ROUND 1 QUESTIONNAIRE
1. The first major change in UI in our mobile devices was the change from buttons to touch
screen, the next major development is said to be gesture recognition which is going to
revolutionize the way we interact with our devices. Pro
Chapter 1: Welcome to the World of Differential Equations
After first and second order differential equations, its natural to want to keep
the fun going, and that means youll be dealing with higher order differential
equations, which I also cover in Part
Chapter 1: Welcome to the World of Differential Equations
Classifying Differential Equations
Tons of differential equations exist in Math and Science Land, and the way
you tackle them differs by type. As a result, there are several classifications
that yo
16
Part I: Focusing on First Order Differential Equations
Recognizing the equilibrium value
As you can see from Figure 1-3, there are many solutions to the equation that
youre trying to solve. As it happens, the actual solution to that differential
equati
Chapter 1: Welcome to the World of Differential Equations
50
45
v
40
35
30
25
Figure 1-2:
A direction
field. 20
1
2
3
4
5
6
7
t
8
9
10
1
2
3
4
5
6
7
t
8
9
10
50
45
v
40
35
30
Figure 1-3: 25
A solution in
a direction
field. 20
15
12
Part I: Focusing on First Order Differential Equations
How about when f(x) = cx, where c is a constant? In this case, f(x) = cx, and
f(x + x) = cx + c x.
So f(x + x) f(x) = c x and (f(x + x) f(x)/x = c. Therefore:
df ^ x h
=c
dx
f ^ x h = cx
Derivative
Chapter 1: Welcome to the World of Differential Equations
Derivatives: The Foundation of
Differential Equations
As I mention in the previous section, a derivative simply specifies the rate at
which a quantity changes. In math terms, the derivative of a fu
Chapter 1: Welcome to the World of Differential Equations
Looks like prices have been going up steadily, as you can see in the graph
of the prices in Figure 1-1. With that large of a price hike, whats the price of
peanut butter going to be a year from now
I
In this part . . .
n this part, I welcome you to the world of differential
equations and start you off easy with linear first order
differential equations. With first order equations, you
have first order derivatives that are raised to the first
power,
Chapter 1
Welcome to the World of
Differential Equations
In This Chapter
Breaking into the basics of differential equations
Getting the scoop on derivatives
Checking out direction fields
Putting differential equations into different categories
Distin