Mathematical Physics Applied Mathematics for Scientists and Engineers Second Edition by Bruce R. Kusse and ErikA. Westwig
Contents of Mathematical Physics eBook
- A Review of Vector and Matrix Algebra Using
- Subscript Summation Conventions
- Notation
- Vector Operations
- Differential and Integral Operations on Vector and Scalar Fields
- Plotting Scalar and Vector Fields
- Integral Operators
- Differential Operations
- Integral Definitions of the Differential Operators
- The Theorems
- Curvilinear Coordinate Systems
- The Position Vector
- The Cylindrical System
- The Spherical System
- General Curvilinear Systems
- The Gradient Divergence and Curl in Cylindrical and Spherical Systems
- Introduction to Tensors
- The Conductivity Tensor and Ohm’s Law
- General Tensor Notation and Terminology
- Transformations Between Coordinate Systems
- Tensor Diagonalization
- Tensor Transformations in Curvilinear Coordinate Systems
- Pseudo-Objects
- The Dirac &Function
- Examples of Singular Functions in Physics
- Two Definitions of &t)
- Functions with Complicated Arguments
- Integrals and Derivatives of (t)
- Singular Density Functions
- The Infinitesimal Electric Dipole
- Riemann Integration and the Dirac &Function
- Introduction to Complex Variables
- A Complex Number Refresher
- Functions of a Complex Variable
- Derivatives of Complex Functions
- The Cauchy Integral Theorem
- Contour Deformation
- The Cauchy Integrd Formula
- Taylor and Laurent Series
- The Complex Taylor Series
- The Complex Laurent Series
- The Residue Theorem
- Definite Integrals and Closure
- Conformal Mapping
