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Multivariable Calculus in the Lab

A collection of Maple V R3 Worksheets

Used in Math 222 at Cornell, Fall 1994

Some Maple Release 7 Versions (and Related) Worksheets are now available here.

This collection of worksheets was written for Maple V R3 on the Macs. It was a first time using these materials, so there are rough edges to be improved upon.

The Mac interface to Maple is a very nice one, although significantly different from the Unix xmaple and Windows interfaces. In particular it supports the pasting of color pictures into worksheets. Also, these worksheets use multi-line input at times, and hence rely on the Mac option that only the enter key sends input to Maple.

The worksheets can be accessed by any of:

Download Entire Collection (as Math_222.sea.hqx) in Mac Format

Table of Contents

Worksheet Summaries

  • Handout 1: Exploration of some quadric surfaces. Level curves.
  • Handout 2: Multivariable limits.
  • Handout 3: Linear approximation of mappings from a plane to itself, level curves, and gradient vector fields.
  • Handout 4: Velocity and acceleration of curves, geometry of reflection.
  • Handout 5: Phase plane sketches. Linear approximation. Relation to div and curl.
  • Handout 6: Least squares, approximation by Taylor series, error estimates., quadric surfaces worksheet.
  • Handout 7: Exploration of relation of local extrema of functions to flowlines of their gradient vector fields.Classification of equilibria.
  • Handout 8: Plots of three dimensional regions associated with triple integrals.
  • Projects for Math 222: A launching point for student projects involving computer use.

Topics and Maple Command Index

animation in 2D
2D Plotting (using_maple)
Limits (week_2) applying a function to each entry of ...
Vector Identities (week_4) binomial coefficients
2D Plotting (using_maple) change of coordinates in quadratic forms
Quadrics and Eigenvalues (week_6) colons
Mac Interface Intro (using_maple) colors, text
Mac Interface Intro (using_maple) combining 2D plots
2D Plotting (using_maple) combining 3D plots
3D Plotting (using_maple) constructing the linear approximation of a transformation
Linear Approximation (week_3) contourplot
3D Plotting (using_maple) contourplot
Surfaces I (week_1) creating vectors
Vector Identities (week_4) cross product
Vector Identities (week_4) curl computation
Vector Identities (week_4) curl of a cross product
Vector Identities (week_4) curves with corners
Curves (week_4) data types in Maple
Maple Data Structures (using_maple) derivatives as matrices
Linear Approximation (week_3) differential equations, direction fields
Fieldplot and Numerical ODEs (week_5) differential equations, numerical solution of
Fieldplot and Numerical ODEs (week_5) differential equations, symbolic solution of
Fieldplot and Numerical ODEs (week_5) differentiation
Basic Maple (using_maple) displaying a precomputed graphics structure
3D Plotting (using_maple) divergence calculation
Vector Identities (week_4) divergence of a cross product
Vector Identities (week_4) dot product
Vector Identities (week_4) draw flows package
Flow Results (week_5) dsolve
Fieldplot and Numerical ODEs (week_5) eigenvalues
Quadrics and Eigenvalues (week_6) eigenvectors
evaluating as a floating point number
flow animations of a vector field
Flow Results (week_5) Frenet frame package
function, evaluating
Basic Maple (using_maple) geometric interpretation of div and curl
Flow Results (week_5) gradient computation
Vector Identities (week_4) gradient in spherical coordinates
Vector Identities (week_4) gradient vector fields, plotting of
Green's theorem for a triangle
Green's Theorem for a Triangle (week_12) grid option in 3D plotting
help, online
Mac Interface Intro (using_maple) hyperboloids
Surfaces I (week_1) implicit curve plotting in 2D
Lagrange Multipliers (week_7) implicit function theorem failure
Implicit Function Example (week_7) implicit plotting in 2D
2D Plotting (using_maple) implicit plotting in 3D
Surfaces I (week_1) integration
Basic Maple (using_maple) integration, 2D numerical
Using Num_int_2D (week_11) integration, numeric
Setup Example (week_8) integration, symbolic
Setup Example (week_8) interrupting calculations
labels option in 3D plotting
Surfaces I (week_1) Lagrange multipliers
Lagrange Multipliers (week_7) Lagrange multipliers numerical example
Lagrange Numerical Example (week_7) laplacian calculation
Vector Identities (week_4) laplacian on vectors
Vector Identities (week_4) least squares derivation
Least Squares (week_6) length of a list, set, ...
Basic Maple (using_maple) level curves
Gradplot Examples (week_3) limits (multivariable) geometrically
Limits (week_2) line integrals, numerical caculation of
Line Integrals (week_10) list of points plotting in 2D
Moebius strip
Orientation 2 (week_11) monkey saddle
Surfaces I (week_1) non-orientable surface example
Orientation 2 (week_11) nondifferentiability while directional derivatives exist
Non Differentiable Surfaces (week_3) nops
Basic Maple (using_maple) numerical solution of systems of equations
Basic Maple (using_maple)
Numerical Solution (week_4) numpoints option in 3D plotting
parameterized surface plotting
Parameterized Surfaces 2 (week_10) parameterized surface plotting in 3D
Surfaces I (week_1) parameterized surface tangent and normal directions
Parameterized Surfaces 2 (week_10) paramterized surface plotting
3D Plotting (using_maple) partial derivatives
Vector Identities (week_4) partial derivatives of functions as opposed to expressions
Vector Identities (week_4) patchcontour style in 3D plotting
3D Plotting (using_maple) plane plotting in 3D
Surfaces I (week_1) plane sections in 3D
Surfaces I (week_1) plot 3D region package
plot region package (2D)
Using Plot Region (week_8) plotting a sequence of points in 2D
Basic Maple (using_maple)
Random Riemann Sums (week_8) plotting differential equation solutions
Fieldplot and Numerical ODEs (week_5) plotting gradient fields
Fieldplot and Numerical ODEs (week_5) plotting parametric curves
Curves (week_4) plotting points in a file
2D Plotting (using_maple) plotting procedures in 3D
Non Differentiable Surfaces (week_3) plotting, 2D
2D Plotting (using_maple) plotting, 3D
3D Plotting (using_maple) plotting, 3D options
3D Plotting (using_maple) polar coordinate plotting
2D Plotting (using_maple) polygonal curves and line integrals
Line Integrals (week_10) polyhedraplot
Linear Approximation (week_3) precision, higher
prompts, new
Mac Interface Intro (using_maple) quadratic forms
Quadrics and Eigenvalues (week_6) quadric surface parameterizations
Parameterized Surfaces 2 (week_10) quadric surfaces and second derivative tests
Quadrics Worksheet (week_6) random number functions
Random Riemann Sums (week_8) reading data from a file
Least Squares (week_6) real_cube_root as a procedure
Non Differentiable Surfaces (week_3) rhs (right hand side of an equation)
Lagrange Numerical Example (week_7) Riemann sums calculation
Random Riemann Sums (week_8) rotation matrices
Quadrics and Eigenvalues (week_6) rotation number of planar curves
Line Integrals (week_10) saving
Mac Interface Intro (using_maple) scalar triple product
Vector Identities (week_4) scratchpads
Mac Interface Intro (using_maple) semi-colons
singular inverses of transformations
Singular Inverses (week_7) singularities of surfaces
Non Differentiable Surfaces (week_3) solving symbolically
Basic Maple (using_maple) solving symbolically
spherical coordinate differential operators
Vector Identities (week_4) spherical coordinate unit vectors
Vector Identities (week_4) subsequences, extracting
Basic Maple (using_maple) substitution
Basic Maple (using_maple) substitution
Limits (week_2) sum
Least Squares (week_6) summing a series
Basic Maple (using_maple) surface integrals, numerical
Using Num_int_2D (week_11) Taylor series, multivariable
Taylor Series (week_6) Taylor series, remainder estimation
Taylor Series (week_6) transform_rect
Linear Approximation (week_3) transformation plotting package
vector field linearization
Flow Results (week_5) view option in 3D plotting
3D Plotting (using_maple) whattype
Basic Maple (using_maple) whitney umbrella
Surfaces I (week_1) whitney umbrella parameterized
Parameterized Surfaces 2 (week_10) wireframe style in 3D plotting
3D Plotting (using_maple)


Many thanks to Mathlab consultant Sung Bae Lee for helping to produce this World Wide Web version.