LECTURE 4, LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS
PO-NING CHEN
Today we will learn the classification of first order equation and learn how to solve the
inear first order equation
y 0 + p(x)y = q(x
Lecture 3
Linear equation
Topics for today
Today, we will learn the following topics:
(1) Classification of first order equations.
(2) Linear first order equations
Classification of first order equati
Lecture 15
Variation of Parameter
Mar 7th, 2017
Outline
Today, we use the method of Variation of Parameter to solve
y 00 + p1 (x)y 0 + p2 (x)y = q(x)
where p1 (x), p2 (x) and q(x) can be arbitrary fun
LECTURE 4, LINEAR EQUATION AND BERNOULLI EQUATION
PO-NING CHEN
Today we derive the formula for the solution of
y 0 + p(x)y = q(x)
(1)
(2)
(3)
(4)
The general formula
Some examples
Initial value proble
Lecture 7
Exact equation
Jan 31, 2017
Exact equation
Today, we begin our discussion on exact equation. Here are the topics for
today
1
Partial Derivatives
2
Implicit differentiation using partial deri
LECTURE 10: 2ND ORDER HOMOGENOUS EQUATION WITH
CONSTANT COEFFICIENT.
PO-NING CHEN
Today, we will learn to solve 2nd order homogenous equation with constant coefficient
y 00 + ay 0 + by = 0
using the c
Lecture 4
Linear equation and
Bernoulli equation.
Topics for today
Today, we will cover the following topics:
(1) Formula for solution of linear equations.
(2) Initial Value Problems for linear equat
Lecture 12
Complex root
Feb 23, 2017
Outline
In this lecture, we will solve
y 00 + ay 0 + by = 0
assuming
r 2 + ar + b = 0,
has complex roots.
Lecture 12 Complex root
Feb 23, 2017
2 / 17
Polynomials w
LECTURE 5: SEPARABLE EQUATION
PO-NING CHEN
Today we will first review the Bernoulli equation and then we will derive the general
solutions of the separable equations.
y0 =
(1)
(2)
(3)
(4)
(5)
F (x)
G(
LECTURE 2, WHAT IS DIFFERENTIAL EQUATION?
PO-NING CHEN
Here are the things we will learn today:
(1)
(2)
(3)
(4)
(5)
(6)
What is a differential equation?
What is an ordinary differential equation?
What
Math 46 Sec 1
Ordinary Differential Equation
What is a differential Equation?
We learned a lot about solving equations in pre-calculus
and calculus. For example, we learned to solve
x^2+ 3x+2=0
or
sin
Lecture 16
Higher order linear equation
Mar 8, 2016
Outline
Today, we introduce higher order linear equation.
We will first go over the general theory of higher order linear equation and
homogenous eq
Lecture 11
Repeated root and reduction of order
Feb 21, 2017
Outline
Last time, we studied 2nd order linear equation with constant coefficients
y 00 + ay 0 + by = 0
where the characteristic equation
r
Lecture 17
Homogenous equation with constant coefficient
Mar 14, 2017
Outline
In this lecture, we look at homogenous equation with with constant
coefficients.
Namely, we study equations of the followi
Lecture 6
Homogeneous equation.
Topics for today
Today, we will solve the homogenous equation
y=f(y/x)
(1) Some examples
(2) General Solution and more examples
General Solution
We also observed that
Lecture 9
Integrating factor for non-exact equation
Feb 14, 2017
Exact equation
We will look at what we can do if the differential equation is not exact.
In the second half of the class, we will begin
Lecture 8
Exact equation II
Feb 2, 2017
Exact equation
Today, we will finish our discuss on exact equation.
We will first see how it relates to what we learned about solving linear
equation and separa
Lecture 2
What is a differential
equation?
Topics for today
Today, we will learn the following topics:
(1) What is a differential equation?
(2) What is a solution?
(3) Particular solution and general
Lecture 14
Method of undetermined coefficients
Mar 2, 2017
Outline
Today, we use the method of undetermined coefficients to solve
y 00 + ay 0 + by = q(x)
where q(x) is either a exponential function, p
Lecture 5
Separable equation.
Topics for today
Today, we will solve the separable equation
y= F(x)/ G(y)
(1) General Solution.
(2) An example related to linear equation
(3) More examples and initial