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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
