AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)
Faculty of Science and Technology (FST)
Department of Mathematics
Undergraduate Program
COURSE PLAN
I. Course Core and Title
MAT 2101: Complex Variables, Laplace and
Z-transformations
II. Credit
3 credit hours (4 hours of theory per week)
III. Nature
Science Core Course for CS, EEE
IV. Prerequisite
MAT 1102: Differential Calculus and Coordinate
Geometry
MAT 1205: Integral Calculus and ODE
SEMESTER: SUMMER 2022-2023
V. Vision:
Our vision is to be the preeminent Department of Mathematics
through creating recognized professionals who will provide
innovative solutions by leveraging contemporary research
methods and development techniques that is in line with the
national and global context.
VI. Mission:
The mission of the Department of Mathematics of AIUB is to
educate students in a student-centric dynamic learning
environment; to provide advanced facilities for conducting
innovative research and development to meet the challenges of
the modern era of technology, and to motivate them towards a
life-long learning process.
VII - Course Description:




Explain Laplace transform, inverse Laplace transform and application of Laplace transform.
Explain complex variables, its properties and complex algebra.
Construct an analytic function.
Explore complex integration using line integrals, Cauchy-residue theorem and Cauchy’s integral
formula.
Mat 1205:
Integral Calculus and ODE
 Apply Laurent’s theorem to express the functions as series.
 Describe singularity, poles, zeros and residue of complex valued function.
 Explain Z-transform, inverse Z-transform and engineering and scientific applications of Ztransform.
.
VIII – Course outcomes (CO) Matrix:
By the end of this course, students should be able to:
COs* CO Description
CO1
**
CO2
**
CO3
CO4
Predict and determine the basic concept of complex
variables.
Compute the Laplace- and Z- transformations for different
functions and sequences.
Analyze the functions to categorize, illustrate or differentiate.
Apply Laplace- and Z-transformations to solve differential
and difference equations.
Level of
Domain***
C
P
A
PO
Assessed
****
3
PO-a-2
3
PO-a-2
4
PO-b-2
3
PO-a-2
C: Cognitive; P: Psychomotor; A: Affective Domain
*
CO assessment method and rubric of COs assessment is provided in later section
**
COs will be mapped with the Program Outcomes (POs) for PO attainment
*** The numbers under the ‘Level of Domain’ columns represent the level of Bloom’s Taxonomy each
CO corresponds to.
**** The numbers under ‘PO Assessed’ column represent the POs each CO corresponds to.
© Dept. of Mathematics, FST, AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)
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IX – Topics to be covered in the classes*:
Week
1
2
3
4
5
Topic
Teaching-Learning
Assessment
Strategy
strategy
Complex numbers, Graphical Lecture delivery, Board Class
representation,
Fundamental work, Solving exercises, Performance
operations,
Conjugates, Discussion
Absolute
value/modulus,
Power of imaginary unit, Polar
form and argument of complex
number.
Complex equations, complex
roots and application of De
Moivre’s theorem.
Complex function and its Lecture delivery, Board Quiz-1
differentiation
(Cauchy- work, Solving exercises, Class
Riemann equations).
Discussion
Performance
Definition of line integral, path
of integration, Evaluation of
line integral along a simple
curve, along a circle and curve
consisting multiple paths.
Singularity: poles, zeros and Lecture delivery, Board Class
residues of a complex function, work, Solving exercises, Performance
Cauchy Residue Theorem Discussion
(CRT).
Integral along a simple closed
curve using CRT.
Definition of Z-transform, its
physical
meaning
and
applications, Z-transform of
some
simple
sequences,
properties of Z- transform.
Z-transform of discrete time Lecture delivery, Board Quiz-2
unit
step
function
and work, Solving exercises, Class
Kronecker delta function.
Discussion
Performance
Use of direct formulae of Ztransform for solving different
problems of x[n].
Inverse Z-Transform by Partial
fraction and integral method.
(Residue theorem).
Solution of linear difference Lecture delivery, Board Quiz-3
equations by Z-transform.
work, Solving exercises, Class
Solution
of systems
of Discussion
Performance
difference equations by Ztransform.
MAT 2101: Complex Variables, Laplace and Z-transformations
Corresponding
COs
CO1, CO3
CO1, CO3
CO3
CO2, CO4
CO4
2
Solving
some
physical
problems by Z-transform.
6
7
8
9
10
11
Midterm Exam
Laurent series.
Lecture delivery, Board Class
Types of improper integral- work, Solving exercises, Performance
using Jordan’s Discussion
Lemma.
Mappings
and
Bilinear
transform.
Definition, Application of
Laplace Transformation, some
important formulae and solving
problems using those formulae.
Definition of Unit Step
Function, Rectangular Pulse,
Laplace Transformation of
Unit Step Function.
Solving
some
problems
associated with unit step
function
by
Laplace
Transformation.
Some important formulae,
solving problems using direct
formulae and property of
inverse Laplace transformation.
Inverse Laplace transformation
using
partial
fraction
(Denominator is formed by the
linear factors, repeated factors,
and quadratic factors).
Inverse Laplace transformation
of f(t) with unit step function.
Solving differential equation
using Laplace transformation.
Solving system of Ordinary
Differential Equations (ODE)
by Laplace Transform.
Solution of some Engineering
problems.
CO1, CO3
Lecture delivery, Board Quiz-1
work, Solving exercises, Class
Discussion
Performance
CO1, CO2
Lecture delivery, Board Class
work, Solving exercises, Performance
Discussion
CO2, CO3
Lecture delivery, Board Quiz-2
work, Solving exercises, Class
Discussion
Performance
CO2
Lecture delivery, Board Quiz-3
work, Solving exercises, Class
Discussion
Performance
CO2, CO4
12
Final Exam
X – Mapping of PO to Courses and K, P, A
PO
PO Indicators Definition
Indicator
(As per the requirement of WKs)
ID
Domain
© Dept. of Mathematics, FST, AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)
K
P
A
3
PO-a-2
Apply information and concepts in natural science with the
familiarity of issues.
Formulate solutions, procedures, and methods using first
PO-b-2 principles of mathematics for engineering sciences.
Cognitive
Level 3
K2
(Applying)
Affective
Level 2
K2
(Responding)
XI – K, P, A Definitions
Indicator
K2
Title
Conceptual based
mathematics
Description
Conceptually based mathematics, numerical analysis, statistics
and the formal aspects of computer and information science to
support analysis and modeling applicable to the discipline
XII – Mapping of CO Assessment Method and Rubric
The mapping between Course Outcome(s) (COs) and The Selected Assessment method(s) and the
mapping between Assessment method(s) and Evaluation Rubric(s) is shown below:
COs
Description
Mapped
POs
CO1 Predict and determine the basic concept
of complex variables.
PO-a-2
CO2 Compute the Laplace- and Ztransformations for different functions
and sequences.
PO-a-2
CO3 Analyze the functions to categorize,
illustrate or differentiate
CO4 Apply Laplace- and Z-transformations to
solve differential and difference
equations.
PO-b-2
PO-a-2
Assessment
Method
Assessment Rubric
Quiz/Term
Question &
Assignment
Quiz/Term
Question &
Assignment
Rubric for
Quiz/Term Question
& Assignment
Rubric for
Quiz/Term Question
& Assignment
Quiz/Term
Question &
Assignment
Quiz/
Quiz/Term
Question &
Assignment
Rubric for
Quiz/Term Question
& Assignment
Rubric for
Quiz/Term Question
& Assignment
XIII – Evaluation and Assessment Criteria
CO1: Predict and determine the basic concept of complex variables.
MAT 2101: Complex Variables, Laplace and Z-transformations
4
Assessment
Criteria
Not
Attended/
Incorrect (0)
Inadequate
(1-2)
Average
(3)
Good
(4)
Excellent
(5)
Evaluation
Criteria
Fundamental
concept
Formulation
Evaluation
Correctly and comprehensively define the term with examples.
Correctness of
answer
Arrived at correct answer with no error showing every step of calculation.
Evaluation Definition
Write formulae to identify the appropriate technique.
Solving Laplace transformation and Z-transformation using different techniques
CO2: Compute the Laplace- and Z- transformations for different functions and sequences.
Assessment
Criteria
Evaluation
Criteria
Fundamental
concept
Formulation
Evaluation
Correctness of
answer
Not
Attended/
Incorrect (0)
Inadequate
(1-2)
Average
(3)
Good
(4)
Excellent
(5)
Evaluation Definition
Identification of differential equations according to their order.
Write formulae to identify the appropriate techniques.
Solving differential equations using Laplace transformation.
Arrived at correct answer with no error showing every step of calculation.
CO3 Analyze the functions to categorize, illustrate or differentiate.
Assessment
Criteria
Evaluation
Criteria
Selection of
Methodology
Formulation
Evaluation
Correctness of
answer
Not
Attended/
Incorrect (0)
Inadequate
(1-2)
Average
(3)
Good
(4)
Excellent
(5)
Evaluation Definition
Identify correct theory for relevant problem(s).
Write formulae to identify the appropriate techniques.
Finding line Integral, expanding a function in Laurent series and solving
complex equations.
Arrived at correct answer with no error showing every step of calculation.
CO4: Apply Laplace- and Z-transformations to solve differential and difference equations.
© Dept. of Mathematics, FST, AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)
5
Assessment
Criteria
Evaluation
Criteria
Fundamental
concepts
Not
Attended/
Incorrect (0)
Inadequate
(1-2)
Average
(3)
Good
(4)
Excellent
(5)
Inadeq
(1-2)
Evaluation Definition
Identification of difference equations according to their order.
Formulation
Write formulae to identify the appropriate techniques.
Evaluation
Correctness of
answer
Solving difference equations using Z-transformation.
Arrived at correct answer with no error showing every step of calculation.
XIV- Course Requirements



Students are expected to attend at least 80% of the class.
Students are expected to participate actively in the class.
For both terms, there will be at least 2 quizzes based on the theoretical knowledge and conceptual
understanding of the topic covered discussed in the classes.
XV – Evaluation & Grading System*
.
The tentative marks distribution for course evaluation are as follows:
1. Attendance ----------------------------------------------- 10%
2. Performance --------------------------------------------- 10%
3. Quiz (at least 2) ----------------------------------------- 40%
4. Mid/final term assessment --------------------------- 40%
Total --------------------------------------------------------- 100%
Grand Total --------- 40% of Midterm + 60% of Final term
Letter
A+
A
B+
B
C+
C
D+
D
F
I
W
UW
Grade Point
4.00
3.75
3.50
3.25
3.00
2.75
2.50
2.25
0.00
Numerical %
90-100
85 - < 90
80 - < 85
75 - < 80
70 - < 75
65 - < 70
60 - < 65
50 - < 60
< 50
Incomplete
Withdrawal
Unofficially Withdrawal
* The evaluation system will be strictly followed as per the AIUB grading policy.
XVI – Textbook/ References
MAT 2101: Complex Variables, Laplace and Z-transformations
6
1) Recommended Readings:


Advanced Engineering Mathematics (10th edition) by Erwin Kreyszig, Herbert Kreyszig,
Edward J. Norminton, published by John Wiley & Sons, Inc.
Complex Variables and Applications – R.V. Churchill and J.W.Brown .
2) Supplementary Readings:





Laplace Transform – Murray R. Spiegel (Schaum’s Outline Series).
Complex Variables and Applications M.R.Spiegel (Schaum’s Outline Series).
The Recurrence Relations in Teaching Students of Informatics by Valentin P.BAKOEV .
Z-Transform and Its Application to Development of Scientific Simulation Algorithms by
ZVONKO FAZARINC, Comput Appl Eng Educ:21:75-88,2013.
Lecture Notes.
XVII - List of Faculties Teaching the Course
FACULTY NAME
SIGNATURE
Khadiza Akter Mitu
Shanta Deb
Rubina Begum Tanjila
XVIII – Verification:
Prepared by:
--------------------------------Khadiza Akter Mitu
Assistant Professor
Department of Mathematics
Moderated by:
--------------------------------Rubina Begum Tanjila
Lecturer
Department of Mathematics
Date:.........................................
Checked by:
Date:.........................................
Certified by:
Approved by:
................................................
Dr. Mohammad Mahmudul
Hasan
Point of Contact
OBE Implementation Committee for
CS
.............................................
Dr. Dip Nandi
Associate Dean,
Faculty of Science &
Technology
..................................................
Mr. Mashiour Rahman
Dean,
Faculty of Science &
Technology
Date:........................................
Date:................................
Date:.........................................
© Dept. of Mathematics, FST, AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)
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