Electrical Circuits and Applications of Matrix Methods: Analysis of Linear Circuits (UMAP)
Author: Sister Mary K. Keller
A unit that exposes the students to several concepts: 1) to be able to construct a system of equations representing an electrical circuit using three laws of circuits; 2) use a computer program to test a system of equations for consistency and to find a unique solution for a system of equations if one exists; and 3) recognize that a system of equations may be over-determined and still have a unique solution.
Table of Contents:
1. ELECTRICAL CIRCUITS
1.1 Introduction
1.2 Laws for Electrical Circuits
1.3 Solving Linear Systems Using an Inverse Matrix
1.4 Consistent and Inconsistent Systems of Linear Equations
1.5 Existence Theorems
1.6 Experiment I
1.7 Experiment II
1.8 Model Exam for Unit 108
2. APPLICATIONS OF MATRIX METHODS: ANALYSIS OF LINEAR CIRCUITS
2.1 Challenge Problem
2.2 Elementary Row Operations
2.3 Exercises Using Elementary Row Operations
2.4 Row Equivalence
2.5 Row Echelon Matrices
2.6 Using Row Echelon Form to Solve Systems of Equations
2.7 Experiment I
2.8 Electrical Circuits Revisited
2.9 An Example of an Electrical Circuit
2.10 Matrix Algebra Applied to Circuit Analysis
2.11 Experiment II
2.12 Model Exam for Unit 112
3. ANSWERS TO MODEL EXAM (U108)
4. ANSWERS TO SOME EXERCISES FROM UNIT 112
5. ANSWERS TO MODEL EXAM (U112)
APPENDIX A
Mathematics Topics:
Application Areas:
Prerequisites:
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