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Numerical Analysis Annette M. Burden

Numerical Analysis By Annette M. Burden

Numerical Analysis by Annette M. Burden


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Summary

Introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work - and why, in some situations, they fail.

Numerical Analysis Summary

Numerical Analysis by Annette M. Burden

This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors 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 readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject.

About Annette M. Burden

Annette M. Burden is a Professor of Mathematics at Youngstown State University (YSU) and for four years served as YSU Interim Distance Education Director. Her master's degree in mathematics was awarded by Youngstown State University and her doctoral degree in mathematics educational technology with a specialization in numerical analysis was awarded by Union Institute & University. Dr. Burden worked under Carnegie Mellon Professor Werner C. Rheinboldt from the University of Pittsburgh for several years. She is past President of the International Society of Technology in Education's Technology Coordinators, was appointed to the MAPLE Academic Advisory Board, and served as co-chair of Ohio's Distance Education Advisory Group. She has also developed numerous upper-level online courses including courses in Numerical Analysis and Numerical Methods. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. Richard L. Burden is Emeritus Professor of Mathematics at Youngstown State University. His master's degree in mathematics and doctoral degree in mathematics, with a specialization in numerical analysis, were both awarded by Case Western Reserve University. He also earned a masters degree in computer science from the University of Pittsburgh. His mathematical interests include numerical analysis, numerical linear algebra, and mathematical statistics. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. He was also named a distinguished chair as the chair of the Department of Mathematical and Computer Sciences. He wrote the Actuarial Examinations in Numerical Analysis from 1990 until 1999. Annette M. Burden is a Professor of Mathematics at Youngstown State University (YSU) and for four years served as YSU Interim Distance Education Director. Her master's degree in mathematics was awarded by Youngstown State University and her doctoral degree in mathematics educational technology with a specialization in numerical analysis was awarded by Union Institute & University. Dr. Burden worked under Carnegie Mellon Professor Werner C. Rheinboldt from the University of Pittsburgh for several years. She is past President of the International Society of Technology in Education's Technology Coordinators, was appointed to the MAPLE Academic Advisory Board, and served as co-chair of Ohio's Distance Education Advisory Group. She has also developed numerous upper-level online courses including courses in Numerical Analysis and Numerical Methods. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. J. Douglas Faires, late of Youngstown State University, pursued mathematical interests in analysis, numerical analysis, mathematics history, and problem solving. Dr. Faires won numerous awards, including the Outstanding College-University Teacher of Mathematics by the Ohio Section of MAA and five Distinguished Faculty awards from Youngstown State University, which also awarded him an Honorary Doctor of Science award in 2006.

Table of Contents

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 9. APPROXIMATING EIGENVALUES. Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method. The QR Algorithm. Singular Value Decomposition. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. 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. Numerical Software and Chapter Summary. Bibliography. Answers to Selected Exercises.

Additional information

GOR011066991
9781305253667
1305253663
Numerical Analysis by Annette M. Burden
Used - Very Good
Hardback
Cengage Learning, Inc
2015-01-01
912
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

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