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DAY # |
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TOPICS |
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READINGS* |
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ASSIGNMENTS |
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1 |
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Introduction
Computer Architecture
Number Representations
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1.1 - 1.2 |
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2 |
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Recursion
Numerical Instability
Errors of Simple Arithmetic Operations |
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1.2 - 1.3 |
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3 |
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Error Propagation
Error Estimation
Condition Numbers |
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1.3 |
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4 |
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Linear Systems of Equations: Cramer's rule
Gaussian Elimination |
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3.1 - 3.2 |
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# 1 |
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5 |
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Linear Systems: Gaussian Elimination
Pivoting
LU Factorization |
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3.3 - 3.4
3.6 |
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# 2 |
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6 |
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Linear System: Error Analysis
Condition Numbers for Linear Systems |
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3.4 |
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7 |
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Linear Systems: Iterative Methods
Convergence of Iterative Schemes. |
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3.7 |
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# 3 |
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8 |
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Roots of Non-Linear Equations: Bisection
Newton-Ralphson Iteration |
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2.1 - 2.4 |
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9 |
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Interpolation of Functions by Polynomials
Lagrange Interpolation. |
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4.1 - 4.3 |
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# 4 |
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10 |
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Interpolation: Triangular Family of Polynomials. |
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4.4 |
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11 |
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Numerical Differentiation and Integration
Error Estimates |
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6.1 - 6.2
7.1 - 7.3
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# 5 |
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12 |
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Ordinary Differential Equations
Initial Value Problems: Euler and Runge-Kutta Methods |
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9.1 - 9.2
9.4 - 9.5 |
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13 |
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In-Class Exam |
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*All readings cited above are from the course text: Mathews, J. H., and K. D. Fink. Numerical Methods using MATLAB®. 3rd ed. Prentice Hall, 1999.
MATLAB® is a trademark of The MathWorks, Inc.