Calculus Animations,Graphics and Lecture Notes

Computer Lab Assignments

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

If you are unfamiliar with or are just learning Mathcad you may want to consider the Intro lab on basic graphs in Mathcad.

Introduction to Basic Graphs

Calculus 1 Labs

Lab Average to Instantaneous

Lab Local Linearity

Graphing and Analysis of Functions

Parametric Eqns 2 Space

Riemann Sums Lab

Animation Riemann Sums

For more examples of Riemann Sums see Riemann Sum Page

The following 2 labs use the tangent line approximation to solve Physics problems.

The first deals with the motion of a mass on a spring.

The second is based on a discussion of planetray motion in the Feynman Lectures and uses the tangent line approximation to plot the trajectory of the earth around the sun.

Mass-Spring and the Tangent Line Approx

Trajectory of the Earth and the Tangent Line Approx

Calculus 2 Labs

Polar Coordinates

Taylor Polynomials

Taylor Series

Numerical Integration

Rectangular Approximation

Trapezoid Rule

Simpson's Rule

A lab on parametric equations in 2 space is included in my Calculus 1 Labs

In some cases parametric equations are taught in Calc1 sometimes Calc2, personally I think it is such a good application of the derivative as instantaneous rate of change I include it in Calc 1.

Differential Equations

The following 2 labs deal with numerical solutions to 1st order differential equations.

1. The first deals with IVPs of the form where dy/dx = f(x)   and dy/dx = f(y)

2. The second deals with the general IVP where dy/dx = f(x,y) This is called Euler's method

dy/dx = f(x) dy/dx =f(y)

dy/dx = f(x.y) --Euler's Method

For a computer lab on projectile motion in the plane click the link below

Projectile Motion

Calculus 3 Labs

Make sure you are familiar with the Basic 3D Graph  Lab first

Basic 3D Graphs

Graphing Contour Diagrams

Parametric Equations in 3 Space

The Contour Gradient Lab describes how to create Vector Field PLots and How to use contour diagrams and gradient fields to locate and classify local extrema for functions of 2 variables.

Contour Gradient Lab

Cylindrical Coordinates

Spherical Coordinates

Parametric Surface Plots





Animation 5

PreCalculus Labs

Before doing the following labs make sure you are familiar with the Basic Graphs in Mathcad  Lab at the top of the page

Power Functions and Exponentials

Translations and Reflections

Before doing the labs on Polynomials and Rational Functions familiarize yourself with lectures on The PreCalculus Page

Polynomial Lab

Rational Function Lab

The following Lab deals with solving systems of equations using the method of Matrix Inverses

Matrix Lab

Linear Regression

Exponential Regression

Power Function Regression Lab

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

©2008-2010 Kelly Liakos

Do you find this site useful? If you would like to continue to access these animations, lesson and files, please consider a small donation. Thank you from Kelly's family!