MATH 310: Applied Linear Algebra

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Sample Applications of Linear Algebra

This page contains links to a number of single-page handouts, one corresponding to the material for each of the 15 weeks of the semester. Each contains a sample of how the linear algebra material is used in other science and engineering disciplines; mainly they are taken (with permission) from the actual textbooks used in those higher courses at UIC.

Week 1: Linear systems--used for electrical networks
Week 2: General solution---as Total Response in Circuits
Week 3: Matrix algebra in electrical networks
Week 4: Determinants used for spanning trees in networks
Week 5: Subspaces used for "superposition" in physics
Week 6: Linear dependence used for dropping nodes in networks
Week 7: "Fourier" basis used for signals in applications
Week 8: Linear transformations used for differential operators in circuits
Week 9: Orthogonality used for Hermite polynomials in quantum mechanics
Week 10: Orthogonal projections used for Fourier coefficients of signals
Week 11: QR-factorization used for eigenvalue problems
Week 12: Linear DIFFERENTIAL systems used for electrical networks
Week 13: Diagonalization "versus" Laplace transforms for differential systems
Week 14: Positive semi-definite quadratic forms for power in networks
Week 15: Positive matrices used for impedance and admittance in networks

These handouts were developed by Professor Steven Smith, with assistance from many faculty in other departments. The project was supported by a summer 1994 grant from the Office of the Vice Chancellor for Academic Affairs, through the Council for Effective Teaching and Learning.