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Applied Mathematical Tools for Physics by Nearing

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  1. Jan 23, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Introduction
    [*] Bibliography
    [*] Basic Stuff
    [LIST]
    [*] Trigonometry
    [*] Parametric Differentiation
    [*] Gaussian Integrals
    [*] erf and Gamma
    [*] Differentiating
    [*] Integrals
    [*] Polar Coordinates
    [*] Sketching Graphs
    [/LIST]
    [*] Infinite Series
    [LIST]
    [*] The Basics
    [*] Deriving Taylor Series
    [*] Convergence
    [*] Series of Series
    [*] Power series, two variables
    [*] Stirling's Approximation
    [*] Useful Tricks
    [*] Diffraction
    [*] Checking Results
    [/LIST]
    [*] Complex Algebra
    [LIST]
    [*] Complex Numbers
    [*] Some Functions
    [*] Applications of Euler's Formula
    [*] Geometry
    [*] Series of cosines
    [*] Logarithms
    [*] Mapping
    [/LIST]
    [*] Differential Equations
    [LIST]
    [*] Linear Constant-Coeffcient
    [*] Forced Oscillations
    [*] Series Solutions
    [*] Some General Methods
    [*] Trigonometry via ODE's
    [*] Green's Functions
    [*] Separation of Variables
    [*] Circuits
    [*] Simultaneous Equations
    [*] Simultaneous ODE's
    [*] Legendre's Equation
    [*] Asymptotic Behavior
    [/LIST]
    [*] Fourier Series
    [LIST]
    [*] Examples
    [*] Computing Fourier Series
    [*] Choice of Basis
    [*] Musical Notes
    [*] Periodically Forced ODE's
    [*] Return to Parseval
    [*] Gibbs Phenomenon
    [/LIST]
    [*] Vector Spaces
    [LIST]
    [*] The Underlying Idea
    [*] Axioms
    [*] Examples of Vector Spaces
    [*] Linear Independence
    [*] Norms
    [*] Scalar Product
    [*] Bases and Scalar Products
    [*] Gram-Schmidt Orthogonalization
    [*] Cauchy-Schwartz inequality
    [*] Infnite Dimensions
    [/LIST]
    [*] Operators and Matrices
    [LIST]
    [*] The Idea of an Operator
    [*] Definition of an Operator
    [*] Examples of Operators
    [*] Matrix Multiplication
    [*] Inverses
    [*] Rotations, 3-d
    [*] Areas, Volumes, Determinants
    [*] Matrices as Operators
    [*] Eigenvalues and Eigenvectors
    [*] Change of Basis
    [*] Summation Convention
    [*] Can you Diagonalize a Matrix?
    [*] Eigenvalues and Google
    [*] Special Operators
    [/LIST]
    [*] Multivariable Calculus
    [LIST]
    [*] Partial Derivatives
    [*] Chain Rule
    [*] Differentials
    [*] Geometric Interpretation
    [*] Gradient
    [*] Electrostatics
    [*] Plane Polar Coordinates
    [*] Cylindrical, Spherical Coordinates
    [*] Vectors: Cylindrical, Spherical Bases
    [*] Gradient in other Coordinates
    [*] Maxima, Minima, Saddles
    [*] Lagrange Multipliers
    [*] Solid Angle
    [*] Rainbow
    [/LIST]
    [*] Vector Calculus 1
    [LIST]
    [*] Fluid Flow
    [*] Vector Derivatives
    [*] Computing the divergence
    [*] Integral Representation of Curl
    [*] The Gradient
    [*] Shorter Cut for div and curl
    [*] Identities for Vector Operators
    [*] Applications to Gravity
    [*] Gravitational Potential
    [*] Index Notation
    [*] More Complicated Potentials
    [/LIST]
    [*] Partial Differential Equations
    [LIST]
    [*] The Heat Equation
    [*] Separation of Variables
    [*] Oscillating Temperatures
    [*] Spatial Temperature Distributions
    [*] Specifed Heat Flow
    [*] Electrostatics
    [*] Cylindrical Coordinates
    [/LIST]
    [*] Numerical Analysis
    [LIST]
    [*] Interpolation
    [*] Solving equations
    [*] Differentiation
    [*] Integration
    [*] Differential Equations
    [*] Fitting of Data
    [*] Euclidean Fit
    [*] Differentiating noisy data
    [*] Partial Differential Equations
    [/LIST]
    [*] Tensors
    [LIST]
    [*] Examples
    [*] Components
    [*] Relations between Tensors
    [*] Birefringence
    [*] Non-Orthogonal Bases
    [*] Manifolds and Fields
    [*] Coordinate Bases
    [*] Basis Change
    [/LIST]
    [*] Vector Calculus 2
    [LIST]
    [*] Integrals
    [*] Line Integrals
    [*] Gauss's Theorem
    [*] Stokes' Theorem
    [*] Reynolds Transport Theorem
    [*] Fields as Vector Spaces
    [/LIST]
    [*] Complex Variables
    [LIST]
    [*] Differentiation
    [*] Integration
    [*] Power (Laurent) Series
    [*] Core Properties
    [*] Branch Points
    [*] Cauchy's Residue Theorem
    [*] Branch Points
    [*] Other Integrals
    [*] Other Results
    [/LIST]
    [*] Fourier Analysis
    [LIST]
    [*] Fourier Transform
    [*] Convolution Theorem
    [*] Time-Series Analysis
    [*] Derivatives
    [*] Green's Functions
    [*] Sine and Cosine Transforms
    [*] Wiener-Khinchine Theorem
    [/LIST]
    [*] Calculus of Variations
    [LIST]
    [*] Examples
    [*] Functional Derivatives
    [*] Brachistochrone
    [*] Fermat's Principle
    [*] Electric Fields
    [*] Discrete Version
    [*] Classical Mechanics
    [*] Endpoint Variation
    [*] Kinks
    [*] Second Order
    [/LIST]
    [*] Densities and Distributions
    [LIST]
    [*] Density
    [*] Functionals
    [*] Generalization
    [*] Delta-function Notation
    [*] Alternate Approach
    [*] Differential Equations
    [*] Using Fourier Transforms
    [*] More Dimensions
    [/LIST]
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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