ENGG2420D
Notes for Lecture 4
Inverse functions
Kenneth Shum
23/9/2015
In this lecture we investigate the inverses of elementary functions in complex
analysis.
Function in general. We rst review the notion of function in mathematics. A function consists o
ENGG2420D
Notes for Lecture 13
Convergence tests
Kenneth Shum
2/11/2015
Complex geometric series
Given a complex number c, the innite series n=0 cn is the complex geometric series. Its convergence depend on the modulus of c:
cfw_
if |c| < 1
n converges
c
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ENGG2420D
Notes for Lecture 10
Cauchy Theorem
Kenneth Shum
19/10/2015
Definitions: If the start point and the end point of a contour C coincide
with each other, then C is called aHclosed contour. For a closed contour, we usually write the contour integral
ENGG2420D
Notes for Lecture 9
Contour integral and path independence
Kenneth Shum
14/10/2015
Recalled that, given a smooth curve C and a continuous complex function
f (z), the contour integral of f (z) along the curve C is defined by
f (z) dz ,
C
b
f (t)
ENGG 2420B Final Review
Eric Qiaosheng Zhang
Department of Information Engineering
The Chinese University of Hong Kong
(slides courtesy by July Xialu Li)
[email protected]
December 1, 2016
Eric Qiaosheng Zhang (CUHK)
ENGG 2420B Final Review
December 1,
Origin and Classification of Differential Equations
First Order Differential Equations
ENGG 2420: Ordinary Differential Equations
Slides by Prof Thierry Blu
Prof. Mayank Bakshi
e-mail: [email protected]
Institute of Network Coding
The Chinese University
ENGG2420D
Notes for Lecture 5
Kenneth Shum
5/10/2015
1
How to represent a curve by parameterization
1.1
Line segment
Task: given two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 , represent
the line segment between z1 and z2 in the complex plane.
1. Me
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ENGG2420D
Notes for Lecture 1
Arithmetic of complex numbers
Kenneth Shum
10/9/2015
Definition: A complex number is defined as an ordered pair of real numbers.
In this lecture note, we shall write a complex number as (x, y), where x and y
are real numbers.
ENGG2420D
Notes for Lecture 6
Complex differentiability at a given point
Kenneth Shum
7/10/2015
Remarks on distance and circle in complex plane: Distance in complex number is measured by the modulus, or the absolute value. Two complex
numbers z1 and z2 ar
ENGG2420D
Notes for Lecture 12
From extended Cauchy integral formula
to Taylor series
Kenneth Shum
28/10/2015
Suppose that f (z) is a function which is analytic in a region close to z = 0.
We draw a small circle with radius r, for some small real number r
ENGG2420D
Notes for Lecture 3
Eulers formula
Kenneth Shum
21/9/2015
There are several definitions of the real exponential function. We start with
this one that defines the real exponential function as a limit:
(
x )n
ex , lim 1 +
.
n
n
The above definitio
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ENGG2420D
Notes for Lecture 8
Harmonic functions and contour integrals
Kenneth Shum
12/10/2015
1
Rules for calculating complex derivatives
df
We also use the notation dz
= f (z).
Basic analytic functions:
1. For positive integer n, z n is analytic on the
Origin and Classification of Differential Equations
First Order Differential Equations
Second order linear differential equations
ENGG 2420: Ordinary Differential Equations
Slides by Prof Thierry Blu
Prof. Mayank Bakshi
e-mail: [email protected]
Institut
Origin and Classification of Differential Equations
First Order Differential Equations
Second order linear differential equations
ENGG 2420: Ordinary Differential Equations
Slides by Prof Thierry Blu
Prof. Mayank Bakshi
e-mail: [email protected]
Institut
Partial Differential Equations
Solving homogenous linear PDEs
ENGG 2420B: Partial differential equations and
Fourier Series
Prof. Mayank Bakshi
e-mail: [email protected]
Institute of Network Coding, CUHK
The Chinese University of Hong Kong
Nov 16 201
Origin and Classification of Differential Equations
First Order Differential Equations
ENGG 2420: Ordinary Differential Equations
Slides by Prof Thierry Blu
Prof. Mayank Bakshi
e-mail: [email protected]
Institute of Network Coding
The Chinese University
Origin and Classification of Differential Equations
ENGG 2420: Ordinary Differential Equations
Slides by Prof Thierry Blu
Prof. Mayank Bakshi
e-mail: [email protected]
Institute of Network Coding
The Chinese University of Hong Kong
October 24 2016
Prof.
The Chinese University of Hong Kong
Faculty of Engineering
Prof. P. Vontobel
ENGG2420C / ESTR2000 (Fall 2017)
Complex Analysis and Differential Equations for Engineers
Homework Assignment 2
Out: 09 October 2017
In: 16 October 2017
1
Derivative
1. (2 Point
1
( Review )
2
( Review )
3
( Review )
4
( Review )
f(z) = u(x,y)+i v(x,y),
If f(z) is not expressed by u(x,y)
+i v(x,y),
5
Important
result!
6
8
9
10
Parameterizati
12
13
14
B
A
16
zk
zj
B
A
17
18
Important
result!
22
23
Important
result!
According to 4.
CA 1-6: Complex Analysis
1 Complex Numbers
2 Functions of One Complex Variable
3 Complex Differentiation
4 Complex Integration and Cauchys Theorem
5 Cauchy Integral Formula
6 Complex Series, Power Series and Taylor Series
(Some pics. are downloaded from t
Complex number
Complex functions
Complex integration
Power series
Ordinary differential equations
Partial Differential Equations
Fourier series
ENGG 2420: Complex Analysis essentials
A survival kit
Prof Mayank Bakshi
e-mail: [email protected]
Fall 2016
P