9.6: Matrix Exponential, Repeated Eigenvalues
x = Ax,
A:nn
(1)
Def.: If x1(t), . . . , xn(t) is a fundamental set of solutions (F.S.S.) of (1), then X (t) = [x1(t), . . . , xn (t)] (n n) is called a f
Mert Ozbayram
Assignment week8 due 08/22/2016 at 11:59pm EEST
math219
This problem set covers basic material from section 7.9 and Chapters 3 and 4.
Variation of parameters for nonhomogeneous systems
Mert Ozbayram
Assignment week9 due 08/22/2016 at 11:59pm EEST
math219
This problem set covers advanced material from Chapters 3 and 4.
Solving higher order linear differential equations.
Variation o
Mert Ozbayram
Assignment week11 due 08/23/2016 at 11:59pm EEST
math219
This problem set covers material from Sections 7.3 7.6.
Heaviside step functions and their Laplace transforms.
Solving initial
MATH 219
Fall 2016
Lecture 2
ur Kisisel
Lecture notes by Ozg
Content: Linear equations; method of integrating factors. (section 2.1).
Suggested Problems:
2.1: 3, 6, 11, 15, 30, 33, 34
1
Linear Equati
Mert Ozbayram
Assignment week12 due 08/23/2016 at 11:59pm EEST
math219
This problem set covers material from Chapter 10.
Boundary value problems.
Eigenfunctions.
Separation of variables.
Fourier serie
MATH 219
Fall 2016
Lecture 3
ur Kisisel
Lecture notes by Ozg
Content: Modeling with first order equations. (section 2.3).
Suggested Problems:
2.3: 2, 3, 5, 13, 16, 19
1
Modeling with first order equa
MATH 219
Fall 2016
Lecture 4
ur Kisisel
Lecture notes by Ozg
Content: Differences between linear and nonlinear equations (section 2.4).
Suggested Problems:
2.4: 2, 6, 7, 10, 14, 22, 23
Recall that a
MATH 219 Introduction to Differential Equations
Credit: (4-0) 4
Catalog description: First order equations and various applications. Higher order linear differential equations.
Power series solutions.
Mert Ozbayram
Assignment week10 due 08/22/2016 at 11:59pm EEST
math219
This problem set covers material from Sections 7.1 and 7.2.
Laplace transforms of basic functions.
Inverse Laplace transforms o
Table of Annihilators and Integrals
1. The annihilator of xk is Dk+1 .
2. The annihilator of eax is D a.
3. The annihilator of xk eax is (D a)k+1 .
4. The annihilator of cos(bx) is D2 + b2 .
5. The an
KNC DERECE DENKLEMLERN SER ZM
y = a n ( x x0 ) n
n =0
kuvvet serisi
m
1) Eer bir kuvvet serisinin ksmi toplamlar dizisinin lim m a n ( x x0 ) n limiti
n =0
var ise a n ( x x0 ) n kuvvet serisine x no
LAPLACE DNM Lineer diferansiyel denklemlerin zmleri iin ok kullanlan yntemlerden birisi integral dnmleridir ve bir integral dnm
F ( s ) = K ( s, t ) f (t )dt
(1)
formundadr. Burada verilen bir f fon
7. BRNC MERTEBEDEN LNEER DENKLEM SSTEMLER MATRSLER Birinci derece lineer diferansiyel denklem sistemlerinin zmnde matris kavram ve zellikleri doal olarak ortaya kmaktadr. Bir matris A(mxn) eklinde
a1
Ch 2.1: Linear Equations; Method of Integrating Factors
A linear first order ODE has the general form
dy = f (t , y ) dt
where f is linear in y. Examples include equations with constant coefficients,
Ch 2.2: Separable Equations
In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation
dy = f ( x, y ) dx
We can rewrite this in the form
M
Ch 2.3: Modeling with First Order Equations
Mathematical models characterize physical systems, often using differential equations. Model Construction: Translating physical situation into mathematical
Ch 2.4: Differences Between Linear and Nonlinear Equations
Recall that a first order ODE has the form y' = f (t, y), and is linear if f is linear in y, and nonlinear if f is nonlinear in y. Examples:
Ch 2.5: Autonomous Equations and Population Dynamics
In this section we examine equations of the form y' = f (y), called autonomous equations, where the independent variable t does not appear explicit
Ch 2.6: Exact Equations & Integrating Factors
Consider a first order ODE of the form
M ( x, y ) + N ( x, y ) y = 0
Suppose there is a function such that
x ( x, y ) = M ( x, y ), y ( x, y ) = N ( x, y
Ch 2.7: Numerical Approximations: Eulers Method
Recall that a first order initial value problem has the form
dy = f (t , y ), y (t0 ) = y0 dt
If f and f / y are continuous, then this IVP has a unique
DFERANSYEL DENKLEMLER 2008-2009 Gz Dnemi Diferansiyel Denklemlerin Snflandrlmas Birok mhendislik, fizik ve sosyal kkenli problemler matematik terimleri ile ifade edildii zaman bu problemler, bilinmeye
MATH 219
Fall 2017
Lecture 6
ur Kisisel
Lecture notes by Ozg
Content: Introduction to systems of first order equations. Review of matrices.
Suggested Problems:
7.1: 19, 23
7.2: 1, 2, 9, 11, 16, 21, 2