Calculus Animations,Graphics and Lecture Notes

1st order Diff Eqs -Motion

About Kelly Liakos
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
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 Applications
Triple Integrals
Unit Tangent Vectors/Unit Normal Vectors
Vectors in General
Vector Valued Functions
Visualizing Limits of Functions of 2 Variables
Special Topics
Scratch Paper
2 Poems

On this page are the lecture notes and animation which discuss one-dimensional motion with air resistance

Notes - 1D Motion with Air Resistance



In this animation note that as terminal velocity is approached the trajectory becomes linear

Position and Velocity

Position First 2 Seconds

Entire Trajectory

The following is an extra credit assignment which extends the ideas discussed to projectile motion in the plane. It also describes how to graph parametric eqns in Mathcad. The extension to 3-D is then obvious.

Projectile Motion in the Plane

Answer to Projectile Motion Exercise

 The Lion and the Antelope

The following is an example which combines parametric equations and 1st order differential equations which gives the trajectroy of a lion chasing down an antelope.

Lion and Antelope-Animation

Notes - The Lion and the Antelope

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

©2008-2010 Kelly Liakos

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