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Overview

Reference: Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10th Edition, 2016.

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Course Coverage

Those chosen are homework coverage.

  • Chapter 1: Mathematical Preliminaries
    • 1.2 Roundoff Errors and Computer Arithmetic
    • 1.3 Algorithms and Convergence
  • Chapter 2, 6, 7, 5
    • Chapter 2: Solutions of Equations in One Variable
      • 2.1 The Bisection Method
      • 2.2 Fixed-Point Iteration
      • 2.3 Newton's Method
      • 2.4 Error Analysis for Iterative Methods
      • 2.5 Accelerating Convergence
    • Chapter 6: Direct Methods for Solving Linear Systems
      • 6.1 Linear Systems of Equations
      • 6.2 Pivoting Strategies
      • 6.5 Matrix Factorization
      • 6.6 Special Types of Matrices
    • Chapter 7: Iterative Techniques in Matrix Algebra
      • 7.1 Norms of Vxectors and Matrices
      • 7.2 Eigenvalues and Eigenvectors
      • 7.3 The Jacobi and Gauss-Seidel Iterative Techniques
      • 7.4 Relaxation Techniques for Solving Linear Systems
      • 7.5 Error Bounds and Iterative Refinement
    • Chapter 5: Initial-Value Problems for Ordinary Differential Equations
      • 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
      • 5.9 Higher-Order Equations and Systems of Differential Equations
      • 5.10 Stability
  • Chapter 3, 9, 8, 4
    • Chapter 9: Approximating Eigenvalues
      • 9.2 The Power Methods
    • Chapter 3: Interpolation and Polynomial Approximation
      • 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
    • Chapter 8: Approximation Theory
      • 8.1 Discrete Least Squares Approximation
      • 8.2 Orthogonal Polynomials and Least Squares Approximation
      • 8.3 Chebyshev Polynomials and Economization of Power Series
    • Chapter 4: Numerical Differentiation and Integration
      • 4.1 Numerical Differentiation
      • 4.3 Elements of Numerical Integration
      • 4.4 Composite Numerical Integration
      • 4.5 Romberg Integration
      • 4.2 Richardson's Extrapolation
      • 4.6 Adaptive Quadrature Methods
      • 4.7 Gaussian Quadrature