Page 6 - Essentials of applied mathematics for scientists and engineers

MOBK070-FM MOBKXXX-Sample.cls March 22, 2007 13:6

vi ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS
2.1.13 Getting to One Nonhomogeneous Condition . . . ................... 20
2.1.14 Separation of Variables . . . ........................................ 21
2.1.15 Choosing the Sign of the Separation Constant. . ....................21
2.1.16 Superposition . .................................................. 22
2.1.17 Orthogonality . .................................................. 22
2.1.18 Lessons .........................................................23
2.1.19 Scales and Dimensionless Variables. ...............................23
2.1.20 Relocating the Nonhomogeneity . . . ............................... 24
2.1.21 Separating Variables . . ........................................... 25
2.1.22 Superposition . .................................................. 25
2.1.23 Orthogonality . .................................................. 25
2.1.24 Lessons .........................................................26
Problems .................................................... 26
2.2 Vibrations . ............................................................. 26
2.2.1 Scales and Dimensionless Variables. ...............................27
2.2.2 Separation of Variables . . . ........................................ 27
2.2.3 Orthogonality . .................................................. 28
2.2.4 Lessons .........................................................29
Problems .................................................... 29
Further Reading ........................................................ 29

3. Orthogonal Sets of Functions ................................................. 31
3.1 Vectors.................................................................31
3.1.1 Orthogonality of Vectors ......................................... 31
3.1.2 Orthonormal Sets of Vectors......................................32
3.2 Functions .............................................................. 32
3.2.1 Orthonormal Sets of Functions and Fourier Series . ................. 32
3.2.2 Best Approximation..............................................34
3.2.3 Convergence of Fourier Series.....................................35
3.2.4 Examples of Fourier Series........................................36
Problems .................................................... 38
3.3 Sturm–Liouville Problems: Orthogonal Functions . ......................... 39
3.3.1 Orthogonality of Eigenfunctions . ................................. 40
Problems .................................................... 42
Further Reading ........................................................ 43

4. Series Solutions of Ordinary Differential Equations . ........................... 45
4.1 General Series Solutions . . ............................................... 45