## Some Worksheets and their HTML

A chance to experiment with and think about some patterns in quadric surfaces.
HTML of Worksheet Before Evaluation
HTML of Worksheet Fully Evaluated
quadric_think.mws as present in the folder Maple 7/Math 222 /Lecture 1 on lab machines.
Surfaces 1
An introduction to three dimensional graphs. Lots of examples of contours. Includes some cases where computer pictures are misleading. Hyperboloids of one and two sheets with an opportunity to look at sections and what they tell us about graphs.
HTML of Worksheet
Maple Worksheet as present in the folder Maple 7/Math 222 /Lecture 1 on lab machines.
Experiments on Linear Approximation and Limits
A chance to experiment with and think about some aspects of linear approximation. Also some material on limits.
HTML of Worksheet Before Evaluation
HTML of Worksheet Fully Evaluated
Experiments3.mws as present in the folder Maple 7/Math 222 /Lecture 3 on lab machines.
Linear_Approximation
Some examples of tangent lines and planes graphically. Efficient generation in Maple of the linear approximation of a function at a point. Use of the transform plots package to geometrically compare the mapping properties of a function with those of its linear approximation.
HTML of Worksheet
Linear_Approximation.mws as present in the folder Maple 7/Math 222 /Lecture 3 on lab machines.
Non_Differentiable_Surfaces
This worksheet looks geometrically at three different kinds of singularities. A high point is the sketch of an argument at the end about why the cube root of (x^3-3xy^2) fails to be differentiable at the origin. A good opportunity to talk about the idea of what it means for an approximation to be linear.
HTML of Worksheet
Non_Differentiable_Surfaces.mws as present in the folder Maple 7/Math 222 /Lecture 3 on lab machines.
Gravitational Experiments
An opportunity to think about level sets for the potential energy in a three body problem.
HTML of Worksheet
gravexp.mws as present in the folder Maple 7/Math 222 /Lecture 4 on lab machines.
PDE Change
A worksheet created by Professor Jeff Diller to illustrate efficient use of Maple in changing coordinates for a partial differential equation.
HTML of Worksheet
PDE_Change.mws as present in the folder Maple 7/Math 222 /Lecture 6 on lab machines.
This worksheet explores the relationship between symmetric matrices and quadratic forms. It shows how the eigenvalues of such a matrix relate to the geometric character of the graph of the quadratic form. It also discusses in the context of an example how the eigenvectors of the symmetric matrix determine a rotation of coordinates making the quadratic form diagonal.
HTML of Worksheet
Quadrics_and_Eigenvalues.mws as present in the folder Maple 7/Math 222 /Lecture 6 on lab machines.
A worksheet intended for people to use as a reinforcement on the correlation between eigenvalue signs and the graphs of quadratic forms. Helping with max-min as well.
HTML of Worksheet
Quadrics_Worksheet.mws as present in the folder Maple 7/Math 222 /Lecture 6 on lab machines.
Taylor Series Experiments
Experiments in apparent convergence and non-convergence of Taylor series.
HTML of Worksheet
Taylorexp.mws as present in the folder Maple 7/Math 222 /Lecture 6 on lab machines.
Taylor Series
Explores multivariate Taylor series. Compares graphically various Taylor polynomials to the original function. Investigates how errors depend upon the size of the region on which the approximation is being used. Uses estimates on the size of partial derivatives to bound errors in Taylor polynomial approximation. (These latter are obtained from Maple graphs of the partial derivatives.)
HTML of Worksheet
Taylor.mws as present in the folder Maple 7/Math 222 /Lecture 6 on lab machines.
Lagrange Multiplier Experiments
A worksheet for people to concretely explore the role of level sets in the Lagrange Multiplier method.
HTML of Worksheet
LagMultExp as present in the folder Maple 7/Math 222 /Lecture 7 on lab machines.
Lagrange Multipliers
The geometry of Lagrange multipliers is explored in the context of the optimization problem for y e^x on an ellipse. Solutions are also obtained numerically using fsolve.
HTML of Worksheet
Lagrange_Multipliers.mws as present in the folder Maple 7/Math 222 /Lecture 7 on lab machines.
Visualization of 3D Integrals
An worksheet using the locally written plot3d_region package.
HTML of Worksheet
plot3dr_exp.mws as present in the folder Maple 7/Math 222 /Lecture on lab machines.
Parameterized Surfaces
A variety of parameterization and reparameterization examples are presented. Many are quadric surfaces. Singularities of parameterizations are discussed. The worksheet also presents the natural frame (T_u, T_v, N) associated with a parameterization.
HTML of Worksheet
Parameterized_Surfaces_2.mws as present in the folder Maple 7/Math 222 /Lecture on lab machines.