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Description: Computers and computation are extremely important components of physics and should be integral parts of a physicist’s education. Furthermore, computational physics is reshaping the way calculations are made in all areas of physics, and Computational skills are fundamental to every students working in the field.
Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. Topics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems.
Key Features:
· Completely revised and updated to reflect the use of MATLAB
· The Second Edition includes new sections on chaos, and more examples in the areas of classical mechanics and quantum mechanics
· Discusses computerized tomography, a topic that is rarely seen at this level
· Contains many more examples of code on the accompanying CD
· Instructor Resources include complete solutions to all the exercises and comments regarding the various exercises
Contents:
Chapter 1: Introduction • MATLAB®- The Language of Technical Computing • Getting Started • A Numerical Example • Code Fragments • A Brief Guide to Good Programming • Debugging and Testing • A Cautionary Note • Elementary Computer Graphics • And in Living Color! • Classic Curves• Monster Curves • Box Counting • The Mandelbrot Set • Logistic Maps, Bifurcation, and Lyapunov Exponents• References
Chapter 2: Functions and Roots • Finding the Roots of a Function • A Recursive Algorithm • Mr. Taylor’s Series • The Newton-Raphson Method • Fools Rush In • Rates of Convergence • Exhaustive Searching • Look Ma, No Derivatives! • Accelerating the Rate of Convergence • MATLAB’s Root Finding Routines • A Little Quantum Mechanics Problem • Computing Strategy • The Propagator Method • The Double Well • A One-Dimensional Crystal • A Note on Fast Algorithms • Impurities • The Kronig-Penney Model • References
Chapter 3: Interpolation and Approximation • Lagrange Interpolation • The Airy Pattern • Hermite Interpolation • Cubic Splines • Tridiagonal Linear Systems • Cubic Spline Interpolation • MATLAB’s Interpolation Routines • Approximation of Derivatives • Richardson Extrapolation • Curve Fitting by Least Squares • Kepler’s Harmony of the World • Gaussian Elimination • MATLAB’s Linear Equation Solver • General Least Squares Fitting • Least Squares and Orthogonal Polynomials • Nonlinear Least Squares • References
Chapter 4: Numerical Integration • Anaxagoras of Clazomenae • Primitive Integration Formulas • Composite Formulas • Errors... and Corrections • Romberg Integration • MATLAB’s Integration Routines • Diffraction at a Knife’s Edge • A Change of Variables • The “Simple” Pendulum • Improper Integrals • The Mathematical Magic of Gauss • Orthogonal Polynomials • Gaussian Integration • Composite Rules • Gauss-Laguerre Quadrature • Multidimensional Numerical Integration • Other Integration Domains • A Little Physics Problem • More on Orthogonal Polynomials • Monte Carlo Integration • Monte Carlo Simulations • References
Chapter 5: Ordinary Differential Equations • Euler Methods • Constants of the Motion • Runge-Kutta Methods • Convergence • Adaptive Stepsizes • Runge-Kutta-Fehlberg • Several Dependent Variables • The N-Particle Linear Chain Model • Second Order Differential Equations • The van der Pol Oscillator • Phase Space • The Finite Amplitude Pendulum •The Animated Pendulum • Another Little Quantum Mechanics Problem • A Second Order Differential Equation in Two Dimensions • Shoot the Moon • Celestial Mechanics • Finite Differences • Successive Over Relaxation (SOR) • Discretization Error • A Vibrating String • Eigenvalues via Finite Differences • The Power Method • Eigenvectors • Finite Elements • An Eigenvalue Problem • References
Chapter 6: Fourier Analysis • The Fourier Series • The Fourier Transform • Properties of the Fourier Transform • The Discrete Fourier Transform • The Fast Fourier Transform • Life in the Fast Lane • Convolution and Correlation • Ranging • Spectrum Analysis • Chaos in Non-Linear Differential Equations • Computerized Tomography • References
Chapter 7: Partial Differential Equations • Classes of Partial Differential Equations • The Vibrating String Again! • Finite Difference Equations • Stability • Back to the String • The Steady-State Heat Equation • Isotherms • Irregular Physical Boundaries • Neumann Boundary Conditions • A Magnetic Problem • Boundary Conditions • The Finite Difference Equations • Another Comment on Strategy • Are We There Yet? • Spectral Methods • The Pseudo-Spectral Method • A Sample Problem • The Potential Step Problem • The Well • The Barrier • Wavepackets in Two Dimensions • And There’s More • References ISBN - 9789380108940
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Pages : 448
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