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Mathematical Methods [2009]
- 1
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Coordinate Systems and Vectors
- 2
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Differentiation
- 3
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Integration: Formalism
- 4
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Integration: Applications
- 5
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Dirac Delta Function
- 6
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Planar and Spatial Vectors
- 7
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Finite-Dimensional Vector Spaces
- 8
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Vectors in Relativity
- 9
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Infinite Series
- 10
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Application of Common Series
- 11
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Integrals and Series as Functions
- 12
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Vectors and Derivatives
- 13
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Flux and Divergence
- 14
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Line Integral and Curl
- 15
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Applied Vector Analysis
- 16
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Curvilinear Vector Analysis
- 17
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Tensor Analysis
- 18
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Complex Arithmetic
- 19
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Complex Derivative and Integral
- 20
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Complex Series
- 21
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Calculus of Residues
- 22
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From PDEs to ODEs
- 23
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First-Order Differential Equations
- 24
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Second-Order Linear Differential Equations
- 25
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Laplace’s Equation: Cartesian Coordinates
- 26
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Laplace’s Equation: Spherical Coordinates
- 27
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Laplace’s Equation: Cylindrical Coordinates
- 28
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Other PDEs of Mathematical Physics
- 29
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Integral Transforms
- 30
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Calculus of Variations
- 31
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Nonlinear Dynamics and Chaos
- 32
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Probability Theory
- 1
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Function Spaces, Linear Operators, and Green's Functions
- 31
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Integral Equations and Green's Functions
- 105
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Integral Equations of the Volterra Type
- 117
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Integral Equations of the Fredholm Type
- 153
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Hilbert–Schmidt Theory of Symmetric Kernel
- 193
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Singular Integral Equations of the Cauchy Type
- 223
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Wiener–Hopf Method and Wiener–Hopf Integral Equation
- 295
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Nonlinear Integral Equations
- 309
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Calculus of Variations: Fundamentals
- 353
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Calculus of Variations: Applications
- 567
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References
- 573
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Index
- I
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Front Matter