# [MATH 4B] - Midterm Exam Guide - Comprehensive Notes for the exam (16 pages long!)

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6 Feb 2017
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UCSB
MATH 4B
MIDTERM EXAM
STUDY GUIDE
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Order of 

 is 1
Order of ODE = the order of the highest derivative that appears
System of ODEs = collection of several ODEs involving a number of unknown functions
What is an Ordinary Differential Equation?
Physical laws are often stated in terms of rates of change --> derivatives
Why Study ODEs?
"y is a function whose derivative is equal to x"
Trying to find y
Solution:  
 


 
with
 
 


 
 
  
Suppose is a continuous function
Ie.   
 
 



 
Examples of ODEs
 
-->
 
 
 
-->
 
 
 
-->
 
 


 
 
The most general ODE of first order has the form:
General First Order ODEs
 
 
for all     
What is a Solution of an ODE?
Linear in terms of y
First Order Linear ODEs
Lecture 1
Tuesday, January 10, 2017
2:00 PM
MATH 4B Page 1
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Linear in terms of y
The function   defines a slope/direction field
Geometric Interpretation of ODEs -- Direction Fields
Lecture 1
MATH 4B Page 2
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