Page 11 - Circuit Analysis II with MATLAB Applications

Appendix B

Differential Equations
Simple Differential Equations ....................................................................................................B-1
Classification ..............................................................................................................................B-3
Solutions of Ordinary Differential Equations (ODE).................................................................B-6
Solution of the Homogeneous ODE ...........................................................................................B-8
Using the Method of Undetermined Coefficients for the Forced Response.............................B-10
Using the Method of Variation of Parameters for the Forced Response..................................B-20
Exercises ...................................................................................................................................B-24

Appendix C

Matrices and Determinants
Matrix Definition ........................................................................................................................C-1
Matrix Operations.......................................................................................................................C-2
Special Forms of Matrices ..........................................................................................................C-5
Determinants...............................................................................................................................C-9
Minors and Cofactors................................................................................................................C-12
Cramer’s Rule...........................................................................................................................C-16
Gaussian Elimination Method ..................................................................................................C-19
The Adjoint of a Matrix............................................................................................................C-20
Singular and Non-Singular Matrices ........................................................................................C-21
The Inverse of a Matrix ............................................................................................................C-21
Solution of Simultaneous Equations with Matrices..................................................................C-23
Exercises ...................................................................................................................................C-30

Appendix D

Constructing Semilog Plots with Microsoft Excel
The Excel Spreadsheet Window.................................................................................................D-1
Instructions for Constructing Semilog Plots...............................................................................D-2

Appendix E

Scaling
Magnitude Scaling ...................................................................................................................... E-1
Frequency Scaling....................................................................................................................... E-1
Exercises ..................................................................................................................................... E-8
Solutions to Exercises................................................................................................................. E-9

Circuit Analysis II with MATLAB Applications v
Orchard Publications