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09-DiffEQs

Differential equations express derivatives of function as functions of y, for example, dy/dx = 3y .

Chapter 9 - Differential Equations

 

9.1 Modeling with Differential Equations

·    Equations involving derivatives.

·    Verbal descriptions are translated into equations involving derivatives and vice versa.

·    Contrasting the solution of an Initial Value Problem with the general solution of a differential equation.

·    Solving logistic differential equations and using them in modeling.

It turns out that natural world can be described using equations using derivatives. How do we interpret these differential equations?
 
 
 

9.2 Slope Fields and Euler's Method

·    Geometric interpretation of DiffEQs via slope fields and the relationship between slope fields and solution curves of DiffEQs.

How can we graphically analyze and interpret differential equations? How can we study them numerically using technology?
 



9.3 Separable Equations

·    Solving separable DiffEQs and using them in modeling.

·    In particular, studying the equation and exponential growth.

·    The importance of the constant of integration.

How do we find the exact solution to a differential equation analytically?
 

6.5 Exponential Growth and Decay

·    The equation y'=ky and exponential growth.

·    The importance of the sign of the growth constant k.

What does exponential growth/decay mean? What are examples of exponential growth and decay from nature?
 
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9A [u9.1: 1, 3, 5, 7, 9, 11, 13] and [u9.2: 1, 3, 7, 9, 13, 27] 
9B [u9.3: 1, 3, 9, 13, 19, 21, 23, 29, 39, 45] 
9C [u6.2: 3,5,9,11,13,15]  
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Nikhil Joshi,
Mar 13, 2014, 11:39 AM
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Nikhil Joshi,
Mar 27, 2018, 12:02 PM