Calculus I

Fall, 2007

**
Course information**

Course syllabus

Course calendar

Homework assignments

Goals for Week 1: Tuesday | Wednesday | Thursday

Information about: Exam 1 | Exam 2 | Exam 3 | Exam 4

KnightVision (for access to exam solutions, scores on assignments, etc.)

Algebra: Codes to messages from grader | Top Algebra Errors Made by Calculus Students

Professor Scofield's homepage

Drop-in calculus help is available on M-Th evenings, 7-9 pm in NH 251

Course calendar

Homework assignments

Goals for Week 1: Tuesday | Wednesday | Thursday

Information about: Exam 1 | Exam 2 | Exam 3 | Exam 4

KnightVision (for access to exam solutions, scores on assignments, etc.)

Algebra: Codes to messages from grader | Top Algebra Errors Made by Calculus Students

Professor Scofield's homepage

Drop-in calculus help is available on M-Th evenings, 7-9 pm in NH 251

**
Questions for additional readings**

Reading 1:
“17th Century mathematics and mathematical notation”

**
Links (primarily to applets)**

A simple
graphing utility

Polar functions

Parametric curves: site 2 | in 3D

Transformations that shift a graph vertically or horizontally

How a parameter may be used to morph one graph into another

Function composition

Cycloids: applet 1 | another one from Maths online

A spirograph applet that can be manipulated to produce popular polar curves

Polar functions

Parametric curves: site 2 | in 3D

Transformations that shift a graph vertically or horizontally

How a parameter may be used to morph one graph into another

Function composition

Cycloids: applet 1 | another one from Maths online

A spirograph applet that can be manipulated to produce popular polar curves

Numerical investigation of a certain type of limit.

Some examples showing why numerical evaluation of limits can be untrustworthy.

Illustrating the (ε-δ) definition of limit

The limit of sin(x)/x as x -> 0

The number*e*: site 1 |
site
2

Some examples showing why numerical evaluation of limits can be untrustworthy.

Illustrating the (ε-δ) definition of limit

Practice:
Given ε (specified value), find δ algebraically.
Solutions provided.

Practice: Given ε (left unspecified), find δ. Solutions provided.

Drill on finding
horizontal and
vertical asymptotes. Solutions provided.Practice: Given ε (left unspecified), find δ. Solutions provided.

The limit of sin(x)/x as x -> 0

The number

The tangent line as the limit of secant lines: site
1 |
site 2

Drill on finding derivatives from the definition of derivative.

Applets on the relationship between a function and its derivative: site 1 | site 2

Differentiability implies continuity, but the converse is not true.

Drill on finding derivatives from the definition of derivative.

Applets on the relationship between a function and its derivative: site 1 | site 2

Differentiability implies continuity, but the converse is not true.

Product
Rule

Chain Rule

The Fundamental Theorem of Calculus

Rolle's Theorem; the Mean Value Theorem

L'Hopital's Rule

Chain Rule

The Fundamental Theorem of Calculus

Rolle's Theorem; the Mean Value Theorem

L'Hopital's Rule

Applet demonstrating Archimedes' use of polygons
to get
approximate area of unit circle

Riemann sums applet

Simpson's rule applet

Get correct antiderivatives using webMathematica's integrator

Volumes of solids

Riemann sums applet

Simpson's rule applet

Get correct antiderivatives using webMathematica's integrator

Volumes of solids

Why
Calculus?

A context for calculus

Connected Calculus (from the*Connected Curriculum Project*)

A relatively-inexpensive book, How to Ace Calculus: the Streetwise Guide

A context for calculus

Connected Calculus (from the

A relatively-inexpensive book, How to Ace Calculus: the Streetwise Guide

This page maintained by:
Thomas L. Scofield

Department of Mathematics and Statistics,
Calvin College