Calculus Animations,Graphics and Lecture Notes

2d 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

The following download is my lecture notes on the second order homogeneous differential equation with constant coefficients

Lecture Notes 2d order homogeneous DEs with constant coefficients

The following downloads are my lecture notes and animations for an application of second order homogeneous differential equations to the motion of a mass on a spring

Lecture Notes Applcication of 2d order eqns to a mass on a spring




critcally damped

The following 2 animations show the relationship between circular motion and the motion of a mass on a spring-first in the undamped case and then the underdamped case



 The following 2 animations show the relationship between circular motion and the linearized pendulum - again the first undamped and the second underdamped



Finally we consider the non-homogeneous 2d order eqn and applications of an RLC circuit which includes both continuous and discontinuous forcing functions.
You may want to review the Unit Step Function Notes on the Differential Equations
Page before examining the discontinuous case.

Lecture Notes RLC Circuit


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

©2008-2010 Kelly Liakos

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