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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

Handouts

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