Maple worksheets on multi-variable calculus |

More calculus topics:

- Infinite Series
- Hyperbolic Functions
- Multi-variable calculus
- The Lambert W function

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Functions of several variables- sevvar.mws

- Examples of functions of two variables
- Functions of three variables

Partial derivatives for functions of two variables- pardiff.mws

- Definition of partial derivatives
- Examples of partial derivatives
- The function f(x,y) = x y
- Geometrical interpretation of partial derivatives
- 2nd order partial derivatives

The chain rule for functions of two variables- chainrule.mws

- The chain rule
- Chain rule examples
- Geometrical illustration of the chain rule
- Implicit differentiation

The tangent plane to a surface and differentiability of a function of two variables- tanplane.mws

- Linear approximation of a function of two variables and tangent planes
- Constructing a tangent plane via tangent lines to two cross-section curves
- Using a tangent plane to help in illustrating partial derivatives
- The concept of differentiability for functions of two variables
- A general formula for the tangent plane to the graph of a function of two variables

Quadratic surfaces and quadratic approximations for functions of two variables- quadsurf.mws

- Quadratic surfaces
- Quadratic approximation examples

Cubic surfaces and cubic approximations for functions of two variables- cubicsurf.mws

- Cubic surfaces
- Cubic approximation examples

Quadratic forms- quadform.mws

- Quadratic forms - determining the nature of the critical points at the origin
- An alternative way of deriving the classification criterion for the nature of the critical point at the origin

Critical points on the graph of a function of two variables- critpts.mws

- Critical points: local maxima and minima and saddle points
- Classifying the critical points of a function of two variables

Classifying the critical points on the graph of a function of two variables-an example- critptex.mws

Classifying the critical points on the graph of a function of two variables-an example- critptex2.mws

Classifying the critical points on the graph of a function of two variables-an example- critptex3.mws

Classifying the critical points on the graph of a function of two variables-an example- critptex4.mws

Limits of functions of two variables- limits.mws

- Limits and continuity of functions of two variables

Mixed second order partial derivatives of a function of two variables- mixedPD.mws

- An example of a function of two variables for which the mixed second order partial derivatives are not equal

Partial derivatives of functions of three variables- pardiff2.mws

- Partial derivatives of functions of three variables
- The chain rule for functions of three variables
- Chain rule examples

The gradient of functions of 2 and 3 variables - directional derivatives- dirderiv.mws

- The gradient of a function of two variables
- The gradient of a function of three variables
- Graphical examples
- The directional derivative of a function of three variables
- The direction of the gradient vector at a point

A directional derivative example- dirderivex.mws

- A directional derivative example

Tangent planes to level surfaces of functions of three variables- tanplane2.mws

- The chain rule in terms of gradient
- The gradient vector as a normal vector to level surfaces
- Examples