| 1. From Excel to MATLAB® |
|
1.1 MATLAB vs. Excel |
|
1.2 Finding Slopes Using MATLAB |
|
1.3 Slopes and Euler’s Number e |
|
1.4 Finding Areas Using MATLAB |
|
1.5 The Fundamental Theorem of Calculus |
|
1.6 Complex Numbers in MATLAB |
|
Problems |
| 2. Discovering Partial Derivatives |
|
2.1 Slopes of Surfaces |
|
2.2 Visualizing Multidimensional Functions |
|
2.3 Curvature of Surfaces |
|
2.4 Partial Derivatives of Vector Fields |
|
2.5 Partial Differential Equations |
|
Problems |
| 3. Discovering Multiple Integrals |
|
3.1 The Volume Under a Surface |
|
3.2 The Area of a Surface |
|
3.3 Volumes in Rectangular Coordinates |
|
3.4 Volumes in Cylindrical Coordinates |
|
3.5 Volumes and Areas in Spherical Coordinates |
|
Problems |
| 4. Discovering Matrices |
|
4.1 Matrix Multiplication |
|
4.2 Solving Linear Equations |
|
4.3 Cramer’s Rule |
|
4.4 Gaussian Elimination |
|
4.5 Matrix Transformations |
|
4.6 Eigenvalues and Eigenvectors |
|
4.7 Raising a Matrix to a Power |
|
4.8 System of Differential Equations |
| |
Problems |
| 5. Discovering Vector Fields |
|
5.1 Vector Fields and the Laws of Nature |
|
5.2 Kepler’s Laws |
|
5.3 The Discovery of Electricity |
|
5.4 Faraday’s Lines of Force |
|
5.5 Maxwell’s Electromagnetic Field |
|
Problems |
| 6. Discovering Partial Differential Equation Solutions |
|
6.1 The Heat Equation |
|
6.2 Waves on a String |
|
6.3 Sound Waves |
|
6.4 Electromagnetic Waves |
|
Problems |
| 7. Discovering Transforms |
|
7.1 The Fourier Transform |
|
7.2 Fourier Series |
|
7.3 The Discrete-Time Fourier Transform |
|
7.4 The Discrete Fourier Transform |
|
7.5 The MATLAB Fast Fourier Transform Function |
|
7.6 The Laplace Transform |
|
7.7 The Z-Transform |
|
Problems |
| Appendix A: Fourier Transform of a Gaussian Function |
Appendix B: Fourier Transform of a comb Function 389
|
| Appendix C: Fourier Transform of a Triangle Function |
| Index |
