Spring 2004, Math 101

March 2004

Be sure to check back often, because assignments may change!

I'll use Maple syntax for some of the mathematical notation on this page. (Paying attention to how I type various expressions is a good way to absorb Maple notation). I will not use it when I think it will make the questions too difficult to read.
All section and page numbers refer to sections from Calculus from Graphical, Numerical, and Symbolic Points of View, Volume 1, 2nd Edition, by Ostebee and Zorn.

Due Monday 3/1 at 10am

Section 2.6 Derivatives of Exponential and Logarithmic Functions; Modelling Growth

To read: All. Be sure to understand Theorem 12 and the section "Proof by picture" that follows.

E-mail Subject Line: Math 101 Name 3/1

1. What is the 47th derivative of f(x)=exp(x)?
exp(x) is Maple notation for the function ex.
2. Do exponential functions model population growth well? Explain.

Reminders:

• Draft of Project 1 is due by 2pm.

Due Wednesday 3/3 at 10am

Section 2.6 Derivatives of Exponential and Logarithmic Functions

To read: Re-read this section, focusing on the derivatives of ex and ln(x), and examples involving them.

Reminders:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 5.
• Just a mid-semester reminder, in case you've lost track: The point of these reading assignments is to give you credit for work you're doing anyway -- reading and beginning to learn the material. As I mentioned at the beginning of the semester, I do not expect you to have completed learning the section by the time you answer these questions! Sometimes you'll be able to answer them correctly, and sometimes you won't -- either way is fine, as long as you make an effort.

Due Friday 3/5 at 10am

Section 2.6 Derivatives of Exponential and Logarithmic Functions

To read: Re-read this section again, focusing this time on the section on modelling growth.

Reminder:

• Begin PS 6.

Due Monday 3/8 at 10am

Section 2.7 Derivatives of Trigonometric Functions: Modeling Oscillation

To read: All. Be sure to understand the section "Differentiating the sine: an analytic proof".

E-mail Subject Line: Math 101 Name 3/8

1. What is limit( (cos(h)-1)/h, h=0)?
2. What is limit( sin(h)/h, h=0)?
3. Why do we care about the limits in the first two questions?

Reminder:

• Put plenty of time and thought into re-writing your projects. Feel free to bring your original rough drafts, or newer drafts, by for a consultation.

Due Wednesday 3/10 at 10am

Section 3.1 Algebraic Combinations: The Product and Quotient Rules

To read: All. Be sure to understand Examples 3, 4, and 5.

E-mail Subject Line: Math 101 Name 3/10

Explain what is wrong with the following calculations and fix them.

1. f(x)=x^2*sin(x). f ' (x)=2*x*cos(x).
2. g(x)=sin(x)/(x^2+1). g ' (x) = cos(x)/(2*x).

Reminder:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 6.

Due Friday 3/12 at 10am

Section 3.2 Composition and the Chain Rule

To read: Through Example 12. We'll consider evidence for why the Chain Rule is true during class.

E-mail Subject Line: Math 101 Name 3/12

Explain what is wrong with the following calculations and fix them.

1. f(x)=sin(x^2). f ' (x) = cos(x^2)+sin(2*x)
2. g(x)=exp(3*x). g ' (x)=exp(3*x).
3. h(x)=(sin(x))^3. h ' (x)= 3*(cos(x))^2.

Reminders:

• Begin PS 7.
• The final draft of Project 1 is due by 4pm Friday.

Monday 3/15- Friday 3/19

Spring Break!

Obviously, No Reading Questions These Days!

Due Monday 3/22 at 10am

Reviewing Differentiation

To read: Review Chapter 2, and make sure it all makes sense now.

Due Wednesday 3/24 at 10am

Reviewing Differentiation

To read: Review Chapter 2 again, and this time, try to get a big picture for how it all fits together. No Reading Questions Today

Reminder:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 7 to class.
• The Differentiation Exam will be given in lab Thursday.

Due Friday 3/26 at 10am

Section 4.3 Optimization

E-mail Subject Line: Math 101 Name 3/26

1. At which x-values can a continuous function f(x) achieve its maximum or minimum value on a closed interval [a,b]?
2. What is the difference between an objective function and a constraint equation?
Reminder:
• Begin PS 8.

Due Monday 3/29 at 10am

Section 4.3 Optimization

To read: Re-read the section carefully. Really work through the examples with pencil and paper and make sense of them.

Due Wednesday 3/31 at 10am

Section 4.7 Building Polynomials to order: Taylor Polynomials

To read: All. Be sure to understand Examples 5 and 8.

E-mail Subject Line: Math 101 Name 3/31

1. Why would you want to find the Taylor polynomial of a function?
2. In your own words, briefly explain the idea of building the Taylor polynomial for a function f(x).

Reminder:

• Rachel's help session is Wednesday night, 7:30-8:30pm in A118 -- if she knows to come! If you plan to meet with her, e-mail her at rzeigowe before 5pm. Give her an idea of what you plan to ask her -- the numbers of the homework questions, or the topic that's causing difficulties.
• Bring questions on PS 8.

Here ends the reading for March
Go to the reading assignments for April!
Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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