List of all pages
- Parametrized surface area example
An example of calculating the surface area of a parametrized surface. - Parametrized surface examples
Examples showing how to parametrize surfaces as vector-valued functions of two variables. - An introduction to parametrized surfaces
An introduction to how a vector-valued function of two variables can be viewed as parametrizing a surface. Interactive graphics illustrate the way in which the function maps a planar region onto a surface. - Normal vector of parametrized surfaces
How to calculate the normal vector from the parametrization of a surface. - Orienting surfaces
How to orient a surface by choosing a normal vector. - Solutions to elementary partial derivative problems
Solutions to sample problems illustrating the partial derivative. - Elementary partial derivative problems
Sample problems illustrating the partial derivative. - Partial derivative examples
Examples of how to calculate partial derivatives. - Introduction to partial derivatives
The concept of partial derivatives is introduced with an illustration of heating costs. Interactive graphics demonstrate the properties of partial derivatives. - Partial derivative by limit definition
Description with example of how to calculate the partial derivative from its limit definition. - Partial fractions
Using algebra to simplify the integral of rational functions. - Definition: Path connected definition
A path connected domain is a domain where every pair of points in the domain can be connected by a path going through the domain. - A path-dependent vector field with zero curl
A counterexample showing how a vector field could have zero curl but still fail to be conservative or path-independent. - Constructing a mathematical model for penicillin clearance
We give a word model for how penicillin should be cleared from the blood and allow you to construct a mathematical model to fit some data. - Penicillin clearance model exercise answers
Answers to selected exercises on developing discrete dynamical systems for the clearance of penicillin. - Penicillin clearance model exercises
Exercises and developing discrete dynamical system models for the clearance of penicillin from the blood. - Definition: Periodic orbit definition
A periodic orbit is a solution to a dynamical system that repeats itself in time. - Introduction to visualizing differential equation solutions in the phase plane
- Definition: Phase space definition
The phase space, or state space, of a dynamical system is the set of all possible states of the system. - Parametrization of a plane
Introduction to how one can parametrize a plane. Interactive graphics illustrate basic concepts.
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