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A Gentle Introduction to Scientific Computing by Dan Stanescu: New
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- Book Title
- A Gentle Introduction to Scientific Computing
- Publication Date
- 2022-05-02
- Pages
- 282
- ISBN
- 9780367206840
關於產品
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
0367206846
ISBN-13
9780367206840
eBay Product ID (ePID)
13057240714
Product Key Features
Number of Pages
272 Pages
Publication Name
Gentle Introduction to Scientific Computing
Language
English
Subject
Numerical Analysis, Computer Science, General
Publication Year
2022
Type
Textbook
Subject Area
Mathematics, Computers
Series
Chapman and Hall/Crc Numerical Analysis and Scientific Computing Ser.
Format
Hardcover
Dimensions
Item Weight
24.1 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
LCCN
2021-056202
Dewey Edition
23/eng20220301
TitleLeading
A
Illustrated
Yes
Dewey Decimal
518.0285
Table Of Content
1. Introduction. 1.1. Scientific Computing. 1.2. MATLAB: what and why? 1.3. A Word of Caution. 1.4. Additional Resources. 2. Vectors and Matrices. 2.1. Unidimensional Arrays: Vectors. 2.2. Bidimensional Arrays: Matrices. 2.3. Matrix Operations. 2.4. Systems of Linear Equations. 2.5. Eigenvalues and Eigenvectors. 2.6. Operation Counts. 2.7. Exercises. 3. Basics of MATLAB. 3.1. Defining and Using Scalar Variables. 3.2. Saving and Reloading the Workspace. 3.3. Defining and Using Arrays. 3.4. Operations on Vectors and Matrices. 3.5. More on Plotting Functions of One Variable. 3.6. Loops and Logical Operators. 3.7. Working with indices and arrays. 3.8. Organizing Your Outputs. 3.9. Number representation. 3.10. Machine epsilon. 3.11. Exercises. 4. Solving Nonlinear Equations. 4.1. The Bisection Method for Root-Finding. 4.2. Convergence Criteria and Efficiency. 4.3. Scripts and Function Files. 4.4. The False Position Method. 4.5. The Newton--Raphson Method for Root-Finding. 4.6 Fixed Point Iteration. 4.7. MATLAB built-in functions. 4.8. Exercises. 5. Systems of Equations. 5.1. Linear Systems. 5.2. Newton's Method for Nonlinear Systems. 5.3. MATLAB built-in functions. 5.4. Exercises. 6. Approximation of Functions. 6.1. A hypothetical example. 6.2. Global Polynomial Interpolation. 6.3. Spline Interpolation. 6.4. Approximation with Trigonometric Functions. 6.5. MATLAB built-in functions. 6.6. Exercises. 7. Numerical Differentiation. 7.1. Basic Derivative Formulae. 7.2. Derivative Formulae Using Taylor Series. 7.3. Derivative Formulae Using Interpolants. 7.4. Errors in Numerical Differentiation. 7.5. Richardson Extrapolation. 7.6. MATLAB built-in functions. 7.7. Exercises. 8. Numerical Optimization. 8.1. The need for optimization methods. 8.2. Line Search Methods. 8.3. Successive Parabolic Interpolation. 8.4. Optimization Using Derivatives. 8.5. Linear programming. 8.6. Constrained nonlinear optimization. 8.7. MATLAB built-in functions. 8.8. Exercises. 9. Numerical Quadrature. 9.1. Basic Quadrature Formulae. 9.2. Gauss Quadrature. 9.3. Extrapolation Methods: Romberg Quadrature. 9.4. Higher-Dimensional Integrals. 9.5. Monte Carlo Integration. 9.6. MATLAB built-in functions. 9.7. Exercises. 10. Numerical Solution of Differential Equations. 10.1. First-order Models. 10.2. Second-order Models. 10.3. Basic Numerical Methods. 10.4. Global error and the order of accuracy. 10.5. Consistency, Stability and Convergence. 10.6. Explicit vs. Implicit Methods. 10.7. Multistep Methods. 10.8. Higher-Order Initial Value Problems. 10.9. Boundary Value Problems. 10.10. MATLAB built-in functions. 10.11. Exercises. Appendix A. Calculus Refresher. A.1. Taylor Series. A.2. Riemann Integrals. A.3. Other Important Results. Appendix B. Introduction to Octave. B.1. The Problem of Choice. B.2. Octave Basics. B.3. Octave Code Examples. Appendix C. Introduction to Python. C.1. The problem of choice. C.2. Python Basics. C.3. Installing Python. C.4. Python Code Examples. Appendix D. Introduction to Julia. D.1. The problem of choice. D.2. Julia Basics. D.3. Julia Code Examples. Appendix E. Hints and Answers for Selected Exercises. Bibliography. Index.
Synopsis
The material requires no previous exposure to an introductory computational science class (i.e. knowledge of a programming language). All mathematical knowledge needed beyond Calculus (and the more useful Calculus notation and concepts) is introduced in the text to make it self-contained. The book will discuss operation counts, emphasize the importance of computational efficiency and highlight the basic methods used to achieve it. To this end, efficiency inserts will be used throughout the text as they become relevant., Kabra, Mansi Kabra, Mansi 2 6 2022-11-11T08:37:00Z 2022-11-11T08:37:00Z 1 236 1348 11 3 1581 16.00 true 2022-11-11T08:37:26Z Standard 2bbab825-a111-45e4-86a1-18cee0005896 2567d566-604c-408a-8a60-55d0dc9d9d6b 9573ef7f-7a2b-4c2b-a2cb-1a9ead6f545c 2 Clean Clean false false false false EN-IN X-NONE X-NONE, This book intends to serve a very broad audience of college students across a variety of disciplines. It exposes its readers to some of the basic tools and techniques used in computational science, with a view to helping them understand what happens 'behind the scenes' when simple tools are used.
LC Classification Number
QA297.S695 2022
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