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Mathematical Methods [2009]

1
Coordinate Systems and Vectors
2
Differentiation
3
Integration: Formalism
4
Integration: Applications
5
Dirac Delta Function
6
Planar and Spatial Vectors
7
Finite-Dimensional Vector Spaces
8
Vectors in Relativity
9
Infinite Series
10
Application of Common Series
11
Integrals and Series as Functions
12
Vectors and Derivatives
13
Flux and Divergence
14
Line Integral and Curl
15
Applied Vector Analysis
16
Curvilinear Vector Analysis
17
Tensor Analysis
18
Complex Arithmetic
19
Complex Derivative and Integral
20
Complex Series
21
Calculus of Residues
22
From PDEs to ODEs
23
First-Order Differential Equations
24
Second-Order Linear Differential Equations
25
Laplace’s Equation: Cartesian Coordinates
26
Laplace’s Equation: Spherical Coordinates
27
Laplace’s Equation: Cylindrical Coordinates
28
Other PDEs of Mathematical Physics
29
Integral Transforms
30
Calculus of Variations
31
Nonlinear Dynamics and Chaos
32
Probability Theory
1
Function Spaces, Linear Operators, and Green's Functions
31
Integral Equations and Green's Functions
105
Integral Equations of the Volterra Type
117
Integral Equations of the Fredholm Type
153
Hilbert–Schmidt Theory of Symmetric Kernel
193
Singular Integral Equations of the Cauchy Type
223
Wiener–Hopf Method and Wiener–Hopf Integral Equation
295
Nonlinear Integral Equations
309
Calculus of Variations: Fundamentals
353
Calculus of Variations: Applications
567
References
573
Index
I
Front Matter
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