Numerical Analysis Notes and Codes. XeLaTeX to compile. (option: '-shell-escape')

• 1.1: Review of Calculus
• 1.2: Round-off Errors and Computer Arithmetic
• 1.3: Algorithms and Convergence
• 1.4: Numerical Software

• 2.1 The Bisection Method
• 2.2 Fixed-Point Iteration
• 2.3 Newton's Method and Its Extensions
• 2.4 Error Analysis for Iterative Methods
• 2.5 Accelerating Convergence
• 2.6 Zeros of Polynomials and Müller's Method
• 2.7 Survey of Methods and Software

• 3.1 Interpolation and the Lagrange Polynomial
• 3.2 Data Approximation and Neville's Method
• 3.3 Divided Differences
• 3.4 Hermite Interpolation
• 3.5 Cubic Spline Interpolation
• 3.6 Parametric Curves
• 3.7 Survey of Methods and Software

• 4.1 Numerical Differentiation
• 4.2 Richardson's Extrapolation
• 4.3 Elements of Numerical Integration
• 4.4 Composite Numerical Integration
• 4.5 Romberg Integration
• 4.6 Adaptive Quadrature Methods
• 4.7 Gaussian Quadrature
• 4.8 Multiple Integrals
• 4.9 Improper Integrals
• 4.10 Survey of Methods and Software

• 5.1 The Elementary Theory of Initial-Value Problems
• 5.2 Euler’s Method
• 5.3 Higher-Order Taylor Methods
• 5.4 Runge-Kutta Methods
• 5.5 Error Control and the Runge-Kutta-Fehlberg Method
• 5.6 Multistep Methods
• 5.7 Variable Step-Size Multistep Methods
• 5.8 Extrapolation Methods
• 5.9 Higher-Order Equations and Systems of Differential Equations
• 5.10 Stability
• 5.11 Stiff Differential Equations
• 5.12 Survey of Methods and Software

• 6.1 Linear Systems of Equations
• 6.2 Pivoting Strategies
• 6.3 Linear Algebra and Matrix Inversion
• 6.4 The Determinant of a Matrix
• 6.5 Matrix Factorization
• 6.6 Special Types of Matrices
• 6.7 Survey of Methods and Software

• 7.1 Norms of Vectors and Matrices
• 7.2 Eigenvalues and Eigenvectors
• 7.3 The Jacobi and Gauss-Siedel Iterative Techniques
• 7.4 Relaxation Techniques for Solving Linear Systems
• 7.5 Error Bounds and Iterative Refinement
• 7.6 The Conjugate Gradient Method
• 7.7 Survey of Methods and Software

• 8.1 Discrete Least Squares Approximation
• 8.2 Orthogonal Polynomials and Least Squares Approximation
• 8.3 Chebyshev Polynomials and Economization of Power Series
• 8.4 Rational Function Approximation
• 8.5 Trigonometric Polynomial Approximation
• 8.6 Fast Fourier Transforms
• 8.7 Survey of Methods and Software

• 9.1 Linear Algebra and Eigenvalues
• 9.2 Orthogonal Matrices and Similarity Transformations
• 9.3 The Power Method
• 9.4 Householder’s Method
• 9.5 The QR Algorithm
• 9.6 Singular Value Decomposition
• 9.7 Survey of Methods and Software

• 10.1 Fixed Points for Functions of Several Variables
• 10.2 Newton’s Method
• 10.3 Quasi-Newton Methods
• 10.4 Steepest Descent Techniques
• 10.5 Homotopy and Continuation Methods
• 10.6 Survey of Methods and Software

• 11.1 The Linear Shooting Method
• 11.2 The Shooting Method for Nonlinear Problems
• 11.3 Finite-Difference Methods for Linear Problems
• 11.4 Finite-Difference Methods for Nonlinear Problems
• 11.5 The Rayleigh-Ritz Method
• 11.6 Survey of Methods and Software