Calculus Animations,Graphics and Lecture Notes

Directional Derivatives/Gradient
Home
Sponsors
Calculus 1- Limits and Derivatives
Calculus 1 - The Second Derivative
Calculus 1 and 3 Formula Sheets
Chain Rule
Computer Lab Assignments
Conic Sections
Differential Equations
Directional Derivatives/Gradient
Double Integrals
Equillibrium Solutions 1st order DEs
1st order Diff Eqs -Motion
Flux Integrals and Surface Integrals
Infinite Sequences
Infinie Series
Level Curves and Level Surfaces
Line Integrals
Optimization and Related Rates
Optimization for Functions of 2 Variables
Parametric Equations 2-space
Parametric Equations 3-space
Partial Derivatives
Polar Coordinate System
Polar Coordinates- Derivatives and Integrals
PreCalculus
Riemann Sums and the Fundamental Theorem of Calculus
2d order Diff EQS-Motion
2d Partial Derivatives
Supplemental Exercises and Solutions
Tangent Planes/ Differential for f(x,y)
Trigonometry
Trigonometry Applications
Triple Integrals
Unit Tangent Vectors/Unit Normal Vectors
Vectors in General
Vector Valued Functions
Visualizing Limits of Functions of 2 Variables
Work
Links
Special Topics
Scratch Paper
2 Poems

The following animations and lecture notes discuss the directional derivative

In Animation1 We see the rate at which f is changing at a point depends on the direction we travel from the pt

Notes - Directional Derivatives and the Gradient

Animation1

The following 2 animations show f changing in the diection of the gradient and opposite to the gradient

gradient

negative gradient

The following Animation shows that as you move along a level curve in the domain, there is no change in the value of f(x,y) on the surface.

Motion Along a Level Curve

 

If you are interested in seeing how I developed these animations visit my companion website

Calculus7.com/creatinganimationsusingmathcad

Creating Animations Using Mathcad

The Smart Bunny-A very short story by Kurt Vonnegut Jr.

Copyright2008-2010@kellyliakos

Send an email regarding this site (no math questions, please).