* This is about wave equation on the whole domain from Chapter 2. Given a domain
D = (, ) (0, ), we denote wave equation by
utt = c2 uxx on D,
(W )c .
(1) (TP38-Exc1) Solve (W )c with datum
u(x, 0) = ex , ut (x, 0) = sin x, x R.
(2)
Let c2 = T /. Solve (W

* This is about wave equation on the whole domain from Chapter 2. Given a domain
D = (, ) (0, ), we denote wave equation by
utt = c2 uxx on D,
(W )c .
(1) (TP38-Exc1) Solve (W )c with datum
u(x, 0) = ex , ut (x, 0) = sin x, x R.
Proof.
1
1
u = (ex+ct + ex

MA3512: Partial Differential Equations
Fall 2015
Lecture 6: Maximum Principle & Fourier Series (I)
Lecturer: Xianpeng Hu
Dates: October 9
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be d

MA3512: Partial Differential Equations
Fall 2015
Lecture 3: Wave Equation (II): Separation of Variables
Lecturer: Xianpeng Hu
Dates: September 18
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They

MA3512: Partial Differential Equations
Fall 2015
Lecture 4: Heat Equation (I)
Lecturer: Xianpeng Hu
Dates: September 25
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside

MA3512: Partial Differential Equations
Fall 2015
Lecture 1: Introduction to PDEs
Lecturer: Xianpeng Hu
Dates: September 4
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outsi

MA3512: Partial Differential Equations
Fall 2015
Lecture 11: Fourier Transform and Laplace Transform
Lecturer: Xianpeng Hu
Dates: November 20
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may

MA3512: Partial Differential Equations
Fall 2015
Lecture 5: Heat Equation (II)
Lecturer: Xianpeng Hu
Dates: October 2
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside t

MA3512: Partial Differential Equations
Fall 2015
Lecture 8: Poissons Equation (I)
Lecturer: Xianpeng Hu
Dates: October 23
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outsi

MA3512: Partial Differential Equations
Fall 2015
Lecture 9: Poisson Equations (II)
Lecturer: Xianpeng Hu
Dates: October 30
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outs

MA3512: Partial Differential Equations
Fall 2015
Lecture 2: Wave Equation (I)
Lecturer: Xianpeng Hu
Dates: September 11
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside

MA3512: Partial Differential Equations
Fall 2015
Lecture 7: Fourier Series (II)
Lecturer: Xianpeng Hu
Dates: October 16
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distributed outside

MA3512: Partial Differential Equations
Fall 2015
Lecture 10: General Eigenvalue Problems
Lecturer: Xianpeng Hu
Dates: November 6
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal
publications. They may be distribute