     Calculus Animations,Graphics and Lecture Notes Vector Valued Functions    Home About Kelly Liakos 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  Vector Valued Functions Position,Velocity, and Acceleration Lecture Notes - Position Vector Circle Vector Helix Vector Parabaloid Notes - Velocity and Acceleration Velocity For a more detailed description of velocity and acceleration see the page on 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 Collision Intersection No Collision Skew Lines-No Intersection Find the equation of the line that is perpindicular to and intersects the lineL1:  x = 7+ t    y = -13 + 2t  z = 8 - 2 tand contains the point (-5,4,2) Notes - the Solution Collision

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

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