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Using R for numerical analysis in science and engineering

By: Bloomfield, Victor A.
Material type: materialTypeLabelBookSeries: Chapman &​ Hall/​CRC the R series. Publisher: Boca Raton CRC Press 2014Description: xxii, 335 p.ISBN: 9781439884485.Subject(s): Science - Data processing | Engineering - Data processing | Numerical analysis | R - Computer program language | Mathematics - General | Mathematics - Number systems | Mathematics - Probability and statistics - GeneralDDC classification: 518.02855133 Summary: Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R. (https://www.crcpress.com/Using-R-for-Numerical-Analysis-in-Science-and-Engineering/Bloomfield/9781439884485)
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Table of Contents:

1. Introduction
1.1. Obtaining and Installing R
1.2. Learning R
1.3. Learning Numerical Methods
1.4. Finding Help
1.5. Augmenting R with Packages
1.6. Learning More about R

2. Calculating

2.1. Basic Operators and Functions
2.2. Complex Numbers
2.3. Numerical Display, Round-Off Error, and Rounding
2.4. Assigning Variables
2.5. Relational Operators
2.6. Vectors
2.7. Matrices
2.8. Time and Date Calculations

3. Graphing

3.1. Scatter Plots
3.2. Function Plots
3.3. Other Common Plots
3.4. Customizing Plots
3.5. Error Bars
3.6. Superimposing Vectors in a Plot
3.7. Modifying Axes
3.8. Adding Text and Math Expressions
3.9. Placing Several Plots in a Figure
3.10. Two- and Three-Dimensional Plots
3.11. The Plotrix Package
3.12. Animation
3.13. Additional Plotting Packages

4. Programming and Functions

4.1. Conditional Execution: If and If Else
4.2. Loops
4.3. User-Defined Functions
4.4. Debugging
4.5. Built-in Mathematical Functions
4.6. Special Functions of Mathematical Physics
4.7. Polynomial Functions in Packages
4.8. Case Studies

5. Solving Systems of Algebraic Equations

5.1. Finding the Zeroes of a Polynomial
5.2. Finding the Zeroes of a Function
5.3. Systems of Linear Equations: Matrix Solve
5.4. Matrix Inverse
5.5. Singular Matrix
5.6. Overdetermined Systems and Generalized Inverse
5.7. Sparse Matrices
5.8. Matrix Decomposition
5.9. Systems of Nonlinear Equations
5.10. Case Studies

6. Numerical Differentiation and Integration

6.1. Numerical Differentiation
6.2. Numerical Integration
6.3. Symbolic Manipulations in R
6.4. Case Studies

7. Optimization

7.1. One-Dimensional Optimization
7.2. Multi-Dimensional Optimization with Optim()
7.3. Other Optimization Packages
7.4. Optimization with Constraints
7.5. Global Optimization with Many Local Minima
7.6. Linear and Quadratic Programming
7.7. Mixed-Integer Linear Programming
7.8. Case Study

8. Ordinary Differential Equations

8.1. Euler Method
8.2. Improved Euler Method
8.3. deSolve Package
8.4. Matrix Exponential Solution for Sets of Linear ODEs
8.5. Events and Roots
8.6. Difference Equations
8.7. Delay Differential Equations
8.8. Differential Algebraic Equations
8.9. rootSolve for Steady State Solutions of Systems of ODEs
8.10. bvpSolve Package for Boundary Value ODE Problems
8.11. Stochastic Differential Equations: Gillespiessa Package
8.12. Case Studies

9. Partial Differential Equations

9.1. Diffusion Equation
9.2. Wave Equation
9.3. Laplace’s Equation
9.4. Solving PDEs with the Reactran Package
9.5. Examples with the Reactran Package
9.6. Case Studies

10. Analyzing Data

10.1. Getting Data into R
10.2. Data Frames
10.3. Summary Statistics for a Single Data Set
10.4. Statistical Comparison of Two Samples
10.5. Chi-Squared Test for Goodness of Fit
10.6. Correlation
10.7. Principal Component Analysis
10.8. Cluster Analysis
10.9. Case Studies

11. Fitting Models to Data

11.1. Fitting Data with Linear Models
11.2. Fitting Data with Nonlinear Models
11.3. Inverse Modeling of ODEs with the FME Package
11.4. Improving the Convergence of Series: Padé and Shanks
11.5. Interpolation
11.6. Time Series, Spectrum Analysis, and Signal Processing
11.7. Case Studies

Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also:

Explains how to statistically analyze and fit data to linear and nonlinear models
Explores numerical differentiation, integration, and optimization
Describes how to find eigenvalues and eigenfunctions
Discusses interpolation and curve fitting
Considers the analysis of time series

Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.


(https://www.crcpress.com/Using-R-for-Numerical-Analysis-in-Science-and-Engineering/Bloomfield/9781439884485)

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