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**Calculus Text Puzzles**

Peter
Jipsen, Chapman University, August 2002
This is the home page for Calculus Text Puzzles: An interactive way of
reading scrambled calculus definitions, examples and proofs. Some
parts of the text on these dynamic webpages can be rearranged easily,
and the reader is given automatic feedback on whether the original
correct form of the text has been
reconstructed.

Click on some of the links below and see how this approach
allows you to (re)discover concepts. This can help with understanding
calculus, and it is more interesting than simply reading the textbook.
It is meant as an intermediate step between studying existing
definitions and proofs versus writing your own. You are encouraged to print out
the unscrambled version of a completed puzzle and keep it as a
study-aid. The pages below require a fairly recent web
browser such as Internet Explorer 5.5+ or Netscape 6+. If you have an
older browser, you may be able to view the previous version of
Calculus Text Puzzles.

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Definitions and results about calculus
(based on Stewarts Calculus, 4th edition).

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Preliminaries: Appendix A

Definitions: Integers, Rational,
Irrational and Real Numbers.

Definitions: Basic set notation.

Definitions: Intervals, open,
closed, half-open.

####
Chapter 1: Functions and Models

Definitions: Functions,
domain, range, symmetry, increasing, decreasing

Definitions: Linear,
Polynomial, Power, Rational, Algebraic, Trigonometric, Exponential,
Logarithmic, Transcendental Functions

Results: Shifting, stretching
and reflecting functions

Exercise: Composition of two functions

####
Chapter 2: Limits, Continuity and Rates of Change

Discussion: Informal and formal definition
of a limit.

Examples: Limits of the form 0/0.

Definitions: Limits, from the
left and right, and to infinity.

Proposition:

Proposition:

Results : Limit laws.
Here are some Proof Puzzles where you can discover why the limit laws
follow from the definition of limits.

Sum of Limits Theorem:

Constant Multiple of Limits Theorem:

Product of Limits Theorem:

Reciprocal of Limits Theorem:

Left-Right Limit Theorem:

Limit Order Theorem:

Squeeze Theorem:

####
Chapter 3: Derivatives

Definitions:
The Derivative at a point and as a function.
(for Netscape 7 or IE+MathPlayer)

Theorem:

Results:
The Rules of Differentiation.
(for Netscape 7 or IE+MathPlayer)

Examples:
Differentiation.
(for Netscape 7 or IE+MathPlayer)
Here are the proofs of the rules.

Power Law: (for Netscape 7 or IE+MathPlayer)

Constant Multiple Law:

Sum Law:

Difference Law:

Product Law:

Quotient Law: (for Netscape 7 or IE+MathPlayer)

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Chapter 4: Applications of Derivatives

Definitions:
Concepts of derivatives related to finding maxima and minima.
(for Netscape 7 or IE+MathPlayer)

Results:
The Mean Value Theorem and some of its consequences.
(for Netscape 7 or IE+MathPlayer)