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