Application problems drawn from the literature of many different fields prepares readers to use the techniques covered to solve a wide variety of practical problems. Systems of Equations. Eigenvalues and Eigenvectors. Interpolation and Curve Fitting.
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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. The handling of artificial singularities for one-dimensional boundary value problems.
The multigrid method and irregular domains for elliptic partial differential equations. Source and decay terms, polar coordinates and problems in two space dimensions for parabolic partial differential equations.
One-dimensional hyperbolic partial differential equations. Numerical dispersion and diffusion and the convection-diffusion equation.
More than fully-worked examples—The examples are each tied carefully to some new concepts. Helps students grasp the sequence of calculations associated with a particular method and gain better insight into algorithm operation.
An extensive set of application problems—Used both as worked examples and exercises. Problems are drawn from the literature of many different fields physics, biology, chemistry, chemical engineering, thermodynamics, heat transfer, electrostatics, ecology, manufacturing, sociology, etc.
Shows students how numerical methods can be applied within the context of real-world problems, and motivates their study of the various numerical techniques. Gives instructors the opportunity to discuss practical implementation issues.
Chapters organized thematically around mathematical problems—Each chapter is devoted to a single type of problem. Within each chapter, the presentation begins with the simplest, most basic methods and progresses gradually to more advanced topics.
Helps students find parallels and better comprehend the topics. Chapter Overviews—Presents several real-world problems relating to the specific mathematical problem that will be treated in the chapter. Places the material into perspective for students and motivates the reader with the broad applicability of numerical methods to real-world problems. Exercise Sets—Features roughly numbered exercises many with multiple parts.
An appropriate balance of theoretical, applications, and coding questions. Provides students with the opportunity to practice with paper, pencil and calculator the sequence of calculations associated with a particular method. Gives students extensive practice in using numerical methods. Gives instructors a reference guide. Requires students to program the techniques themselves. Getting Started. Floating Point Numbers. Floating Point Arithmetic. Bisection Method. Method of False Position.
Fixed Point Iteration. Accelerating Convergence. Roots of Polynomials. Systems of Equations. Gaussian Elimination. Pivoting Strategies. Error Estimates. LU Decomposition. Direct Factorization. Special Matrices. Nonlinear Systems. Eigenvalues and Eigenvectors. The Power Method. The Inverse Power Method.
Reduction to Tridiagonal Form. Eigenvalues of Tridiagonal and Hessenberg Matrices. Interpolation and Curve Fitting. Lagrange Form of the Interpolating Polynomial. Optimal Interpolating Points. Piecewise Linear Interpolation. Hermite and Hermite Cubic Interpolation. Numerical Differentiation and Integration. Continuous Theory and Key Numerical Concepts. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations.
Solving the Discrete Equations: Relaxation Schemes. Irregular Domains. More General Parabolic Equations. Non-Dirichlet Boundary Conditions. Polar Coordinates. Problems in Two Space Dimensions. Advection Equation, I: Upwind Differencing. Convection-Diffusion Equation. The Wave Equation. Appendix A. Important Theorems from Calculus. Appendix B. Answers to Selected Problems. His passion for explaining things as clearly and understandably as possible, his thorough research of the literature for bringing relevant and pedagogically sound examples from outside mathematics, and his crisp and clear style will certainly make this text an instant success.
This is one of the better texts in Numerical Analysis that I have ever seen, and I congratulate the author for producing such a gem. Chapter 1 in particular is a gem. The treatments of floating point number systems and of floating point arithmetic are especially good. These are topics that are often glossed over in other books, and which are often difficult for students to grasp.
The book is extremely well written: the style is clear, the prose flows smoothly, the pace is unhurried, the tone is friendly and conversational, the examples and exercises are interesting and-relevant, and the amount of detail is far greater than in any textbook of its kind that I have ever seen. For these reasons, it will certainly appeal to my students. The style is a very readable compromise between proof and technical detail on the one hand, and concepts with applications on the other.
I think he addresses this fundamental challenge in a way that my students would like. Bradie has decided to include lots of worked examples accompanied by plots. The plots facilitate the inclusion of such a large number of examples, by succinctly communicating the point of each. This reduces the effort needed to understand the ideas behind the example, I think students simply will not read the book if it takes too much effort.
Bradie can include more exercises than is typical because the illustrations ease the communication. He gives a mathematics review on what is needed at the beginning of each chapter. The book is well written and student-friendly. It provides a lot of examples and exercise problems. The book is written in the way that is easy for students to read.
For instance, for each method, there is at least one fully worked example that helps students to understand the concept and the method.
ISBN 13: 9780130130549
Jutaxe You will be informed within 7 days if your order is not approved. Signed out You have successfully signed out and will be required to sign back in should you need to download more resources. Bradie can include more exercises than is typical because the illustrations ease the communication. Gas Dynamics, Volume 1 Maurice J. If you do not have an IRC account, you can request access here. The style is a very readable compromise between proof and technical detail on the one hand, and concepts with applications on the other. A special order item has limited availability and the seller may source this title from another supplier.
Friendly Introduction to Numerical Analysis, A
Solution Manual A Friendly Introduction to Numerical Analysis 1st Edition Brian Bradie