## Computer and Portfolio Exercises

### One Variable Calculus

Reformed Math 112 : Basic Syllabus:
A hypertext index to a large range of activities and assignments for a second semester calculus course at Cornell. Lots of very valuable advice as well.
Some Analyzer* Actvities
A locally produced sampler of 10 short problems to highlight interesting elementary uses.
Simple ODE and Taylor Activities
Sailing and Vectors
Ithaca College Projects Table of Contents
A listing of activities and projects from the Instructional Materials developed at IC with NSF support and published by John Wiley.

### Multivariable Calculus

#### Quick Experimentation Worksheets

Quadric_think
Maple 7 Worksheet
Linear_Approx and Limit Experiments
Maple 7 Worksheet
Gravitational Experiments
Maple 6 Worksheet
Taylor Experiments
Maple 7 Worksheet
Lagrange Multiplier Experiments
Maple 7 Worksheet

#### Larger Assignments

Early Graphs:
Some exploration exercises to start off a multivariable calculus class. One example looks at quadric surfaces as a function of parameter. Another asks people to produce functions matching some graphical desacriptions. A third compares an implicit curve with the implicit curve of some of its algebraic approximations.
Early Graphs2:
Another set of such exercises. Quadric related.
Multivariable limits:
Mostly uses a variety of techniques to establish non-existence of limits. Can be correlated with the Maple worksheet Multivariable Limits
Linear approximation:
Looks at the geometry of a map from R^2 to itself, as well as its linear approximation somewhere. Can be correlated with the Maple worksheet Linear Approximation.
Velocity and Acceleration:
One example looks at velocity and acceleration of a particular curve, and graphics to identify maxima and minima. Another compares the phase portrait of a nonlinear vector field on the plane with that of its linearization somewhere. Can be correlated with the Maple worksheet Curves.
Taylor Series and Least Squares:
One exercise uses a symbolic algebra system to derive and and fit a least squares approximation to an equation of state. The other problems look at multivariable Taylor series and error estimates associated. Can be correlated with the Maple worksheets Least Squares and Taylor Series .
Phase Plane and Gradient Vector Fields:
Relates the max/min properties of quadratic forms to the phase portraits of their associated gradient vector fields.
Roots as Functions of Coefficients:
Studies the dependence of root as a function of coefficient, especially near a multiple root of a cubic equation.
Implicit Solution and Volterra Models:
Uses implicit differentiation and related techniques to estimate behavior along an implicitly defined predator-prey relation.

### Linear Algebra

Orientation Activity
Markov Chains
Row Operations Documentation
2-d Geometry
Determinants and Eigenvectors

### Discrete Mathematics

Message Transfer Using Powers Mod a Prime

### Differential Equations

Numerical experiments
Flow Lines, Vector Fields, Numerical Integration, Div and Curl

### Complex Variables

Conformal Mapping V1a
Conformal Mapping V1b

### Geometry

Compositions of Three Reflections in Sketchpad
Strip Patterns.

### General Resources

Additions, Corrections or Feedback on this page to:
mathlab@math.cornell.edu
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Last Update: August 23, 2002