PURE AND APPLIED > VECTOR DIFFERENTIAL CALCULUS
Vector differential calculus, essential
for interpretating streamlines.
Welcome to your first course on calculus in 3-dimensional space, or more simply called vector calculus. Now it is time to use what you know about the calculus in high school and see how it operates as points move front and back, left and right, and now, up and down.
Most of the work on vector calculus must be credited to J. Willard Gibbs and Oliver Heaviside. During their time, there was a diversion over the use of vectors and quaternions. Many of you wouldn't even see the word 'quaternions' in a high school because it was these two man who popularize the use of vectors particularly in Heaviside's publication, 'Electromagnetic Theory'.
On a personal note, I particulary like vector calculus because we can readily see its applications in the real world. I always like to picture myself in 3-dimensional space as I walk out of my school and see all the vectors at work which affects my motion. Let's start by looking at differentials first.
Oliver Heaviside
Torsion
Frenet Frame
Divergence and Curl
Magnetic Fields
Vector differential calculus, essential
for interpretating streamlines.
Most of the work on vector calculus must be credited to J. Willard Gibbs and Oliver Heaviside. During their time, there was a diversion over the use of vectors and quaternions. Many of you wouldn't even see the word 'quaternions' in a high school because it was these two man who popularize the use of vectors particularly in Heaviside's publication, 'Electromagnetic Theory'.
On a personal note, I particulary like vector calculus because we can readily see its applications in the real world. I always like to picture myself in 3-dimensional space as I walk out of my school and see all the vectors at work which affects my motion. Let's start by looking at differentials first.
CONCEPT CONTENTS
> INTRODUCTION
> VECTOR FUNCTION OF ONE VARIABLE
> THE FIRST DERIVATIVE
> PARAMETER IN TERMS OF ARC LENGTH
> VELOCITY AND ACCELERATION
> CURVATURE
> ACCELERATION COMPONENTS
> MULTIPLE APPROACHES TO PROBLEMS
> FINDING UNIT TANGENT AND UNIT NORMAL
> UNIT BINORMAL AND TORSION
> INTERPRETATION OF TORSION
> FRENET-SERRET EQUATIONS
> FUNDAMENTAL THEOREM OF SPACE CURVES
Notable Mathematicians
J. Willard GibbsOliver Heaviside
Important Theorems
CurvatureTorsion
Frenet Frame
Divergence and Curl
Applications
StreamlinesMagnetic Fields
