The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Lecture 46
II.Fourier Series
PHYS2124 Mathematical Methods in Physics I
PHYS2124 Mathematical Methods in Physics I
GyuBoong Jo
II.Fourier Series
GyuBoong Jo
1 / 31
Periodic Functions in Physics I
? Def.
The function f (x) is periodic if f (x + p) = f (
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Assignment #1 PHYS 2124 Mathematical Methods in Physics ( I):
Due: Feb. 18 2014
Problem 1
Find each of the following in x + iy form. (4pt each)
(a) sin(i ln i) (b) ei/4+(ln 2)/2 (c) cosh(2i) (d) (1)sin i
1+i
)
(e) ln( 1i
Problem 2
Find the disk of converg
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Assignment #3P HYS 2124 Mathematical Methods in Physics ( I):
Due: March 11 2014
In order to put his system into mathematical form at all, Newton had to devise the concept of differential
quotients and profound the laws of motion in the form of differenti
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Assignment #2 P HYS 2124 Mathematical Methods in Physics ( I):
Due: Feb. 27 2014
II. Fourier Seires
Problem 1
Expand the periodic functions (defined on the interval [, ] in a sinecosine Fourier series.
(5pt each)
(a)
(b)
f (x) = (1 + x) for < x <
f (x)
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
convergence is like that of the
alternating harmonic series. Physically this means that our
Supplementary
square wave contains a lot of highfrequency components. If the electronic apparatus will
not pass these components, our squarewave input will emerg
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Lecture 23
I.Complex Numbers
PHYS2124 Mathematical Methods in Physics I
GyuBoong Jo
PHYS2124 Mathematical Methods in Physics I
I.Complex Numbers
GyuBoong Jo
1 / 35
Complex numbers: x+iy form I
In this chapter, we shortly review the complex numbers whic
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Supplementary
Phasor  Superposition of Oscillation I
Adding up several sinusoidal waves is a common in various systems such as
optics and a series RC circuit. For example, in a series of RC circuit, the
voltage across the resistor and the capacitor is gi
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
CHAPTER
2
Complex Numbers
1. INTRODUCTION
You will probably recall using imaginary and complex numbers in algebra. The
general solution of the quadratic equation
(1.1)
az 2 + bz + c = 0
for the unknown z, is given by the quadratic formula
b b2 4ac
.
(1.2)
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
CHAPTER
7
Fourier Series and Transforms
1. INTRODUCTION
Problems involving vibrations or oscillations occur frequently in physics and engineering. You can think of examples you have already met: a vibrating tuning fork,
a pendulum, a weight attached to a
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Lecture 79
III. Firstorder differential equation (Part 2)
PHYS2124 Mathematical Methods in Physics I
GyuBoong Jo
PHYS2124 Mathematical Methods in Physics I
III. Firstorder differential equation (Part 2)
GyuBoong Jo
1 / 15
Special types of differentia
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Lecture 79
III. Firstorder differential equation (Part 1)
PHYS2124 Mathematical Methods in Physics I
GyuBoong Jo
PHYS2124 Mathematical Methods in Physics I II. Firstorder differential equation (Part 1)
GyuBoong Jo
1 / 24
dt
are firstorder equations,
The Hong Kong University of Science and Technology
Mathematical Methods in Physics I
PHYS 2124

Spring 2014
Word of Mouth 26:4 March/April 2015
pictures. Language, Speech, and Hearing Services in Schools,
41, 459473.
Villaume, S. K. (1988). Creating context within text: An
investigation of primarygrade childrens character
RESOURCE
REVIEW
Building Academic Voca