1. A first course in numerical methods [2011]
- Book
- xxii, 552 p. : ill. (some col.) ; 26 cm.
- Numerical algorithms
- Roundoff errors
- Nonlinear equations in one variable
- Linear algebra background
- Linear systems : direct methods
- Linear least squares problems
- Linear systems : iterative methods
- Eigenvalues and singular values
- Nonlinear systems and optimization
- Polynomial interpolation
- Piecewise polynomial interpolation
- Best approximation
- Fourier transform
- Numerical differentiation
- Numerical integration
- Differential equations.
- Numerical algorithms
- Roundoff errors
- Nonlinear equations in one variable
- Linear algebra background
- Linear systems : direct methods
- Linear least squares problems
- Linear systems : iterative methods
- Eigenvalues and singular values
- Nonlinear systems and optimization
- Polynomial interpolation
- Piecewise polynomial interpolation
- Best approximation
- Fourier transform
- Numerical differentiation
- Numerical integration
- Differential equations.
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA297 .A748 2011 | Unknown 2-hour loan |
CME-108-01, MATH-114-01
- Course
- CME-108-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- Course
- MATH-114-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
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
(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
- 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
(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)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA297 .B84 2011 | Unknown 2-hour loan |
CME-108-01, MATH-114-01
- Course
- CME-108-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- Course
- MATH-114-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- 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
(source: Nielsen Book Data)9780131911710 20160617
- (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
(source: Nielsen Book Data)9780131911710 20160617
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
QA297 .B72 2006 | Unknown 2-hour loan |
CME-108-01, MATH-114-01
- Course
- CME-108-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- Course
- MATH-114-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- Book
- xii, 563 p. : ill. ; 25 cm.
- 1 Scientific Computing2 Systems of Linear Equations3 Linear Least Squares4 Eigenvalues Problems5 Nonlinear Equations6 Optimization7 Interpolation8 Numerical Integration and Differentiation9 Initial Value Problems for ODEs10 Boundary Value Problems for ODEs11 Partial Differential Equations12 Fast Fourier Transform13 Random Numbers and Simulation.
- (source: Nielsen Book Data)9780071122290 20160527
(source: Nielsen Book Data)9780071122290 20160527
- 1 Scientific Computing2 Systems of Linear Equations3 Linear Least Squares4 Eigenvalues Problems5 Nonlinear Equations6 Optimization7 Interpolation8 Numerical Integration and Differentiation9 Initial Value Problems for ODEs10 Boundary Value Problems for ODEs11 Partial Differential Equations12 Fast Fourier Transform13 Random Numbers and Simulation.
- (source: Nielsen Book Data)9780071122290 20160527
(source: Nielsen Book Data)9780071122290 20160527
Engineering Library (Terman)
Engineering Library (Terman) | Status |
---|---|
On reserve: Ask at circulation desk | |
Q183.9 .H4 2002 | Unknown 2-hour loan |
Q183.9 .H4 2002 | Unknown 2-hour loan |
Q183.9 .H4 2002 | Unknown 2-hour loan |
CME-108-01, MATH-114-01
- Course
- CME-108-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing
- Course
- MATH-114-01 -- Introduction to Scientific Computing
- Instructor(s)
- Ying, Lexing