math problem that had an impact (however small) on your life? If so, describe the impact it had.
- Do you know of any mathematics that has had an impact on your life?

- Your expectations in this course.
- What do you expect to put into this course, and what would you really like to get out of this Calculus course?
- How do your expectations compare with those of the instructor that are printed in lthe syllabus?
- What do you think would be the most helpful thing that could be done in this course to help you succeed?

- Read the Introduction
- Read Section 1.1 Four ways to represent a function
Find the following:

- The definition of a function
- Four different ways to specify a function, and examples of each
- How to identify the domain of a function
- How to identify intervals on which a function is increasing or decreasing
- How to tell if a function is even or odd

- Turn in 1.1 #2, 6, 7, 18, 22, 29, 32, 39, 43, 46, 56, 63, 68
- Extra Credit (3): Write down the name (first and last) and something interesting about 3 students in your section of Calculus, at least one of whom is from a culture different from your own. Indicate which is/are from a different culture.

Find the following:

- How to classify the following families of functions from equations:
- Linear
- Power
- Root
- Polynomial
- Rational
- Trigonometric
- Exponential
- Logarithmic

- Make a scatterplot
- Find an appropriate model for a given data set
- Interpolate values from a model

- Transformations: Determine the effect on the graph of y = f(x) of each of:
- y = f(x-h) (Subtracting h from the input)
- y = f(x) + k (Adding k to the function values)
- y = af(x) (Multiplying the function values by a)
- y = f(x/b) (Dividing the input by b)

- The definitions of f+g, f-g, f*g, f/g, and f composed with g, and their domains.
- How to break complicated functions down into simple ones.

Read 1.5 Exponential functions

Find the following:

- Learn the laws of exponents
- Limits of exponential functions as x goes to infinity and -infinity
- The definition of Euler's number, e

Read 1.6 Inverse functions and logarithms

Find the following:

- Determine whether a function is one-to-one or not.
- Find inverse functions graphically and algebraically
- Learn the laws logarithmic functions
- Solve exponential equations using logarithms and vice versa

Read 2.1 The tangent and velocity problems.

- Find the slope of a secant line to a function at 2 points
- Find an average velocity
- Estimate the slope of a curve at a point
- Estimate an instantaneous velocity

Read 2.2 The limit of a function.

- Find one and two sided limits graphically.
- Estimate one and two sided limits numerically.
- Learn the definition of a limit.
- Given a function f, a point
*a*, and a number*ε*> 0, find the limit*L*and an appropriate number*&delta*> 0 so that

|f(*x*) - L| <*ε*whenever |*x - a*|<*&delta*.

2.2 #1, 5, 8, 15, 19, 30

Read 2.3 Calculating Limits.

- Use the limit laws to find one and two sided limits.
- Apply the squeeze theorem to find limits.

Read 2.4 Continuity

- Learn the definition of continuity of a function at a point.
- Tell when a function is continuous from the left or the right.
- Tell when a function is continuous on an interval.
- Learn the theorems for continuity that follow from the laws of limits.
- Learn which functions are continuous in their domains (Theorem 7)
- Evaluate limits of continuous functions (Theorem 8), and of composite continuous functions (Theorem 9).
- Learn the Intermediate Value theorem (Theorem 9) and apply it to finding the root of a continuous function.

Read 2.5 Limits involving infinity

- Learn the definition of the limit of f(x) as x approaches infinity.
- Identify horizontal asymptotes
- Learn what it means to say that a limit is infinity
- Identify vertical asymptotes

Read 2.6 Derivtives and Rates of Change

- Learn the definition the derivative f'(a).
- Write the equation of the tangent line to a function f at x=a
- Estimate the derivative from a graph.
- Find an instantaneous rate of change

Read 2.7 The derivtive as a function

- Learn the definition the derivative f'(x).
- Given a graph of f(x), sketch the graph of f'(x)
- Given an expression for f(x), find a formula for f'(x)

Read 2.8 What does f' say about f?

- Find how the sign and direction of f' are related to f.
- Find how the sign of f'' is related to f.
- Given a graph of f, find f' and f''.

Read 3.1 Derivatives of Polynomial and Exponential Functions

- Learn rules 1, 2, 3, 4, 8, 9 on page 5 of the reference pages
- Write an expression as a polynomial and differentiate
- Differentiate c*e^x.

Read 3.2 Product and Quotient rules.

- Learn to product rule for differentiation.
- Learn the quotient rule for differentiation.

Read 3.3 Derivatives of trig functions

- Derivatives of basic trig functions: sin(x), cos(x)
- Derivatives of other trig functions: tan(x), sec(x), cot(x), csc(x)

Read 3.4 The Chain Rule

- Learn Differentiation Rule #7
- Apply the chain rule to all of functions we have learned so far.

Read 3.5 Implicit differentiation

- Learn to differentiate implicitly

Read 3.6 Inverse Trig functions and derivatives

- Solve equations of the form trig(x) = a
- Simplify expressions of the form trig(trig^-1(x))
- Learn Differentiation Rules #19-24

Turn in 3.6 #1, 10, 17, 18, 22, 35, 39

Read 3.7 Derivatives of logarithmic and exponential functions.

- Learn derivatives of a^x, ln(x), log_a(x)
- Learn the Logarithmic Differentiation technique

- Find all critical points of a function.
- Learn the Extreme Value Theorem
- Find absolute extreme values of a function on a closed interval

4.2 #5, 11, 28, 30, 43, 59, 62

Last Update: December 7, 2009

Ronald K. Smith

Graceland University

Lamoni, IA 50140

rsmith@graceland.edu