Chapter 1 Mathematical Preliminaries and Error Analysis
Section 1.1 Review of Calculus and Taylor's Theorem
Section 1.2 Round-off Errors and Computer Arithmetic
Section 1.3 Convergence and Algorithms
Chapter 2 Solutions of Equations
Section 2.1 The Bisection Method
Section 2.2 Fixed-Point Iteration
Section 2.3 The Newton-Raphson Method and Its Extensions
Section 2.4 Error Analysis for Iterative Methods
Chapter 6 Direct Methods for Solving Linear Systems
Section 6.1 Gaussian Elimination for Linear Systems of Equations
Section 6.2 Pivoting Strategies
Section 6.3 & 6.4 Matrix Inversion and The Determinant
Section 6.5 Matrix Factorization
Section 6.6 Factorization of Special Types of Matrices
Chapter 7 Iterative Techniques in Matrix Algebra
Section 7.1 Norms of Vectors and Matrices
Section 7.2 Eigenvalues and Eigenvectors
Section 7.3 The Jacobi and Gauss-Seidel Iterative Techniques
Section 7.4 Relaxation Techniques (i.e. SOR iterative method)
Chapter 3 Iterpolation
Section 3.1 Interpolation and Lagrange Polynomials
Section 3.3 Divided Differences
Section 3.4 Hermite Interpolation
Section 3.5 Cubic Spline Interpolation
Chapter 8
Section 8.1 Discrete Least Squares Approximation