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Unformatted text preview: and bring lecture slides to the lecture. Print Do “Exercises” given at the end of each lecture. Do Do homework every week. Do Read the textbook and the slides. Read Make use of instructor’s office hours. Make If you want to get a very good grade… If Read the textbook thoroughly. Read Read optional references too. Read Do more than given “Exercises”. Do Exercises” Use and be familiar with Matlab. Use Matlab. Complex Numbers Complex Add, Subtract, Multiply, Divide Add, Linear Algebra Linear Matrix Multiply, Inverse, Sets of Linear Eq. Matrix Linear Ordinary Differential Equations Linear Laplace Transform to Solve ODE’s Laplace ODE’ Linearization Linearization Logarithms Logarithms Modeling of Physical Systems Modeling Mechanical, Electrical, Thermal, Fluid Mechanical, Dynamic Responses Dynamic 1st and 2nd Order Systems of ODE’s 1st ODE’ 5 6 Complex Numbers Prerequisites: Complex Numbers Ordered pair of two real numbers Ordered Euler’s identity Euler Conjugate Conjugate Addition Addition Polar form Polar Magnitude Magnitude Phase Phase Multiplication Multiplication 7 8 Logarithm Laplace transform The logarithm of x to the base b is written The The logarithm of 1000 to the base 10 is 3, i.e., The One of most important math tools in the course! One Definition: For a function f(t) (f(t)=0 for t<0), Definition: Properties: Properties: (s: complex variable) f(t) 0 t F(s) Why? We denote Laplace transform of f(t) by F(s). We 9 Summary & Exercises Prerequisites Prerequisites Complex numbers, Linear Algebra, Logarithm, Complex Laplace transform Dynamics Dynamics Next Next Introduction Introduction Exercises Exercises Buy the course textbook and keep it! Buy Review today’s slides on complex numbers and Review today’ logarithm Read Chapter 1 and 2 of the textbook. Read 11 10...
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This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.

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