AMS 361 Lecture 1: AMS 361 Introduction Lecture
17 May 2018
School
Department
Course
Professor
1/23/18
Tuesday, January 23, 2018
5:30 PM
1. Differential Equation (DE)
a. F (y(x), y'(x), x) =0
b. y(x) is not needed but y'(x) is needed
i. y(x) is dependent variable (DV)
ii. X is independent variable (IV)
# IV
1
2
# DV
1
Ordinary DE (70%)
Partial DE (6%)
2
System of ordinary DE's (19%)
System of Partial DE's (5%)
2. Linear vs. Nonlinear equations
a. Nonlinear (There is an exponent other than 1 in the dependent
variable)
b. Linear
c. Linear
d. Nonlinear
e. Nonlinear
f. Nonlinear
g. Nonlinear
3. First Order vs. Higher Order
a. 2nd Order
b. 1st Order
c. 3rd Order
4. Homogeneous vs. Inhomogeneous DE
a. Homogeneous (The exponents in each term add up to
4)
b. Homogeneous
c. Inhomogeneous
5. Solution: A function that satisfies a DE
a.
i. is a solution
ii. is a solution
6. General Solution: A family of solutions with a constant
7. Particular Solution
8. Singular Solution
