Ordinary Differential Equations for Scientists and Engineers
MATH 331

Fall 2015
Math 331
Page 1 of 7
Homework Assignment 7
Notes: Try to answer all the questions by demonstrating all the steps of
your calculations, and return your answers (including this homework sheet)
back to t
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
HOMEWORK 01 DUE ON OCTOBER 7TH
ORDINARY DIFFERENTIAL EQUATION, FALL 2016
Instructions : (1) Homework must be written up on paper; (2) Please show all
your work; (3) 5 problems will be randomly chosen
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Fall 2015
Suggested Exercises II
October 23, 2015
Find general solution
1. xy + y = x3
y
y + x = x2 (y x3 )dx + xdy = 0
My = 1, Nx = 1 Exact
4
(y x3 )dx = yx x + h(y) =
4
y = x + h (y) = x
= yx
2.
x4
4
= (r
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Fall 2015
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Ordinary Differential Equations for Scientists and Engineers
MATH 331

Fall 2015
I
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Section 2.8: Modeling: Forced Oscillations.
Resonance
March 711, 2016
1 / 23
Forced Oscillations of motions of a massspring system
The forced oscillations is modeled by the nonhomogeneous ODE
my + c
Section 2.4: Modeling of Free Oscillations of a
MassSpring System
February 2226, 2016
1 / 20
Summary
Free Oscillations of a MassSpring System:
Undamped MassSpring System
Damped MassSpring System:
Cas
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
HOMEWORK 03 DUE ON OCTOBER 26TH
ORDINARY DIFFERENTIAL EQUATION, FALL 2016
Instructions : (1) Homework must be written up on paper; (2) Please show all
your work; (3) 5 problems will be randomly chosen
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
HOMEWORK 01 DUE ON SEPTEMBER 23RD
ORDINARY DIFFERENTIAL EQUATION, FALL 2016
Instructions : (1) Homework must be written up on paper; (2) Please show all
your work; (3) 5 problems will be randomly chos
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
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Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
Homework 6, M 331.2
due 10/26/16
Please hand in your home work before class, have it neatly written, organized
(the grader will not decipher your notes), stapled, with your name and student ID
on top.
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Summer 2014
EE114/EE214A, Autumn 2017
Course Information
General Information
Course: EE114/EE214A, Fundamentals of Analog Integrated Circuit Design
Lectures: Tue & Thu, 10:3011:50am, Gates B01
Review Session: Fri
Section 1.5. Linear ODEs. Bernoulli Equation.
Population Dynamics
February 2, 2016
1 / 20
Summary
Linear firstorder ODE: Homogeneous Linear ODE and
Nonhomogeneous Linear ODE
Reduction to Linear Form.
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Spring 2015
Jinguo Lian
Math331 Notes
November 5, 2014
6.3
Unit Step Function(Heaviside Function).
Second Shifting Theorem(tShifting)
In this section, we shall now reach the point where the Laplace transform met
Ordinary Differential Equations for Scientists and Engineers
MATH 331

Spring 2015
Jinguo Lian
Math331 Notes
September 8, 2014
1.2
1.2.1
Directional Fields and Eulers Method
Preliminary
The tangent line to an implicit function
2 2
Find the tangent line to the circle x + y = 1 at the