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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.
 Spring '08
 KHAN
 Mechanical Engineering

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