{"product_id":"fundamentals-of-numerical-mathematics-for-physicists-and-engineers-9781119425670","title":"Fundamentals of Numerical Mathematics for","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntroduces the fundamentals of numerical mathematics and illustrates its applications to a wide variety of disciplines in physics and engineering Applying numerical mathematics to solve scientific problems, this book helps readers understand the mathematical and algorithmic elements that lie beneath numerical and computational methodologies in order to determine the suitability of certain techniques for solving a given problem. It also contains examples related to problems arising in classical mechanics, thermodynamics, electricity, and quantum physics.    Fundamentals of Numerical Mathematics for Physicists and Engineers is presented in two parts. Part I addresses the root finding of univariate transcendental equations, polynomial interpolation, numerical differentiation, and numerical integration. Part II examines slightly more advanced topics such as introductory numerical linear algebra, parameter dependent systems of nonlinear equations, numerical Fourier analysis, and ordinary di\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAbout the Author ix\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Solution Methods for Scalar Nonlinear Equations \u003c\/b\u003e\u003cb\u003e3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Nonlinear Equations in Physics 3\u003c\/p\u003e \u003cp\u003e1.2 Approximate Roots: Tolerance 5\u003c\/p\u003e \u003cp\u003e1.2.1 The Bisection Method 6\u003c\/p\u003e \u003cp\u003e1.3 Newton’s Method 10\u003c\/p\u003e \u003cp\u003e1.4 Order of a Root-Finding Method 13\u003c\/p\u003e \u003cp\u003e1.5 Chord and Secant Methods 16\u003c\/p\u003e \u003cp\u003e1.6 Conditioning 18\u003c\/p\u003e \u003cp\u003e1.7 Local and Global Convergence 20\u003c\/p\u003e \u003cp\u003eProblems and Exercises 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Polynomial Interpolation \u003c\/b\u003e\u003cb\u003e29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Function Approximation 29\u003c\/p\u003e \u003cp\u003e2.2 Polynomial Interpolation 30\u003c\/p\u003e \u003cp\u003e2.3 Lagrange’s Interpolation 33\u003c\/p\u003e \u003cp\u003e2.3.1 Equispaced Grids 37\u003c\/p\u003e \u003cp\u003e2.4 Barycentric Interpolation 39\u003c\/p\u003e \u003cp\u003e2.5 Convergence of the Interpolation Method 43\u003c\/p\u003e \u003cp\u003e2.5.1 Runge’s Counterexample 46\u003c\/p\u003e \u003cp\u003e2.6 Conditioning of an Interpolation 49\u003c\/p\u003e \u003cp\u003e2.7 Chebyshev’s Interpolation 54\u003c\/p\u003e \u003cp\u003eProblems and Exercises 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Numerical Differentiation \u003c\/b\u003e\u003cb\u003e63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 63\u003c\/p\u003e \u003cp\u003e3.2 Differentiation Matrices 66\u003c\/p\u003e \u003cp\u003e3.3 Local Equispaced Differentiation 72\u003c\/p\u003e \u003cp\u003e3.4 Accuracy of Finite Differences 75\u003c\/p\u003e \u003cp\u003e3.5 Chebyshev Differentiation 80\u003c\/p\u003e \u003cp\u003eProblems and Exercises 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Integration \u003c\/b\u003e\u003cb\u003e87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 87\u003c\/p\u003e \u003cp\u003e4.2 Interpolatory Quadratures 88\u003c\/p\u003e \u003cp\u003e4.2.1 Newton–Cotes Quadratures 92\u003c\/p\u003e \u003cp\u003e4.2.2 Composite Quadrature Rules 95\u003c\/p\u003e \u003cp\u003e4.3 Accuracy of Quadrature Formulas 98\u003c\/p\u003e \u003cp\u003e4.4 Clenshaw–Curtis Quadrature 104\u003c\/p\u003e \u003cp\u003e4.5 Integration of Periodic Functions 112\u003c\/p\u003e \u003cp\u003e4.6 Improper Integrals 115\u003c\/p\u003e \u003cp\u003e4.6.1 Improper Integrals of the First Kind 116\u003c\/p\u003e \u003cp\u003e4.6.2 Improper Integrals of the Second Kind 119\u003c\/p\u003e \u003cp\u003eProblems and Exercises 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II \u003c\/b\u003e\u003cb\u003e129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Numerical Linear Algebra \u003c\/b\u003e\u003cb\u003e131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 131\u003c\/p\u003e \u003cp\u003e5.2 Direct Linear Solvers 132\u003c\/p\u003e \u003cp\u003e5.2.1 Diagonal and Triangular Systems 133\u003c\/p\u003e \u003cp\u003e5.2.2 The Gaussian Elimination Method 135\u003c\/p\u003e \u003cp\u003e5.3 LU Factorization of a Matrix 140\u003c\/p\u003e \u003cp\u003e5.3.1 Solving Systems with LU 145\u003c\/p\u003e \u003cp\u003e5.3.2 Accuracy of LU 147\u003c\/p\u003e \u003cp\u003e5.4 LU with Partial Pivoting 150\u003c\/p\u003e \u003cp\u003e5.5 The Least Squares Problem 160\u003c\/p\u003e \u003cp\u003e5.5.1 QR Factorization 162\u003c\/p\u003e \u003cp\u003e5.5.2 Linear Data Fitting 173\u003c\/p\u003e \u003cp\u003e5.6 Matrix Norms and Conditioning 178\u003c\/p\u003e \u003cp\u003e5.7 Gram–Schmidt Orthonormalization 183\u003c\/p\u003e \u003cp\u003e5.7.1 Instability of CGS: Reorthogonalization 187\u003c\/p\u003e \u003cp\u003e5.8 Matrix-Free Krylov Solvers 193\u003c\/p\u003e \u003cp\u003eProblems and Exercises 204\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Systems of Nonlinear Equations \u003c\/b\u003e\u003cb\u003e209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Newton’s Method for Nonlinear Systems 210\u003c\/p\u003e \u003cp\u003e6.2 Nonlinear Systems with Parameters 220\u003c\/p\u003e \u003cp\u003e6.3 Numerical Continuation (Homotopy) 224\u003c\/p\u003e \u003cp\u003eProblems and Exercises 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Numerical Fourier Analysis \u003c\/b\u003e\u003cb\u003e235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Discrete Fourier Transform 235\u003c\/p\u003e \u003cp\u003e7.1.1 Time–Frequency Windows 243\u003c\/p\u003e \u003cp\u003e7.1.2 Aliasing 246\u003c\/p\u003e \u003cp\u003e7.2 Fourier Differentiation 251\u003c\/p\u003e \u003cp\u003eProblems and Exercises 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Ordinary Differential Equations \u003c\/b\u003e\u003cb\u003e261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Boundary Value Problems 262\u003c\/p\u003e \u003cp\u003e8.1.1 Bounded Domains 262\u003c\/p\u003e \u003cp\u003e8.1.2 Periodic Domains 275\u003c\/p\u003e \u003cp\u003e8.1.3 Unbounded Domains 277\u003c\/p\u003e \u003cp\u003e8.2 The Initial Value Problem 279\u003c\/p\u003e \u003cp\u003e8.2.1 Runge–Kutta One-Step Formulas 281\u003c\/p\u003e \u003cp\u003e8.2.2 Linear Multistep Formulas 287\u003c\/p\u003e \u003cp\u003e8.2.3 Convergence of Time-Steppers 297\u003c\/p\u003e \u003cp\u003e8.2.4 A-Stability 301\u003c\/p\u003e \u003cp\u003e8.2.5 A-Stability in Nonlinear Systems: Stiffness 315\u003c\/p\u003e \u003cp\u003eProblems and Exercises 330\u003c\/p\u003e \u003cp\u003eSolutions to Problems and Exercises 335\u003c\/p\u003e \u003cp\u003eGlossary of Mathematical Symbols 367\u003c\/p\u003e \u003cp\u003eBibliography 369\u003c\/p\u003e \u003cp\u003eIndex 373\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407053988183,"sku":"9781119425670","price":92.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119425670.jpg?v=1730498011","url":"https:\/\/bookcurl.com\/products\/fundamentals-of-numerical-mathematics-for-physicists-and-engineers-9781119425670","provider":"Book Curl","version":"1.0","type":"link"}