Maple worksheets on multi-variable calculus

 

More calculus topics:


The following Maple worksheets can be downloaded.

They are all compatible with Classic Worksheet Maple 10.

Partial derivatives

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  

Critical points

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