Introduction to Computational Engineering with MATLAB®

1. MATLAB Programming. 1.1. The MATLAB Development Environment. 1.2. Variables and Values. 1.3. MATLAB Scripts. 1.4. Input and Output. 1.5. For Loops. 1.6. Control Constructs. 1.7. Vectors and Matrices in MATLAB. 1.8. MATLAB Functions. 1.9. Functions Operating on Vectors. 1.10. Importing Data Into MATLAB. 1.11. Text Strings in MATLAB. 1.12. Exercises. 2. Graphical Data Analysis. 2.1. Using the Plot Tool. 2.2. Basic Line Plots. 2.3. 3-D Plots. 2.4. Exercises. 3. Statistical Data Analysis. 3.1. Introduction to Statistics. 3.2. Common Statistical Functions. 3.3. Moving Window Statistics. 3.4. Probability Distributions. 3.5. Generating Random Numbers. 3.6. Statistics on Matrices. 3.7. Plots of Statistical Data. 3.8. Central Limit Theorem. 3.9. Sampling and Confidence Intervals. 3.10. Statistical Significance. 3.11. Exercises. 4. Using the Symbolic Math Toolbox. 4.1. Throwing a Ball Up. 4.2. Symbolic Algebra. 4.3. Symbolic Calculus. 4.4. Symbolic Differential Equations. 4.5. Exercises. 5. Introduction to Linear Algebra. 5.1. Working with Vectors. 5.2. Working with Matrices. 5.3. Geometric Transforms. 5.4. Systems of Linear Equations. 5.5. Elimination. 5.6. LU Decomposition. 5.7. Linear System Applications. 5.8. Under-determined Systems. 5.9. Over-determined Systems and Vector Projections. 5.10. Least Squares Regression. 5.11. Left-Divide Operator. 5.12. Exercises. 6. Application of Eigenvalues and Eigenvectors. 6.1. Introduction to Eigenvalues and Eigenvectors. 6.2. Eigenvector Animation. 6.3. Finding Eigenvalues and Eigenvectors. 6.4. Properties of Eigenvalues and Eigenvectors. 6.5. Diagonalization and Powers of A. 6.6. Change of Basis and Difference Equations. 6.7. Systems of Linear ODEs. 6.8. Singular Value Decomposition (SVD). 6.9. Principal Component Analysis (PCA). 6.10. Eigenvector Animation Code. 6.11. Exercises. 7. Computational Numerical Methods. 7.1. Optimization. 7.2. Data Interpolation. 7.3. Numerical Differentiation. 7.4. Numerical Integration. 7.5. Numerical Differential Equations. 7.6. Exercises. A. Linear Algebra Appendix. B. The Number e. Bibliography. Index.