Computing in Scilab

Cover
Computing in Scilab
Title
Copyright
Contents
Figures
Tables
1 Matrices and Vector Spaces
1.1 Introduction
1.2 Creation of a Matrix
1.3 Nature of the Matrix
1.4 Matrix Operation
1.5 Vector Algebra
1.6 Applications
1.6.1 Coordinate conversion (Cartesian to cylindrical coordinate system)
1.6.2 Coordinate conversion (Cartesian to spherical coordinate system)
1.6.3 Orthogonal vectors
1.6.4 Centre of mass of a system
1.6.5 Electrical circuits (Mesh analysis)
1.6.6 Electrical circuits (Nodal analysis)
1.6.7 Force on a test charge
1.6.8 Principal axes of moment of inertia
1.6.9 Matrix representation of differential operator
1.6.10 Position–Momentum commutation
1.6.11 Matrix representation of the Laplace operator
1.6.12 Wave function for stationary states
1.7 Exercises
2 Plotting and Graphics Design
2.1 Introduction
2.2 Formatting of the Coordinate Axes
2.2.1 Font size
2.2.2 Font colour
2.2.3 Typeface
2.2.4 Axis position
2.2.5 Tick marks
2.2.6 Logarithmic axes
2.2.7 Polar plot
2.3 Formatting of the Line Styles
2.3.1 Thickness
2.3.2 Line style
2.3.3 Line colour
2.4 Formatting of the Markers
2.4.1 Marker style
2.4.2 Marker: Size and colour
2.4.3 Thickness and line mode
2.5 Formatting of the Title
2.6 Formatting of the Legend
2.7 Applications
2.7.1 Trajectory of a projectile
2.7.2 Superposition of collinear harmonic oscillations
2.7.3 Beats
2.7.4 R-C Circuit
2.7.5 R-L Circuit
2.7.6 Maximum power transfer theorem
2.7.7 Diode characteristics
2.7.8 Specific heat of solids
2.7.9 Spectral radiance of a blackbody radiation
2.7.10 Miller indices
2.7.11 Linear interpolation
2.7.12 Gradient of a scalar field
2.8 Exercises
3 Least Square Curve Fitting
3.1 Introduction
3.2 Fitting of Linear Data
3.3 Fitting of Non-Linear Data
3.4 Polynomial Fitting
3.5 Fitting with Built-in Scilab Function – ‘datafit’
3.6 Applications
3.6.1 Refractive index of water
3.6.2 Spring constant
3.6.3 Cauchy’s constant of a prism
3.6.4 RC Time constant
3.6.5 Coefficient of electronic heat capacity and Debye’s temperature
3.6.6 Lennard–Jones potential
3.6.7 Spectral radiance of blackbody radiation
3.7 Exercises
4 Ordinary Differential Equation
4.1 Introduction
4.2 Euler’s Method
4.2.1 First order differential equation
4.2.2 Second order differential equation
4.3 Modified Euler’s Method
4.4 Second Order Runge–Kutta Method
4.5 Fourth Order Runge–Kutta Method
4.5.1 First order differential equation
4.5.2 Second order differential equation
4.6 Comparison of the Four Methods
4.7 Finite Difference Method
4.8 Applications
4.8.1 Radioactive decay
4.8.1.1 Built-in Scilab function
4.8.1.2 Euler’s method
4.8.1.3 Modified Euler’s method
4.8.1.4 Second order Runge–Kutta Method
4.8.1.5 Fourth order Runge–Kutta method
4.8.1.6 Graphical representation of the solution
4.8.2 Orthogonal trajectory
4.8.3 Square wave ´ Triangular wave
4.8.3.1 Built-in function and graphical representation
4.8.4 Sinusoidal wave
4.8.4.1 Built-in function
4.8.4.2 Euler’s method
4.8.4.3 Modified Euler’s method
4.8.4.4 Second order Runge–Kutta method
4.8.4.5 Fourth order Runge–Kutta method
4.8.4.6 Graphical representation
4.8.5 Freely falling object
4.8.6 Atwood’s machine
4.8.7 Simple pendulum
4.8.8 Mass–spring system
4.8.9 Series L-C-R circuit
4.8.10 Schrödinger equation
4.8.10.1 Infinite potential well
4.8.10.2 Hydrogen atom: Coulomb potential
4.8.10.3 Harmonic oscillator
4.8.11 Lagrangian dynamics
4.9 Exercises
5 Integration and Differentiation
5.1 Introduction
5.2 Built-in Scilab Functions for Integration
5.2.1 intg
5.2.2 integrate
5.3 Trapezoidal Rule
5.4 Simpson’s 1/3 – Rule
5.5 Simpson’s 3/8 – Rule
5.6 Differentiation
5.7 Applications
5.7.1 Integration in cylindrical coordinates
5.7.1.1 Line integral
5.7.1.2 Surface integral
5.7.1.3 Volume Integral
5.7.2 Total charge
5.7.3 Electric flux density
5.7.4 Planck’s law for blackbody radiation
5.7.5 Specific heat of solids
5.7.6 Dirac delta function (Shifting property)
5.7.7 Cornu’s spiral and Fresnel’s diffraction pattern
5.7.8 Arc length
5.7.9 Motion of an object
5.8 Exercises
6 Special Functions
6.1 Introduction
6.2 Bessel Function of the First Kind
6.3 Legendre Polynomial
6.4 Laguerre Polynomial
6.5 Hermite Polynomial
6.6 Improper Integrals – Quadrature Methods
6.6.1 Gauss–Legendre quadrature
6.6.2 Gauss–Laguerre quadrature
6.6.3 Gauss–Hermite quadrature
6.7 Applications
6.7.1 Simple pendulum
6.8 Exercises
7 Fourier Analysis
7.1 Introduction
7.2 Periodic Functions
7.3 Fourier Series
7.4 Harmonics
7.5 Fourier Series Expansion of Periodic Functions
7.5.1 Fourier series expansion of (x2)
7.5.2 Fourier series expansion of saw-tooth wave
7.5.3 Fourier series expansion of a square wave
7.5.4 Fourier series expansion of a triangular wave
7.5.5 Fourier series expansion of output of half wave rectifier
7.6 Fast Fourier Transform
7.6.1 FFT of a sine wave
7.6.2 FFT of the sum of two cosine wave signals
7.6.3 FFT of a noisy signal
7.6.4 FFT of a square wave
7.6.5 FFT of a Gaussian curve
7.7 Summary
7.8 Exercises
8 Algebraic and Transcendental Equations
8.1 Introduction
8.2 Equation Solver in Scilab
8.2.1 Division operator
8.2.2 Built-in Scilab function – ‘linsolve’
8.2.3 Built-in Scilab function – ‘fsolve’
8.3 Gauss–Seidel Method
8.4 Gaussian Elimination Method
8.5 ‘pivoting’ Gaussian Elimination Method
8.6 Bracketing Method: Bisection Method
8.7 Bracketing Method: Regula Falsi Method
8.8 Open Method: Secant Method
8.9 Open Method: Newton–Raphson Method
8.10 Applications
8.10.1 Trajectory of a particle
8.10.2 Matrix inverse
8.10.3 Determinant of a matrix
8.10.4 Fraunhofer diffraction pattern
8.10.5 Bound state of proton and neutron
8.10.6 Central angle of an elliptical orbit
8.10.7 Bearing angle of a boat
8.11 Exercises
Appendix
1 Matrices and Vector Spaces (vectors.sci)
1.1 Distance between two points
1.2 Coordinate conversion
2 Plotting and Graphics Design (plot.sci)
2.1 Formatting of coordinate axes
2.2 Formatting of the line styles
2.3 Formatting of the markers
2.4 Formatting of the legend
3 Least Square Curve Fitting
3.1 Exponential Fitting
3.2 Polynomial Fitting
4 Ordinary Differential Equation (differentiation.sci)
4.1 Euler’s Method (for first order differential equation)
4.2 Euler’s Method (for second order differential equation)
4.3 Modified Euler’s Method
4.4 Second order Runge–Kutta Method (for first order differential equation)
4.5 Fourth Order Runge–Kutta Method (for first order differential equation)
4.6 Fourth Order Runge–Kutta Method (for second order differential equation)
4.7 Finite Difference Method
5 Integration and Differentiation (integrate.sci)
5.1 Trapezoidal Rule
5.2 Simpson’s 1/3 – Rule
5.3 Simpson’s 3/8 – Rule
5.4 Line Integral in Cylindrical Coordinates
5.5 Surface Integral in Cylindrical Coordinates
5.6 Volume Integral in Cylindrical Coordinates
6 Special Functions (special_func.sci)
6.1 Legendre Polynomials
6.1.1 Function for the recursion relation
6.1.2 Function for the summation series
6.2 Laguerre Polynomials
6.2.1 Function for the recursion relation
6.2.2 Function for the summation series
6.3 Hermite Polynomials
6.3.1 Function for the recursion (probabilists’)
6.3.2 Function for the recursion (physicists’)
6.4 Gauss–Legendre Quadrature
6.5 Gauss–Laguerre Quadrature
6.6 Gauss–Hermite Quadrature
7 Fourier analysis (fourier.sci)
7.1 Periodic Functions
7.2 Fourier Series
8 Algebraic and Transcendental Equations (numerical_techniques.sci)
8.1 Gauss–Seidel Method
8.2 Gaussian Elimination Method
8.3 ‘pivoting’ Gaussian Elimination Method
8.4 Inverse of a Matrix
8.5 Determinant of a Matrix
8.6 Bisection Method
8.7 Regula Falsi Method
8.8 Secant Method
8.9 Newton–Raphson Method
References
Index
A
B
C
D
E
F
G
H
I
L
M
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O
P
Q
R
S
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V
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