THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineering
Additional Exercise III
1. Consider the following limit of Riemann sum of a function f on [a, b]. Identify f
and express the limit as a denite integral, where
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 3
Due Date: October 28, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on h
Lecture Note 13
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1510
Calculus for Engineers
Produced by Jeff Chak-Fu WONG
1
TABLE OF C ONTENT
Total area
Areas between f and g
The mean value the
Lecture Note 12
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1510
Calculus for Engineers
Produced by Jeff Chak-Fu WONG
1
TABLE OF C ONTENT
Area Under Graph
(a) Left Sum and Right Sum
(b) Avera
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers
Suggested Solution to Extra Exercise Set 2
If you find any errors/typos, please email them to:
math1510@math.cuhk.edu.hk
2
1. State whether the indicated functio
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of coursework 4 (Take home)
Name:
Student No.:
Class:
I acknowledge that I am aware of University policy and regulations on hones
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Solution to Pre-coursework Exercise 3
1. Fill in the blanks and construct an upper bound and a lower bound of
3
.
6 + 4 cos
Ans:
1
cos
1
4
4 cos
4
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of coursework 5
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academ
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Solution to Pre-tutorial Exercise 4
1. Compute the derivative of each of the following function at the given point by using
the formal definition (fi
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Solution to Pre-coursework Exercise 5
1. (a) Factor theorem states that if P (x) is a polynomial and P (a) = 0, then x a
is a factor of P (x).
By usi
Lecture Note 14
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1510
Calculus for Engineers
Produced by Jeff Chak-Fu WONG
1
TABLE OF C ONTENT
Power Series
Finding Where a Power Series Converges
Lecture Note 15
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1510
Calculus for Engineers
Produced by Jeff Chak-Fu WONG
1
TABLE OF C ONTENT
Representing Functions as Power Series
Taylor AND Ma
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Copyright Reserved
The Chinese University of Hong Kong
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Course Examination 1st Term, 2012-13
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Course Code & Title
CALCULUS FOR ENGINEERS
MATH1510B
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THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 6
Due Date: December 6, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on h
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of Quiz 2
Name:
Student No.:
Class:
Final Result:
1. Answer all questions. Please show the work with as much detail as possible f
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Homework 1
Due Date: September 18, 2014
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Homework 6
Due Date: 2nd December 2014
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Suggested Solution to Coursework 5
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on hone
j;1l '7J
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1~
Not to be taken away
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WiHlffi1if 1'fIrfilEIJ
Copyright Reserved
The Chinese University of Hong Kong
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Course Examination 1st Tenn, 2013-14
Course Code
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested Solution to Extra Exercise Set 3
If you find any errors/typos, please email them to:
math1510@math.cuhk.edu.hk
2
Theorem 1 Let f be defined
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH 1510B Calculus for Engineers (Fall 2016)
by Dr. Liu Chun Lung (Kelvin)
Topic 5 : Applications of Differentiation
Linearization
Linearization of a function f (x) at a point (a, f (a) means
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Coursework 3
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academic work, and of the dis
Lecture Note 10
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1020
General Mathematics
Produced by Jeff Chak-Fu WONG
1
V ECTORS
V ECTORS
2
A vector is a quantity that has both magnitude and dire
Chap 1 Preliminaries Page 1
Chap 1 Preliminaries Page 2
Chap 1 Preliminaries Page 3
Chap 1 Preliminaries Page 4
Chap 1 Preliminaries Page 5
Chap 1 Preliminaries Page 6
Chap 1 Preliminaries Page 7
Chap 1 Preliminaries Page 8
Chap 1 Preliminaries Page 9
Cha
Calculus for Engineers
Jeff Chak-Fu WONG1
August 2015
1 Copyright
c 2015 by Jeff Chak-Fu WONG
2
Contents
The Fundamental Theorem of Calculus
22.1 Introduction . . . . . . . . . . . . . . . . . . . . .
22.2 Part I of The Fundamental Theorem Of Calculus
22.
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
Calculus for Engineers
Jeff Chak-Fu WONG
Note on Fourier Series
If you have spotted any errors/typos, please email them to:
jwong@math.cuhk.edu.hk
1
Definition 1 Definition of Fourier series Un
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 4
Due Date: November 16, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
Calculus for Engineers
Jeff Chak-Fu WONG1
August 2015
1 Copyright
c 2015 by Jeff Chak-Fu WONG
2
Contents
Antiderivatives
19.1 Introduction . . . . . . . . . . . . .
19.2 Integration: Integral of a function .
19.3 Indefinite valuedness of integration.
19.4
Lecture Note 13
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MATH1020
General Mathematics
Produced by Jeff Chak-Fu WONG
1
T HE C ROSS P RODUCT
HE
C ROSS P RODUCT
2
Find the Cross Product of Two Vec
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Quiz 1
Name:
Student No.:
Class:
Final Result:
1. Answer all questions. Show work to justify all answers.
2. The quiz lasts 40 minutes.
3. If you fin