Maple worksheets giving an introduction to calculus, limits and continuity. |

Basic calculus topics:

- Calculus introduction, limits and continuity
- Introduction to derivatives
- Implicit and parametric differentiation
- Applications of differentiation
- Integration and area
- Integration techniques
- Applications of integration

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.- Examples.

Using the procedure eval_lim/Limit to evaluate limits from a typical calculus text-limits5.mws

- Examples.

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