Maple worksheets giving an introduction to calculus, limits and continuity.
Basic calculus topics:
The following Maple worksheets can be downloaded.
They are all compatible with Classic Worksheet Maple 10.
Introduction - intro.mws
- Introduction .. the basic problems of differential and integral calculus.
- The equations and gradients of tangent lines.
A procedure for constructing secant to tangent animations - tgt_anim.mws
- A procedure which gives the line through two points: linethrough.
- Secant lines.
- A procedure for constructing secant to tangent animations: secant_to_tangent.
- Tangent lines.
- A procedure for finding and plotting tangent lines: findtangent.
Limits - limmits.mws
- The concept of the limit of a function and limit notation.
- First non-trivial example of the limit of a function: (x^3-8)/(x-2) -> 12 as x -> 2.
- Finding limits algebraically.
- Using the Maple procedure: limit.
- Graphical illustration of limits.
Evaluating limits using basic properties of limits - limits2.mws
- Properties of limits.
- Replacing the function in a limit by a function that is continuous at the limiting point.
- The Squeeze Theorem for limits.
- Two special trigonometric limits.
Infinite limits - limits3.mws
- Intoductory example and definitions involving one-sided limits.
- Vertical asymptotes.
A procedure for evaluating limits - limits4.mws
- A procedure for evaluating limits that shows the working for "evaluation by hand": eval_lim/Limit.
Using the procedure eval_lim/Limit to evaluate limits from a typical calculus text - limits5.mws
Continuous and discontinuous functions - contfcns.mws
- Introductory example of a discontinuous function
- More examples of discontinuous functions.
- Breaking down checking of continuity of a function at a point into three steps.
More on continuity of functions - contfcns2.mws
- Removable and non-removable discontinuities.
- Continuity on general intervals and classes of continuous functions.
- The Intermediate value Theorem.
Calculus procedures - calculus.zip
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