# Multivariable Mathematics With Maple- Linear Algebra, Vector Calculus And Differential Pdf

### Multivariable Mathematics With Maple- Linear Algebra, Vector Calculus And Differential Pdf Features:

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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

1. 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
2. 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
3. Bases and Coordinates ……………………………………. 67 1. Coordinates in the Plane ………………………………. 67 2. Higher Dimensions ……………………………………. 71 3. The Vector Space of Piecewise Linear Functions ………….. 74 4. Periodic PL Functions ………………………………… 77 5. Temperature at Equilibrium Revisited …………………… 82
4. Aﬃne Transformations in the Plane ………………………… 86 1. Transforming a Square ………………………………… 87 2. Transforming Parallelograms …………………………… 89 3. Area ………………………………………………… 91 4. Iterated Mappings — Making Movies with Maple …………. 93 5. Stretches, Rotations, and Shears ……………………….. 95 6. Appendix: Maple Code for iter and film ……………….. 99
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5. Eigenvalues and Eigenvectors ……………………………… 101 1. Diagonal matrices …………………………………… 101 2. Nondiagonal Matrices ………………………………… 102 3. Algebraic Methods …………………………………… 104 4. Diagonalization ……………………………………… 109 5. Ellipses and Their Equations ………………………….. 113 6. Numerical Methods ………………………………….. 118
6. Least Squares — Fitting a Curve to Data …………………… 124 1. A Formula for the Line of Best Fit …………………….. 125 2. Solving Inconsistent Equations ………………………… 132 3. The Stats Package …………………………………… 134
7. Fourier Series …………………………………………… 137 1. Periodic Functions …………………………………… 137 2. Computing Fourier Coeﬃcients ……………………….. 143 3. Energy …………………………………………….. 147 4. Filtering ……………………………………………. 149 5. Approximations ……………………………………… 150 6. Appendix: Almost Periodic Functions ………………….. 151
8. Curves and Surfaces ……………………………………… 156 1. Curves in the Plane — Maps from R to R2 ……………… 156 2. Curves in R3 ……………………………………….. 160 3. Surfaces ……………………………………………. 160 4. Parametrizing Surfaces of Revolution …………………… 162
9. Limits, Continuity, and Diﬀerentiability …………………… 168 1. Limits — Functions from R to R ………………………. 168 2. Limits — Functions from R2 to R ……………………… 171 3. Continuity ………………………………………….. 172 4. Tangent Planes ……………………………………… 174 5. Diﬀerentiability ……………………………………… 176
10. Optimizing Functions of Several Variables …………………. 181 1. Review of the One-Variable Case ………………………. 181 2. Critical Points and the Gradient ………………………. 184 3. Finding the Critical Points ……………………………. 184 4. Quadratic Functions and their Perturbations ……………. 186 5. Taylor’s Theorem in Two Variables ……………………. 190
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11. Completing the Square ……………………………….. 193 7. Constrained Extrema ………………………………… 195
12. Transformations and their Jacobians ……………………… 201 1. Transforming the Coordinate Grid …………………….. 202 2. Area of Transformed Regions …………………………. 205 3. Diﬀerentiable Transformations ………………………… 207 4. Polar Coordinates …………………………………… 210 5. The Area Integral ……………………………………. 212 6. The Change-of-Variables Theorem …………………….. 214 7. Appendix: Aﬃne Approximations ……………………… 216 8. Appendix: Gridtransform …………………………….. 217
13. Solving Equations Numerically …………………………… 219 1. Historical Background ……………………………….. 219 2. The Bisection Method ……………………………….. 220 3. Newton’s Method for Functions of One Variable …………. 222 4. Newton’s Method for Solving Systems ………………….. 224 5. A Bisection Method for Systems of Equations …………… 228 6. Winding Numbers …………………………………… 229
14. First-order Diﬀerential Equations …………………………. 235 1. Analytic Solutions …………………………………… 235 2. Line Fields …………………………………………. 239 3. Drawing Line Fields and Solutions with Maple ………….. 243
15. Second-order Equations …………………………………. 246 1. The Physical Basis …………………………………… 247 2. Free Oscillations …………………………………….. 247 3. Damped Oscillations …………………………………. 251 4. Overdamping ……………………………………….. 253 5. Critical Damping ……………………………………. 254 6. Forced Oscillations …………………………………… 255 7. Resonance ………………………………………….. 258
16. Numerical Methods for Diﬀerential Equations ……………… 261 1. Estimating e with Euler’s Method ……………………… 261 2. Euler’s Method for General First-order Equations ……….. 265 3. Improvements to Euler’s Method ………………………. 268 4. Systems of Equations ………………………………… 270
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17. Systems of Linear Diﬀerential Equations …………………… 276 1. Normal Coordinates …………………………………. 277 2. Direction Fields ……………………………………… 281 3. Complex Eigenvalues ………………………………… 283 4. Systems of Second-order Equations ……………………..

The part of Maple would be to vividly exemplify them and also to expand the assortment of issues which we’re able to successfully resolve. For the most out of this publication, the reader ought to work through the exercises and examples as they happen. By way of instance, once the text cites the snippet of Maple code.The purpose of the first chapter will be to provide a quick summary of how to use Maple to perform algebra, plot charts, solve equations, etc.. Much could be achieved with one-line computations. For instance. To download this book you can visit below.