Directions: Solve the following problems with complete explanations in spaces provided.
Where required provide accurate graphs.
1. Match differential equations with the corresponding slope fields. Explain.
y y (2 y )
Worksheet 1 (Sec. 1.1 and 1.2)
Directions: Provide complete solutions for the following problems.
Verify that the function y (cos x) ln(sec x tan x) is an explicit solution of the
y y tan x
Group Mini-Project 3
Professor Iaroslav Kryliouk
1) Under which circumstances did Edward Lorenz discover chaos?
2) Under which circumstances did Edward Lorenz discover chaos?
First of all, let's see what’s Chaos?
Chaos means s
variables represented gross features of the weather, such as the speed of the global
westerly wind. After being given 12 numbers to represent the weather pattern at the
starting time, the computer would advance the weather in six hour time-steps, each
9.3 Euler’s Method by Hand
Ex. 1. Given/y'=Dwith y(0)=1. Estimate y(2) using h = 0.5
Press the MATH key and press the up arrow once to get to 0:So|ver. Press ENTER.
If there is an equation entered at the top, press up arrow. Pr
4.So|ve the given IVP. Show all work
[1+1y2 +cosx—2xy]%=y(y+sinx), y(0)=1.
(Answer: xy2 —-ycosx— tan y=—1——)
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M b¥ -2 SMM/ 8mm 9.
235:, ,AAAMCWB E3: L +Cg,w_-2MO d =' d
2C15(-Gi+d®m+é(a)g LL w) M .243
cm) @ %
7.6 integration Tables Worksheet
Use the indicated entry in the Table of Integrals to evaluate the integral.
a55 an 0 A
, 2 1. Ice coéycosgxldx Formula 80
gig/f“ .9 ”$15” '1' C
2. [#413 -3 dx Formula 39 (Use u-substitution with u =2x ;
. [2 pts.) Find the general solu u .
ﬂM2—5M+4=b 31125' '/_
3+ 9'4, 4352 ’ i ‘ "
\A 4L m»
/M"pts.] Two roo .
m2 = 3 +i . What is the corresponding homogeneous linear differential equation with constant
Ml: _ L m2: 3% / L
.2. x Q A 2K
Chapter 4 Solving Differential Equations
4.1 History of a few Mathematician who worked on related Differential
4.2 Solving System of linear equations with applications
4.3 Solving System of linear equations using Matrix Notation
4.4 Euler equati
Chapter 3 Laplace equations and its applications
History of integral transform
Inverse Laplace and Unit Step Function
Dirac delta function and Constructing Differential equations
Convolution Theorem and periodic funct
Chapter 5: PDE in Aplication
5.2 PDE forms
A 2 B
C 2 D E
5.3 Review from past
a) Lagrange multiplier derivation
b) Continuity equation derivation
c) Phase Space idea and Generalized coordinates
5.4 Euler - Lag
Quiz #3 Math 2A
1- a) What must be the conditions for
b) What must be the conditions for
c) Explain why
f (t )
to have Laplace transform?
to have inverse Laplace transform?
is a good model for differentiation of
U (t a )
d) Explain why Lapl
1- Derive a formula to solve
Solve the following differential equations.
X AX F (t )
dt 3x 3 y 4
dy 2 x 2 y 1
0 0 1
X 2 0 0 X and X (0) 5
1 2 4
2-Solve for one of the solutions of the following differential equations
a ) x