Introduction to Scientific Computing and Data Analysis

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction to Scientific Computing

   • Mark H. Holmes

   Pages 1-29

3. Solving A Nonlinear Equation

   • Mark H. Holmes

   Pages 31-70

4. Matrix Equations

   • Mark H. Holmes

   Pages 71-120

5. Eigenvalue Problems

   • Mark H. Holmes

   Pages 121-181

6. Interpolation

   • Mark H. Holmes

   Pages 183-229

7. Numerical Integration

   • Mark H. Holmes

   Pages 231-274

8. Initial Value Problems

   • Mark H. Holmes

   Pages 275-325

9. Optimization

   • Mark H. Holmes

   Pages 327-396

10. Data Analysis

    • Mark H. Holmes

    Pages 397-451

11. Back Matter

    Pages 453-497

    PDF

This textbook provides and introduction to numerical computing and its applications in science and engineering.  The topics covered include those usually found in an introductory course, as well as those that arise in data analysis.  This includes optimization and regression based methods using a singular value decomposition.  The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science.  The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used.  The MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.

• Scientific Computing
• Data Analysis
• Optimization
• Interpolation
• Nonlinear Equations
• Numerical Linear Algebra
• Numerical Integration
• Singular Value Decomposition
• Conjugate Gradient Method
• partial differential equations

“The material is accompanied by many examples, exercises, as well as diagrams and tables of resulting data which are produced by MATLAB for which the programs are available on the author's website. The book is intended for beginners in scientific computing with basic knowledge in calculus, matrix algebra, and differential equations. … a good reading for the more advanced scientific engineer or lecturer in this field who may find numerous suggestions for working or teaching.” (Gudula Rünger, zbMATH 1368.65002, 2017)

• Department of Mathematical Sciences, Rensselaer Polytechnic University, Troy, USA

  Mark H. Holmes

Mark Holmes is a Professor at Rensselaer Polytechnic Institute.  His current research interests include mechanoreception and sleep-wake cycles. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.

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