Mathematica for Physicists and Engineers

ISBN-13: 9783527414246 / Angielski / Miękka / 2023 / 320 str.

India) Monteiro Puttur Antony P. (St. Philomena College

Spis treści

CHAPTER 1 - Preliminary Notions1.1 Introduction1.2 Versions of Mathematica1.3 Getting Started1.4 Simple Calculations1.4.1 Arithmetic Operations1.4.2 Approximate Numerical Results1.4.3 Algebraic Calculations1.4.4 Defining Variables1.4.5 Using the Previous Results1.4.6 Suppressing the Output1.4.7 Sequence of Operations1.5 Built-in Functions1.6 Additional Features1.6.1 Arbitrary-Precision Calculations1.6.2 Value of Symbols1.6.3 Defining, Naming and Evaluating Functions1.6.4 Composition of Functions1.6.5 Conditional Assignment1.6.6 Warnings and Messages1.6.7 Interrupting Calculations1.6.8 Using Symbols to Tag ObjectsCHAPTER 2 - Basic Mathematical Operations2.1 Introduction2.2 Basic Algebraic Operations2.3 Basic Trigonometric Operations2.4 Basic Operations with Complex NumbersCHAPTER 3 - Lists and Tables3.1 Lists3.2 Arrays3.3 Tables3.4 Extracting the Elements from the Array/TablesCHAPTER 4 - Two-Dimensional Graphics4.1 Introduction4.2 Plotting Functions of a Single Variable4.3 Additional Commands4.4 Plot Styles4.5 Probability Distribution4.5.1 Binomial Distribution4.5.2 Poisson Distribution4.5.3 Normal or Gaussian DistributionCHAPTER 5 - Parametric, Polar, Contour, Density and List Plots5.1 Introduction5.2 Parametric plotting5.3 Polar Plots5.3.1 Polar Plots of Circles5.3.2 Polar Plots of Ellipses, Parabola and Hyperbola5.4 Implicit Plots5.5 Contour Plots5.6 Density Plots5.7 List Plots5.8 LogPlot, LogLogPlot, ErrorListPlot5.9 Least Square FitCHAPTER 6 - Three-Dimensional Graphics6.1 Introduction6.2 Plotting The Functions of Two Variables6.3 Parametric Plots6.4 3D Plots in Cylindrical and Spherical Coordinates6.5 ContourPlot3D6.6 ListContourPlot3D6.7 ListSurfacePlot3D6.8 Surface of RevolutionCHAPTER 7 - Matrices7.1 Introduction7.2 Properties of Matrices7.3 Types of Matrices7.4 The Rank of the Matrix7.5 Special Matrices7.6 Creation of the Matrix7.6.1 Extraction of the Sub Matrices or the Elements of the Matrices7.7 Properties of the Special Matrices7.8 The Direct Sum of Matrices7.9 The Direct Product of Matrices7.10 Examples from Group Theory7.10.1 SO(3) Group7.10.2 SU(n) Group7.10.3 SU(2) Group7.10.4 SU(3) GroupCHAPTER 8 - Solving Algebraic and Transcendental Equations8.1 Solving Systems of Linear Equations8.1.1 Number of Equations Equal to the Number of Unknowns8.1.2 Number of Equations Less Than the Number of Unknowns8.1.3 Number of Equations More Than the Number of Unknowns8.2 Non- Linear Algebraic Equations8.3 Solving Transcendental EquationsCHAPTER 9 - Eigenvalues and Eigenvectors of a Matrix: Matrix Diagonalization9.1 Introduction9.2 Eigenvalues and Vectors of a Matrix9.2.1 Distinct Eigenvalues having Independent Eigenvectors9.2.2 Multiple Eigenvalues having Independent Eigenvectors9.2.3 Multiple Eigenvalues not having Independent Eigenvectors9.3 The Cayley-Hamilton Theorem9.4 Diagonalization of a Matrix9.4.1 Gram-Schmidt Orthogonalization Method9.4.2 Diagonalizability of a Matrix9.4.3 Case of a Non-diagonalizable Matrix9.5 Some More Properties of Special Matrices9.6 Power of a Matrix9.6.1 Roots of a Matrix9.6.2 Exponential of a Matrix9.6.3 Logarithm of a Matrix9.7 Power of a Matrix by Diagonalization9.8 Bilinear, Quadratic and Hermitian Forms9.9 Principal Axes TransformationCHAPTER 10 - Differential Calculus10.1 Introduction10.2 Limits10.2.1 Evaluation of the Limits Using L' Hospital?s Rule10.2.2 Application of L' Hospital?s Rule for "Indeterminate Form10.2.3 Evaluation of the Limit Using Taylor's Theorem of Mean10.3 Differentiation10.3.1 Computation of Partial Derivatives10.3.2 Total Derivative10.4 Derivatives of Functions in Parametric Forms10.4.1 Chain Rule for a Function of Two Independent Variables10.4.2 Chain Rule for a Function of Three Independent Variables10.5 Rolle's Theorem10.6 Mean Value Theorem10.7 Series10.8 Maxima and Minima10.8.1 First Derivative Test10.8.2 Second Derivative Test10.8.3 Maximum and Minimum Values of a Function in a Closed Interval10.8.4 Maxima and Minima of Two Variables10.9 Differential Equations10.9.1 Simple Harmonic Oscillator10.9.2 LCR Circuit- Discharging of a Condenser through LR CircuitCHAPTER 11 - Integral Calculus11.1 Introduction11.1.1 Indefinite Integral11.1.2 Definite Integral11.1.3 Numerical Value of the Integral11.1.4 Assumptions in Evaluating the Integral11.1.5 Multiple Integrals11.1.6 Triple Integral11.2 Evaluation on Indefinite Integrals11.3 Evaluation of Definite Integrals11.3.1 Numerical Value of the Integral11.3.2 Options for Integration11.4 Two and Three-Dimensional Integrals11.5 Evaluation of the Integral in Polar Coordinates11.6 Evaluation of Special Integrals11.7 Orthogonal Polynomials11.8 The Area between Curves11.9 The Application of Green's Theorem in a PlaneCHAPTER 12 - Dirac Delta Function12.1 Introduction12.2 The Limiting Form of Dirac Delta Function12.3 Integral Representation of the Dirac Delta Function12.4 Some Important Properties of the Dirac Delta Function12.5 The Three-Dimensional Dirac Delta FunctionCHAPTER 13 - Fourier Transform13.1 Introduction13.2 Fourier Transforms13.3 Scaling Property13.4 Shifting Property13.5 Fourier Sine and Cosine Transforms13.6 Fourier Transform of the Derivative13.7 Inverse Fourier Transform13.8 Convolution13.9 Convolution Theorem for Fourier Transforms13.10 Parseval's TheoremCHAPTER 14 - Laplace Transforms14.1 Introduction14.2 Some Simple Examples14.3 Properties of the Laplace Transform14.3.1 Linearity14.3.2 Shifting Property14.3.3 Scaling14.4 Laplace Transform of Derivative14.5 Laplace Transform of Certain Special Functions14.6 Laplace Transform of Error and Complementary Error Functions14.7 The Evaluation of Certain Class of Definite Integrals Using Laplace Transform14.8 The Inverse Laplace Transform14.8.1 Inverse Laplace Transform of Standard Functions14.8.2 Shifting Property14.8.3 Inverse Laplace Transforms of Derivatives14.9 Solving the Differential Equation by Laplace Transform14.10 Convolution Theorem14.11 Graphical Treatment of the ConvolutionCHAPTER 15 - Vectors15.1 Definition and Properties15.2 Vector Differentiation15.3 Directional Derivative15.4 Unit Vector Normal to the Surface15.5 Gradient, Divergence and Curl in Cartesian Coordinate system15.5.1 Gradient15.5.2 Divergence15.5.3 Curl15.5.4 Laplacian Operator15.5.5 Examples15.6 Expressing the Gradient, Divergence and Curl in Other Coordinate Systems15.6.1 Spherical Coordinate System15.6.2 Cylindrical Coordinate System15.7 Vector PlotsCHAPTER 16 - Linear Vector Spaces and Quantum Mechanics16.1 Introduction16.2 Linear Independence, Basis and Dimension16.3 Dimension of the Vector Space16.4 Basis of the Vector Space16.5 Completeness16.6 Scalar Product in a Linear Vector Space16.7 Norm of the Vector16.8 Orthonormal Basis16.9 Linear Independence of Functions16.10 Hilbert Space16.11 Completeness in Functional Space16.12 Dirac Ket and Bra Notation16.12.1 The Scalar Properties of the Kets and Bras16.12.2 Schwartz Inequality16.12.3 The Orthonormal States16.12.4 Basis16.12.5 Probability Density16.13 The Hermitian and Skew-Hermitian Operators in Dirac Ket and Bra Notation16.14 Expectation Values16.15 Matrix Representation of the Linear OperatorCHAPTER 17 - Applications of Mathematica to Quantum Mechanics17.1 Introduction17.2 A Particle in a One-Dimensional Box17.3 A Particle in a Two-Dimensional Box17.4 The Hydrogen Atom Problem17.4.1 The Orthonormal Property of the Hydrogen Atom Wave Functions17.5 One-Dimensional Linear Harmonic Oscillator Atom Problem17.6 Three-Dimensional Harmonic Oscillator Problem17.7 Miscellaneous ProblemsReferencesIndex

O autorze

K. B. Vijaya Kumar is a professor of physics in the Department of Physics at the N.M.A.M Institute of Technology, Nitte, India. His research is focused on theoretical and computational nuclear and particle physics. Prof. K. B. Vijaya Kumar was a Commonwealth Academic Staff fellow (1998-1999), a World Academy of Sciences-UNESCO fellow at the Institute of Theoretical Physics, Beijing (2003-2006), and visiting scientist at the Research Center Jülich, Germany (2005) and at the Institute for Theoretical Physics, University of Tübingen, Germany (2006- 2009).Dr. Antony Prakash Monteiro is working in the Department of Physics at St. Philomena College, Puttur, India. He has more than thirteen years of teaching experience at undergraduate and postgraduate levels and has authored several books in various fields of physics. He is the recipient of the Vision Group on Science and Technology Award for Research Publications 2017-18 for his high-impact research publications. His research interest is aimed at computational and theoretical nuclear and particle physics.