DCO10111 Basic Calculus and Linear Algebra
Topic 2: Complex Numbers
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textbook and various res

DCO10111 Basic Calculus & Linear Algebra
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Re(z) = a
Im(z) = b
Re(z) = 5
Im(z) = 4
Topic 2: Complex Numbers (CCCU)
DCO10111 Basic Calculus & Linear Algebra
Example: z = 5 + 4i
The number a is called
the real part of z and
the number b is c

DCO10111 Basic Calculus and Linear Algebra
Topic 6: Integration and Applications
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textbook an

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F (x + x) F (x)
= f (z)
x
Topic 6: Integration and Applications (CCCU)
DCO10111 Basic Calculus and Linear Algebra
Therefore, we have
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which would be the area under the graph of f in the interval
[x, x + x] as well as the

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Topic 3 (Part 1): Matrix and Determinants (CCCU)
DCO10111 Basic Calculus & Linear Algebra
Semester A
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Matrix is defined by the English mathematician James Sylvester (left) in
1850 and basic operations of matrices are introduced by

DCO10111 Basic Calculus and Linear Algebra
Topic 3 (Part 1): Matrix and Determinants
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textboo

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2 / 24
Topic 3 (Part 2): Systems of Linear Equations
DCO10111
(CCCU) Basic Calculus & Linear Algebra
a 1 x1 + a 2 x2 + + a n xn = 0
The equation with b = 0 is being called
homogeneous linear equation, i.e.
Definition: Homogeneous Linear

DCO10111 Basic Calculus & Linear Algebra
Semester A
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Topic 1: Vector Algebra (CCCU)
DCO10111 Basic Calculus & Linear Algebra
Semester A
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where the positioning of the upper case letters is important. The A is
the initial point and so is listed

Semester A
Topic 4: Functions, Limit and Continuity (CCCU)
DCO10111 Basic Calculus and Linear Algebra
Semester A
1. Algebraic (i.e. Real numbers could be added, subtracted, multiplied
and divided (except by 0)
2. Relational (i.e. Real numbers could be com

DCO10111 Basic Calculus and Linear Algebra
Topic 1: Vector Algebra
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textbook and various reso

DCO10111 Basic Calculus and Linear Algebra
Topic 5: Differentiations and Applications
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textbo

DCO10111 Basic Calculus and Linear Algebra
Topic 4: Functions, Limit and Continuity
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on textbook

1 x defined on the interval (, 1].
Semester A
Topic 5: Differentiations and Applications (CCCU)
DCO10111 Basic Calculus and Linear Algebra
f (x) = lim
Semester A
f (x + h) f (x)
h0
h
p
1 (x + h) 1 x
= lim
h0
h
1x h 1x
1x h+ 1x
= lim
h0
h
1x h+ 1x
1 x h (

DCO10111 Basic Calculus & Linear Algebra
Tutorial 2: Suggested Solutions (CCCU)
DCO10111 Basic Calculus & Linear Algebra
Now, try to figure out the formula to
compute this angle.
(Hint: Draw a picture to describe the
scenario, i.e. a vector v and x-axis.)

DCO10111 Basic Calculus and Linear Algebra
Topic 3 (Part 2): Systems of Linear Equations
Division of Computer Studies, Community College of City University
Lecturer: Desmond Yau-Chat TSOI
desmond.tsoi@cityu.edu.hk
Semester A
Lecture notes are based on tex