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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
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
setoptions3d
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)

## Acknowledgement

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