DSP Undergradref - EEL 3105 Analytical Methods in EE Topic...

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Unformatted text preview: EEL 3105 Analytical Methods in EE Topic 6: Linear Differential Equations Dr. Liuqing Yang Department of ECE University of Florida http://www.yang.ece.ufl.edu Dr. Liuqing Yang Outline • Differential Equations Basics • Solution of Linear Differential Equations • Constant-Coefficient Linear Differential Equations 2 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Roadmap • Differential Equations Basics – Definition and Classification – Examples – Solutions and Initial Conditions • Solution of Linear Differential Equations • Constant-Coefficient Linear Differential Equations 3 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Definition and Classification 4 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Ordinary vs. Partial 5 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Linear vs. Nonlinear 6 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Solutions and Initial Conditions 7 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Roadmap • Differential Equations Basics • Solution of Linear Differential Equations – Problem Setup and Notation – Principle of Superposition – Complementary Solution and Particular Solution • Constant-Coefficient Linear Differential Equations 8 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Problem Setup and Notation 9 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Special Cases 10 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Uniqueness of Solution 11 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Principle of Superposition 12 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Complementary Solution and Particular Solution 13 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Complementary Solution 14 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Particular Solution 15 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Roadmap • Differential Equations Basics • Solution of Linear Differential Equations • Constant-Coefficient Linear Differential Equations (CCLDE) – Complementary Solution – Particular Solution 16 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Eigenfunctions of CCLDE 17 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Complementary Solution: Method 18 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Complementary Solution: Result 19 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Particular Solution: Method of Undetermined Coefficients 20 © Dr. Liuqing Yang, University of Florida Dr. Liuqing Yang Undetermined Coefficients: The General Method 21 © Dr. Liuqing Yang, University of Florida ...
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This note was uploaded on 09/17/2009 for the course EEL 5525 taught by Professor Yang during the Fall '09 term at University of Florida.

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