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Topics. Computer Algebra Systems Input-Output Analysis Accuracy of Computations Analyzing Networks. 1.1. Computer Algebra Systems. Computer systems/packages that can do linear algebra: 1. Library of routines: LINPACK, IMSL. 2. Symbolic systems: Maple, Mathematica, Reduce, MATLAB.

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  1. Topics • Computer Algebra Systems • Input-Output Analysis • Accuracy of Computations • Analyzing Networks

  2. 1.1. Computer Algebra Systems Computer systems/packages that can do linear algebra: 1. Library of routines: LINPACK, IMSL. 2. Symbolic systems: Maple, Mathematica, Reduce, MATLAB. 3. Free packages: SciLab, MuPAD, Octave.

  3. 2. Input-Output Analysis

  4. 3. Accuracy of Computations FORTRAN code for Gaussian forward elimination: DO I = 1, N DO J = I+1, N F = A[ J, I ] / A[ I, I ] DO K = I, N A[ J, K ] = A[ J, K ]  F*A[ I, K ] ENDDO ENDDO ENDDO • Caveat Emptor: • Partial pivoting prevents errors caused by small pivots. • Solutions are unreliable for ill-conditioned systems.

  5. 4. Analyzing Networks Electrical network of a car : Highest load: Both hi-beam headlights & brake lights are on.

  6. Kirchhoff’s laws: Current Law: For any point in a network, the flow in equals the flow out. Voltage Law:Around any circuit the total drop equals the total rise. Example: Current law: Voltage law:

  7. Wheatstone bridge: Current law: Voltage law: Top node: Left leg: Left node: Right leg: Right node: Upper loop: Bottom node: Lower loop: Outer loop:

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