Multivariable Mathematics With Maple- Linear Algebra, Vector Calculus And Differential.pdf

Multivariable Mathematics with Maple
Linear Algebra, Vector Calculus
and Di
erential Equations
by James A. Carlson and Jennifer M. Johnson

c 1996 Prentice-Hall
Introduction ...................................................... 1
1. Introduction to Maple ............................................. 3
1. A Quick Tour of the Basics .................................... 4
2. Algebra ....................................................... 6
3. Graphing ..................................................... 9
4. Solving Equations ............................................ 12
5. Functions .................................................... 15
6. Calculus ..................................................... 18
7. Vector and Matrix Operations ............................... 24
8. Programming in Maple ...................................... 27
9. Troubleshooting ............................................. 35
2. Lines and Planes ................................................. 36
1. Lines in the Plane ........................................... 36
2. Lines in 3-space .............................................. 39
3. Planes in 3-space ............................................ 41
4. More about Planes ........................................... 43
3. Applications of Linear Systems ................................... 49
1. Networks .................................................... 49
2. Temperature at Equilibrium ................................. 52
3. Curve-Fitting — Polynomial Interpolation .................... 58
4. Linear Versus Polynomial Interpolation ....................... 61
5. Cubic Splines ................................................ 64
4. Bases and Coordinates ........................................... 67
1. Coordinates in the Plane ..................................... 67
2. Higher Dimensions ........................................... 71
3. The Vector Space of Piecewise Linear Fun