Calculus Animations,Graphics and Lecture Notes

Vector Valued Functions

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

Vector Valued Functions Position,Velocity, and Acceleration

Lecture Notes - Position

Vector Circle

Vector Helix

Vector Parabaloid

Notes - Velocity and Acceleration


For a more detailed description of velocity and acceleration see the page on

 Unit Tangents/Unit Normals.

Unit Tangents/Unit Normals

Lines in 2 space

Notes - Lines in 2space

x= 2 + 3t y = 3 - 2t

x = -1 + 8t y = -3 + 5 t

Example 3

Lines in 3 Space

Notes - Lines in 3 Space


Intersection No Collision

Skew Lines-No Intersection

Find the equation of the line that is perpindicular to and intersects the line

L1:  x = 7+ t    y = -13 + 2t  z = 8 - 2 t

and contains the point (-5,4,2)

Notes - the Solution


For a discussion and animations of flow fields and orthognal trajectories go to the differential equations page

Flow Fields and Orthognal Trajectories

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

©2008-2010 Kelly Liakos

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