Physics Basics Series
- Basics of Classical Mechanics.
- Basics of Quantum Mechanics.
- Basics of Electrodynamics.
- Basics of Optics.
- Basics of Mathematical Tools for Physics.
- Basics of Plasma Physics.
- Basics of Solid State Physics.
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Welcome to Basics of Mathematical Tools for Physics at StarkEffects.com
Notes on math that helps in the study of physics.
Basics of Mathematical Tools for Physics
Notes on special functions, differential equations, linear algebra and a host of other math topics . The wonderful art we call mathematics probably had its birth in explanations of the physical world. As this art has developed, it has informed our understanding of the physical world and even opened views to the world that were not avialable on the basis of experience alone. Today, we have a huge array of mathematical techniques of analysis that we can use to study the physical world around us. The purpose of this tutorial is serve as my personal notes taken during the study of these mathematical tools specifically applied to physics. I hope you enjoy the descriptions of analytical methods I provide here and invite your criticism to improve my own understanding as well as the value of this work. Throughout these pages, the techniques described will be those that provide a way to understand our observations of the physical world. Have fun.
- Coordinate Systems and Transformations
- Numbers
- Algebra
- Geometry
- Trigonometry
- Functions
- Vector Analysis
- Calculus
- Differentiation
- Integration
- Differential Equations
- Ordinary Diff EQ
- Partial Diff EQ
- Tensors
- Linear Algebra
- Series
- Complex Functions
- Fourier Analysis
- Orthogonal Functions
- Special Functions
- Gamma Function
- Bessel Functions
- Legendre Functions
- Hermite Functions
- Laguerre Functions
- Chebyshev Polynomials
- Hypergeometric Functions
- Integral Transforms
- Integral Equations
- Green's Functions
- Calculus of Variations
- Approximation Methods
Coordinate Systems and Transformations
Numbers
Algebra
Geometry
Trigonometry
Functions
Vector Analysis
Calculus
Differentiation
Integration
Differential Equations
Ordinary Diff EQ
Partial Diff EQ
Tensors
Linear Algebra
Series
Complex Functions
Fourier Analysis
Orthogonal Functions
Special Functions
Gamma Function
Bessel Functions
Legendre Functions
Hermite Functions
Laguerre Functions
Chebyshev Polynomials
Hypergeometric Functions
Integral Transforms
Integral Equations
Green's Functions
Calculus of Variations
Approximation Methods
Quick Science & Math References
- Our Solar System.
- Earth Facts.
- The Metric System.
- Trigonometric Identities.
- Vector & Tensor Identities.
- Explicit Forms of Vector Operators
- Light & Electromagnetic Spectrum.
- Common Laser Wavelengths.
- Human Physiology Facts.
- Human History Timeline
- Geologic Timeline
- Cambrian Explosion
- Life on Earth Timeline
- ASCII Codes and HTML Display Codes
- Thousands of HTML Symbol Codes
- HTML Symbol Codes for Greek Letters
- The Best Way to put Equations on your Web Page
Physics Basics Series
- Basics of Classical Mechanics.
- Basics of Quantum Mechanics.
- Basics of Electrodynamics.
- Basics of Optics.
- Basics of Mathematical Tools for Physics.
- Basics of Plasma Physics.
- Basics of Solid State Physics.
Math Basics Series
- Numbers
- Arithmetic
- Algebra
- Geometry
- Analysis
Technology Basics Series
- Basics of Remote Sensing.
- Basics of Digital Signal Processing.
- Critical Electronic Circuits
- Infrared Imaging Basics
Knowledge Branches
- Information Theory
- How Reading Works in the Brain
- Psychology of Learning
- Logic
WORK IN PROGRESS
- What is the Stark Effect?
- The Chemistry of Love &/or Addiction
- Critical Thinking: How to question what you see, read or hear.
- Aristotle's Prior Analytics - the birth of Logic.
- Optical Solutions, lenses that solve problems
- Fractals
- PTC - Photon Transfer Curve or Mean Variance Analysis
- 3-D Noise
- Laser Primer
- Rail Guns
- Special Relativity
- Radar Technology
- Acousto-optic Cells
- Harmonic Generation for Laser Frequency Doubling (SHG) and Tripling -using non-linear crystals.
- Measurement: Accuracy & Precision.
- Things you should know about computer modeling of physical phenomena!
- Giant Magneto-resistance
- Peltier Cooling
- Pyro-Electric Detectors
- Piezo-Electric Crystals
- Laser Speckle
- FFT and DFT the fast fourier transform and the discrete fourier transform
- Fabry Perot Etalon
- The Hydrogen Atom.
- PCA (Principal Component Analysis)
- Energy per mass in fuels such as Hydrogen, Gasoline, Kerosene, HMX etc...
- Nobel prize winning work on the CCD
- How does a CCD work and what are the normal characteristics of a CCD
- Nobel Prize Winning work on Giant Magneto-resistance
- FROG -frequency resolved optical gating
- Optical Wavefront Sensing
- THz imaging and time-domain spectroscopy
- Camera Calibration
- Laser Designators
- Resampling