Error Analysis
An error may be defined as the difference between the measured value and the actual value. For example, if the two operators use the same device or instrument for a measurement, it is not necessary that they may get the similar results. The difference that occurs between both the measurements is referred to as an ERROR. In this topic we will discuss about error calculation in scientific experiment and computation.
- Introduction to Error
- Introduction to Precision
- Stability in Computational Science
- Limitations of Computational Physics
Inerpolation & Extrapolation
Extrapolation and interpolation are both used to estimate hypothetical values for a variable based on other observations. Here we will examine the differences between them and their applications. In this chapter we will discuss and visulize following topics:
- Lagrange interpolation
- Cubic spline interpolations
- Richardson extrapolation
Numerical Differentiation
In this chapter we will discuss and visulize following topics:
- Approximation of derivatives
- Curve fitting by least squares
- Nonlinear least squares
Numerical Integration
In this chapter we will discuss and visulize following topics:
- Trapezoidal Rule
- Simpson's Rule
- The simple pendulum
- Multidimensional numerical integration
- Monte Carlo numerical integration
Ordinary & Partial differential equation
In this chapter we will discuss and visulize following topics:
- Euler methods
- Runge-Kutta Methods
- Second order differential equation
- Phase space of a simple harmonic oscillator
- One-Dimensional Schroedinger equation
- Laplaces equation
- Wave equations and heat equation
- Wave equations and heat equation
Fourier Series and Transforms
Fourier series and laplace transforms are the strong tool to solve the intricate problem of Physics. In this chapter we will discuss following problems;
- Fourier series representation: even & odd functions
- Fourier series expansion of familier functions
- Laplace transform
- Use of Fourier transform in solving partial differential equations
- Use of Laplace transform in solving partial differential equations.
Differential Equations
In this chapter we will discuss and visulize following topics:
- Bassels’s, Legendre’s, Hermite’s,Laguerre’s differential equations
- Associated Legendre and Laguerre polynomials
- Application in Solving Problems of Physics