A tentative list of topics to be covered with
approximate dates:
Aug 25 - Sep 1:
Introductory Material (Chapter 1):
- Approximations in Scientific Computing
- Computer Arithmetic
Sep 6 - 15:
Systems of Linear Equations (Chapter 2):
- Linear Systems
- Existence & Uniqueness
- Sensitivity & Conditioning
- Solving Linear Systems
- Special Types of Linear Systems
- Software for Linear Systems
Sep 20 - 27:
Linear Least Squares (Chapter 3):
- Linear Least Squares Problems
- Existence & Uniqueness
- Problem Transformations
- Orthogonalization Methods
- Singular Value Decomposition
- Comparison of Methods
Oct 4 - 6:
Eigenvalue Problems (Chapter 4):
- Eigenvalues and Eigenvectors
- Existence and Uniqueness
Oct 11 - 18:
Nonlinear Equations (Chapter 5):
- Nonlinear Equations
- Existence & Uniqueness
- Sensitivity & Conditioning
- Convergence Rates & Stopping Criteria
- Nonlinear Equations in One Dimension
- Systems of Nonlinear Equations
Oct 20 - 25:
Optimization (Chapter 6):
- Optimization Problems
- Existence and Uniqueness
- Sensitivity and Conditioning
- Optimization in One Dimension (Newton's Method)
- Unconstrained Optimization (Steepest Descent, Newton's Method, and Conjugate Gradient)
Oct 27 - Nov 1:
Numerical Integration & Differentiation (Chapter 8):
- Numerical Quadrature
- Existence, Uniqueness, and Conditioning
- Numerical Quadrature (Newton-Cotes, Gaussian Quadrature, Composite Quadrature)
- Numerical Differentiation
- Richardson Extrapolation
- Software
Nov 8 - 17:
IVPs for Ordinary Differential Equations (Chapter 9):
- ODE's
- Existence, Uniqueness, and Conditioning
- Numerical Solution of ODEs
- Software
Nov 22 - Dec 6:
Partial Differential Equations (Chapter 11):
- Time-Dependent Problems (Finite Difference Approximations)
- Time-Independent Problems (Finite Difference Methods)
- Iterative Methods for Linear Systems
- Software
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