WY Wong/SL Tan
UECM2033 Elementary Real Analysis
UECM 2033 Elementary Real Analysis
Reference book:
1. Walter Rudin, Principle of mathematical analysis, McGraw-Hill
2. Bartle And Sherbert, Introductio
Chapter 5
Integration
5.1 Introduction
There is often confusion among students of calculus between integral and
antiderivative. The integral is the limit of a Riemann sum which gives
(informally) the
WY Wong/Tan Sin Leng UECM2033
Elementary Real Analysis
Chapter 3
Continuous Functions
3.1 Introduction
We will study the class of continuous functions in this chapter. Works of
Bolzano in 1817 and Cau
WY Wong /SL Tan UECM2033 Elementary Real Analysis
Chapter 7
Topology of R
Introduction
The first six chapters have been devoted primarily to the theory for single
variable calculus. The functions have
WY Wong /SL Tan UECM2033 Elementary Real Analysis
Chapter 6
Sequences of Functions
6.1 Introduction
In Chapter 2, we have talked about sequences of numbers, how they converge
or diverge. In this chapt
Faculty:
Course:
Year:
Session:
Tutorial 1
FES
AM/FM
Two/Three
Jan. 2016
Unit Code:
UECM2033
Unit Title:
Elementary Real Analysis
Lecturer/Tutor: Tan Sin Leng/Tan Sin Leng
0. (a) If we have two real n
Faculty:
Course:
Year:
Session:
Tutorial 2
FES
AM/FM
Two/Three
Jan. 2016
Unit Code:
UECM2033
Unit Title:
Elementary Real Analysis
Lecturer/Tutor: Tan Sin Leng/Tan Sin Leng
1
1. For n N , show that cos
Faculty:
Course:
Year:
Session:
LKC FES
AM/FM
Two/Three
Jan. 2016
Unit Code:
UECM2033
Unit Title:
Elementary Real Analysis
Lecturer/Tutor: Tan Sin Leng/Tan Sin Leng
Tutorial 3
1. (a) What can be said
WY Wong /SL Tan UECM2033 Elementary Real Analysis
Chapter 4
The Derivative
4.1 Introduction
The derivative is a measure of how a function changes as the variable in the
domain of the function changes.
WY Wong/Tan Sin Leng UECM2033
Elementary Real Analysis
Chapter 2
Sequences and Series
2.1 Sequences
Definition 2.1.1 (Sequence)
A sequence is a function x : N R .
Instead of writing the image of x as