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COMPUTATIONAL PHYSICS
The aim of the book “Computational Physics” is to serve as textbook on applied Computational Physics. Contents of this book together with those of 7 monographs of the author listed in the references form a coherent course text, i.e., lecture notes for a 2-semester course for final year undergraduate students of Physics and Mathematics major for the course titled Computational Physics. Instead of solving problems of unphysical numerical analysis, this book illustrates use of different computational methods by solving problems of Physics and mathematical Physics. For example, root finding methods have been illustrated by calculating bound state energy of Quantum Well. This is the 1st Mathematica-based textbook titled “Computational Physics”. Every computational method considered has been illustrated by thoroughly worked out exercise. This pedagogical feature of the book is very important. The book has been designed for use in classroom as well as in Computational Physics Lab.
LECTURE NOTES ON PHYSICS (Second Edition)
Based on more than 20 years of teaching experience of the author, “Lecture Notes on Physics” contains his lecture notes on 4 different courses: Mathematical Physics, Classical Mechanics, Classical Electrodynamics, and Solid State Physics for undergraduate students of Physics major. Written with perfection, this is highly polished 2nd edition of the book. The 1st edition was also published by American Academic Press in January 2016.
Newtonian Mechanics
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Numerical Exploration of Fourier Transform and Fourier Series
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform. This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical data Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation
A First Course in Complex Analysis
This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.
Mathematical Problem Factories
A problem factory consists of a traditional mathematical analysis of a type of problem that describes many, ideally all, ways that the problems of that type can be cast in a fashion that allows teachers or parents to generate problems for enrichment exercises, tests, and classwork. Some problem factories are easier than others for a teacher or parent to apply, so we also include banks of example problems for users. This text goes through the definition of a problem factory in detail and works through many examples of problem factories. It gives banks of questions generated using each of the examples of problem factories, both the easy ones and the hard ones. This text looks at sequence extension problems (what number comes next?), basic analytic geometry, problems on whole numbers, diagrammatic representations of systems of equations, domino tiling puzzles, and puzzles based on combinatorial graphs. The final chapter previews other possible problem factories.
The Navier–Stokes Problem
The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on R+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution (, ) to the NSP exists for all ≥ 0 and (, ) = 0). It is shown that if the initial data 0() ≢ 0, (,) = 0 and the solution to the NSP exists for all ε R+, then 0() := (, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 21(R3) × C(R+) is proved, 21(R3) is the Sobolev space, R+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
Monte Carlo Methods
This book is intended for undergraduate students of Mathematics, Statistics, and Physics who know nothing about Monte Carlo Methods but wish to know how they work. All treatments have been done as much manually as is practicable. The treatments are deliberately manual to let the readers get the real feel of how Monte Carlo Methods work. Definite integrals of a total of five functions (), namely Sin(), Cos(), e, loge(), and 1/(1+2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions (). It is shown that results agree with known exact values better if () is proportional to (). Deviation from the proportionality results in worse agreement. This b...
Aspects of Differential Geometry V
Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.
Numerical Solutions of Initial Value Problems Using Mathematica
The book contains a detailed account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.
