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Book
xix, 756 p. : ill. ; 24 cm.
This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.
(source: Nielsen Book Data)9780321797056 20160608
Engineering Library (Terman)
CME-204-01, ME-300B-01

2. Numerical analysis [2011]

Book
xiv, 872 p. : col. ill. ; 26 cm.
  • 1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software. 2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. Fixed-Point Iteration. Newton's Method and its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and Muller's Method. Survey of Methods and Software. 3. INTERPOLATION AND POLYNOMIAL APPROXIMATION. Interpolation and the LaGrange Polynomial. Data Approximation and Neville's Method Divided Differences. Hermite Interpolation. Cubic Spline Interpolation. Parametric Curves. Survey of Methods and Software. 4. NUMERICAL DIFFERENTIATION AND INTEGRATION. Numerical Differentiation. Richardson's Extrapolation. Elements of Numerical Integration. Composite Numerical Integration. Romberg Integration. Adaptive Quadrature Methods. Gaussian Quadrature. Multiple Integrals. Improper Integrals. Survey of Methods and Software. 5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods. Error Control and the Runge-Kutta-Fehlberg Method. Multistep Methods. Variable Step-Size Multistep Methods. Extrapolation Methods. Higher-Order Equations and Systems of Differential Equations. Stability. Stiff Differential Equations. Survey of Methods and Software. 6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS. Linear Systems of Equations. Pivoting Strategies. Linear Algebra and Matrix Inversion. The Determinant of a Matrix. Matrix Factorization. Special Types of Matrices. Survey of Methods and Software. 7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Iterative Techniques for Solving Linear Systems. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Survey of Methods and Software. 8. APPROXIMATION THEORY. Discrete Least Squares Approximation. Orthogonal Polynomials and Least Squares Approximation. Chebyshev Polynomials and Economization of Power Series. Rational Function Approximation. Trigonometric Polynomial Approximation. Fast Fourier Transforms. Survey of Methods and Software. 9. APPROXIMATING EIGENVALUES. Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method.The QR Algorithm.Singular Value Decomposition. Survey of Methods and Software. 10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS. Fixed Points for Functions of Several Variables. Newton's Method. Quasi-Newton Methods. Steepest Descent Techniques. Homotopy and Continuation Methods. Survey of Methods and Software. 11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Linear Shooting Method. The Shooting Method for Nonlinear Problems. Finite-Difference Methods for Linear Problems. Finite-Difference Methods for Nonlinear Problems. The Rayleigh-Ritz Method. Survey of Methods and Software. 12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS. Elliptic Partial-Differential Equations. Parabolic Partial-Differential Equations. Hyperbolic Partial-Differential Equations. An Introduction to the Finite-Element Method. Survey of Methods and Software.
  • (source: Nielsen Book Data)9780538735643 20160607
This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded "Numerical Analysis, Third Edition".
(source: Nielsen Book Data)9780538735643 20160607
This well-respected text gives an introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject.
(source: Nielsen Book Data)9780538733519 20160607
Engineering Library (Terman)
CME-108-01, MATH-114-01
Book
933 p. ; 24 cm
  • (NOTE: Each chapter begins with An Overview.) 1. Getting Started. Algorithms. Convergence. Floating Point Numbers. Floating Point Arithmetic. 2. Rootfinding. Bisection Method. Method of False Position. Fixed Point Iteration. Newton's Method. The Secant Method and Muller's Method. Accelerating Convergence. Roots of Polynomials. 3. Systems of Equations. Gaussian Elimination. Pivoting Strategies. Norms. Error Estimates. LU Decomposition. Direct Factorization. Special Matrices. Iterative Techniques for Linear Systems: Basic Concepts and Methods. Iterative Techniques for Linear Systems: Conjugate-Gradient Method. Nonlinear Systems. 4. Eigenvalues and Eigenvectors. The Power Method. The Inverse Power Method. Deflation. Reduction to Tridiagonal Form. Eigenvalues of Tridiagonal and Hessenberg Matrices. 5. Interpolation and Curve Fitting. Lagrange Form of the Interpolating Polynomial. Neville's Algorithm. The Newton Form of the Interpolating Polynomial and Divided Differences. Optimal Interpolating Points. Piecewise Linear Interpolation. Hermite and Hermite Cubic Interpolation. Regression. 6. Numerical Differentiation and Integration. Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations. 7. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations. 8. Second-Order One-Dimensional Two-Point Boundary Value Problems. Finite Difference Method, Part I: The Linear Problem with Dirichlet Boundary Conditions. Finite Difference Method, Part II: The Linear Problem with Non-Dirichlet Boundary Conditions. Finite Difference Method, Part III: Nonlinear Problems. The Shooting Method, Part I: Linear Boundary Value Problems. The Shooting Method, Part II: Nonlinear Boundary Value Problems. 9. Finite Difference Method for Elliptic Partial Differential Equations. The Poisson Equation on a Rectangular Domain, I: Dirichlet Boundary Conditions. The Poisson Equation on a Rectangular Domain, II: Non-Dirichlet Boundary Conditions. Solving the Discrete Equations: Relaxation Schemes. Local Mode Analysis of Relaxation and the Multigrid Method. Irregular Domains. 10. Finite Difference Method for Parabolic Partial Differential Equations. The Heat Equation with Dirichlet Boundary Conditions. Stability. More General Parabolic Equations. Non-Dirichlet Boundary Conditions. Polar Coordinates. Problems in Two Space Dimensions. 11. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation. Advection Equation, I: Upwind Differencing. Advection Equation, II: MacCormack Method. Convection-Diffusion Equation. The Wave Equation. Appendices. Appendix A. Important Theorems from Calculus. Appendix B. Algorithm for Solving a Tridiagonal System of Linear Equations. References. Index. Answers to Selected Problems.
  • (source: Nielsen Book Data)9780131911710 20160617
For one or two-semester undergraduate/graduate-level courses in Numerical Analysis/Methods in mathematics departments, CS departments, and all engineering departments. This student-friendly text develops concepts and techniques in a clear, concise, easy-to-read manner, followed by fully-worked examples. Application problems drawn from the literature of many different fields prepares students to use the techniques covered to solve a wide variety of practical problems.
(source: Nielsen Book Data)9780131911710 20160617
Engineering Library (Terman)
CME-108-01, MATH-114-01
Book
xvi, 745 p. : ill. (some col.) ; 26 cm.
  • First Order Differential Equations-- Second Order Linear Equations-- Higher Order Linear Equations-- Series Solutions of Second Order Linear Equations-- The Laplace Transform-- Systems of First Order Linear Equations-- Numerical Methods-- Nonlinear Differential Equations and Stability-- Partial Differential Equations and Fourier Series-- Boundary Value Problems and Sturm-Liouville Theory-- Answers to Problems-- Index.
  • (source: Nielsen Book Data)9780471319993 20160527
Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working knowledge of calculus. The environment in which instructors teach, and students learn differential equations has changed enormously in the past few years and continues to evolve at a rapid pace. Computing equipment of some kind, whether a graphing calculator, a notebook computer, or a desktop workstation is available to most students. The seventh edition of this classic text reflects this changing environment, while at the same time, it maintains its great strengths - a contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. In addition many new problems have been added and a reorganisation of the material makes the concepts even clearer and more comprehensible. Like its predecessors, this edition is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of differential equations as they apply to engineering and the sciences.
(source: Nielsen Book Data)9780471319993 20160527
Engineering Library (Terman)
CME-204-01, ME-300B-01