Lesson 5: First Order Differential Equations
Tutorials
T.1) Setting harvest rates to control the catfish population
This is a problem from an area of mathematical engineering called control theory. If your university has an
electrical engineering departm
Differential Equations&Mathematica
Authors: Bruce Carpenter, Bill Davis and Jerry Uhl 2001-2007
Publisher: Math Everywhere, Inc.
Version 6.0
DE.02 Transition from Calculus to DiffEq:
The Forced Oscillator DiffEq
y! @tD + b y @tD + c [email protected] = f @tD
LITERACY
HW 71
1. Sec. 3.6: 3. We have
x00 + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375; x0 (0) = 0:
The characteristic equation is r2 + 100 = 0 =) r =
mentary solution is
10i: The compli-
xc (t) = c1 cos 10t + c2 sin 10t:
r = 5i is not a root of the characteristi
NAME:_
NETWORK ID:_
MCB 450 Spring 2014
Exam II
March 11th, 2014
Form A
Choose the BEST answer from the available choices.
Only non-graphing calculators are permitted for use on this exa
48 iterations
Differential Equations&Mathematica
1.0
Authors: Bruce Carpenter, Bill Davis and Jerry Uhl 2001-2007
0.5
Publisher: Math Everywhere, Inc.
Version 6.0
DE.04 Modern DiffEq Issues
LITERACY
1
3
4
x
- 0.5
L.1)
When you start a car trip, you go to
:[email protected] tD,
:
at
Differential Equations&Mathematica
:
Authors: Bruce Carpenter, Bill Davis and Jerry Uhl 2001-2007
at
DE.03 Laplace Transform and Fourier Analysis
LITERACY
L.1)
Look at these calculations of
-s t
0 E f @tD t
and the Laplace transform of f
Notes on Diffy Qs
Differential Equations for Engineers
by Ji Lebl
r
July 16, 2010
2
A
Typeset in LTEX.
Copyright c 20082010 Ji Lebl
r
This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0
United States License. To view
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MATH 285 G1 Exam 2 (B)
March 18, 2016
Instructor: Pascaleff
Problem Possible Actual
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20
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20
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INS
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MATH 285 G1 Exam 3 (B)
April 18, 2016
Instructor: Pascaleff
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INSTRUCTIONS:
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20
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1
Orthogonality formulas
Z L
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MATH 285 G1 Exam 2 (A)
March 18, 2016
Instructor: Pascaleff
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20
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INS
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MATH 285 G1 Exam 3 (A)
April 18, 2016
Instructor: Pascaleff
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INSTRUCTIONS:
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1
Orthogonality formulas
Z L
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MATH 285 G1 Exam 3 (C)
April 18, 2016
Instructor: Pascaleff
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INSTRUCTIONS:
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1
Orthogonality formulas
Z L
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MATH 285 G1 Exam 1 (B)
February 17, 2016
Instructor: Pascaleff
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MATH 285 G1 Exam 1 (C)
February 17, 2016
Instructor: Pascaleff
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20
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100
NAME:
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MATH 285 G1 Exam 2 (C)
March 18, 2016
Instructor: Pascaleff
Problem Possible Actual
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20
2
20
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NAME:
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MATH 285 G1 Exam 1 (A)
February 17, 2016
Instructor: Pascaleff
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Math 285 - Intro Differential Equations,
HW 7 Solutions
Graded Problems: Sec. 9.1: 18 (3 pts), Sec. 9.2: 7 (3 pts), 12 (3 pts)
Section 9.1
13.
f (t) =
0, < t 0;
1,
0<t
1) a0 ;
1
a0 =
Z
1
f (t) dt =
Z
1 dt = 1.
0
2) an for n 1;
1
an =
Z
1
f (t) cos nt dt =
Math 285 - Intro Differential Equations,
HW 4 Solutions
Graded Problems: Sec. 3.2: 18 (2.5 pts), Sec. 3.3: 12 (2.5 pts), 20 (3 pts)
Section 3.2
18.
y = Aex + Bex cos x + Cex sin x.
Since y(0) = 1, we have A + B = 1.
Using y 0 = Aex + Bex (cos x sin x) + C
Math 285 Things to review before the semester.
Partial fractions: Be able to solve for A and B:
1
A
B
=
+
(x a)(x b)
xa xb
Properties of the exponential and the logarithmic functions:
ea+b = ea eb ;
ln (ab) = ln (a) + ln (b)
b ln (a) = ln (ab );
eln (a) =
Math 285 Practice problems to review before the
semester.
Partial fractions: Find the values of A and B for which the following
equality holds:
A
B
1
=
+
(x 2)(x 3)
x2 x3
Properties of the exponential and the logarithmic functions:
Determine which of the
Math 285 Final practice solutions
Problem 1: This is a constant coefficients equation, so we look for a solution
of the form y = erx . The characteristic equation for r is:
r5 4 r4 + 4 r3 = 0
which has solutions r = 0 (three times), and r = 2 (twice). The
Math 385 Midterm 3 practice solutions
Problem 1: This is a typical Sine Fourier series calculation (with L = 2).
The result is
X
bn sin (
n=1
where
nt
)
2
(
8 for n even
bn = 8 n 32
n3 3 for n odd
n
Problem 2: Given the forcing to this oscillator, we lo
Math 285 X1: Intro Differential Equations
Spring 2015,
Sample Exam 1
Show all of your work !
Name:
1.
(15 points)
2.
(15 points)
3.
(15 points)
4.
(15 points)
5.
(20 points)
6.
(20 points)
TOTAL:
(100 points)
1
1. Solve the following initial value problem
Math 285 X1: Intro Differential Equations
Spring 2015 Exam 2, April 8
Show all of your work !
Name:
1.
(25 points)
2.
(25 points)
3.
(25 points)
4.
(25 points)
TOTAL:
(100 points)
1
1. Find a general solution of the following nonhomogeneous differential e
Differential Equations
Authors: Bill Davis and Jerry Uhl
1996-2013
DE.01 Transition from Calculus to DiffEq:
The Exponential Differential Equation
y @tD +r [email protected] = [email protected]
BASICS
B.1) The unforced exponential differential equation, the most important differe
Differential Equations
Authors: Bill Davis and Jerry Uhl
1996-2013
DE.01 Transition from Calculus to DiffEq:
The Exponential Differential Equation
y @tD +r [email protected] = [email protected]
GIVE IT A TRY!
G.3) Visualizing the effect of the forcing functions on solutions of y
Differential Equations
Authors: Bill Davis and Jerry Uhl
1996-2013
DE.01 Transition from Calculus to DiffEq:
The Exponential Differential Equation
y @tD +r [email protected] = [email protected]
GIVE IT A TRY!
G.2) Steady state for y @tD + r [email protected] = f @tD
G.2.a.i) Steady state for
Differential Equations
Authors: Bill Davis and Jerry Uhl
1996-2013
DE.01 Transition from Calculus to DiffEq:
The Exponential Differential Equation
y @tD +r [email protected] = [email protected]
GIVE IT A TRY!
G.4) Sometimes the starter value on y[0] makes little difference; somet
Differential Equations
Authors: Bill Davis and Jerry Uhl
1996-2013
DE.01 Transition from Calculus to DiffEq:
The Exponential Differential Equation
y @tD +r [email protected] = [email protected]
GIVE IT A TRY!
Preliminary Stuff
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