Complex Variables and Transforms
What you'll learn
- Complex variables and transforms such as Laplace, Fourier Transforms
Requirements
- High School Level Math
Description
This course is an undergrad level course designed to be studied by any one having understanding of College Level Math and Calculus.
This course can be divided into two parts. First part is related to complex numbers, complex variables and functions. While the second part is related to Transforms and Series.
After successfully completing this course, student is expected to be able define, understand and describe complex number system, complex functions, complex variables, transforms and series. Student is also expected to be able to analyze problems involving functions of complex variables, transforms and series (Fourier, Laplace, z Transforms and Fourier Series), limits, continuity, differentiability.
Topics:
Introduction to Complex Number: Complex Variable, Argand’s Diagram, Modulus and Argument of a Complex Number, Polar Form, De Moivre’s Theorem.
Complex Functions: Analytical Functions, Harmonic and Conjugate, Harmonic Functions.
Cauchy-Riemann Equations : Line Integrals, Cauchy’s Theorem, Cauchy’s Integral Formula, Independence of Path, Two Methods of Integration.
Fourier Series and Transform: Fourier Series / Transform of periodic / non-periodic functions, Properties of Fourier Transform, Inverse Fourier Transform, Convolution Theorem.
Laplace Transform: Laplace Transform of elementary functions, Concept and properties of Region of Convergence (ROC), Properties of Laplace Transform, Inverse Laplace Transform, Convolution Theorem, Heaviside Expansion Formula, Solution of Ordinary Differential Equations by Laplace Transform.
z- Transforms: basics and few numerical problems.
Who this course is for:
- College Students, University Freshers, High School students
Instructor
![Yasir Amir](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 64 64"%3E%3C/svg%3E){kind=avatar}
- 4.2 Instructor Rating
- 28 Reviews
- 197 Students
- 7 Courses
M Yasir Amir Khan
Specialization: Control Systems- Nonlinear, Linear and Neural Control.
Education:
MS Electrical Engineering N.U.S.T (PNEC) CGPA 4.0/4.0 2008
BE Electrical Engineering N.U.S.T (PNEC) CGPA 3.81/4.0 2003
HSSC Pre-Engineering Federal Board (Bahria College) 72% 1999
SSC Science Federal Board (Bahria College) 81% 1997
Distinction:
1- President of Pakistan Gold Medal for securing First Position in MS.
2- President of Pakistan Gold Medal for securing First Position in B.E.
3- Rector NUST Gold Medal for Best Final Year Project in B.E.
Teaching Experience: Total: 15+ years
Bahria University (Karachi) August 2014 – till to date.
Faculty Member (Teaching and Research)
HITEC University (Taxila) Sep 2011 -- August 2013 2 years
Faculty Member (Teaching and Research)
NUCES-FAST (Karachi) May 2008 – August 2011 3 years 3m
Faculty Member (Teaching and Research)
NUST (PNEC) May 2005- May 2006. 1 year
Lab-Engineer (Laboratory Demonstrations)
Other Experience:
Consultant Electronic Engineer (Part-Time) May 2005 – August 2014
Projects via Online Workplaces:
Altanova (Pakistan) Dec 2003- April 2005 1 year 6m
Design Engineer US Based Test Board Design/ Fabrication Firm
Publications:
Journal Papers
[1] M. Yasir Amir, V. Abbas, “Modeling and Neural Control of Quadrotor Helicopter”, in Yanbu Journal of Engineering and Science, ISSN 1658-5321, Vol 2, pp 35-48, Yanbu Saudi Arabia, April 2011.
[2] M Yasir Amir, Vali Uddin Abbas, “Modeling, Simulation and Neural Control of Wheeled Inverted Pendulum”, in Yanbu Journal of Engineering and Science, ISSN 1658-5321, Vol 11, pp 51-59, Yanbu Saudi Arabia, Dec 2015.
[3] M. Yasir Amir, H. Rahseed, U Shahid, “Voice Controlled Robot using Neural Network based Speech Recognition using Linear Predictive Coding”, in BUJICT (former HEC Y-Category), ISSN 1999-4974, Vol 9, pp 47-49 , Bahria University, Pakistan, Sept 2016.
[4] M. Yasir Amir, H. Rahseed, U Shahid, “Recent Advancements on Drivable Free Space Estimation using Monocular Vision”, in BUJICT (former HEC Y-Category), ISSN 1999-4974, Vol 10, Issue 1, pp 51-55 , Bahria University, Pakistan, June 2017.
[5] M Yasir, Vali Uddin, Umer, “Advanced Robust Control Techniques: Comparison and Application to highly nonlinear system”, in BUJICT (HEC Z-Category), ISSN 1999-4974, Vol 11, Issue 2, pp 29-34 , Bahria University, Pakistan, December 2018.Conference Papers
[1] M. Yasir Amir, V. Abbas, “Modeling of Quadrotor Helicopter Dynamics”, in Proc of International Conference on Smart Manufacturing Applications, ISBN: 78-89-962150-0-4, Gyeonggi-do, S. Korea, May 2008, pp100-105.
[2] Vali Abbas, M. Yasir Amir, “Mulitlayer Perceptron for Direct Inverse Control of a Nonlinear System”, in Proc of International Conference on Computer Control and Communication, ISBN: 978-1-4244-3313-1, Karachi, February 2009, pp1-5.
[3] Yasir Amir et. al., “Modeling and Simulation approach for an Industrial Manufacturing Execution System,” in Proc. of 3rd IEEE International Conference on Systems Engineering and Technology, ISBN 978-1- 4799-1028-1, Shah Alam, Malaysia, 19-20 August 2013, pages 26-31.
Books
[1] M. Yasir Amir, Modeling and Neural Control of Quadrotor Helicopter: MATLAB-SIMULINK Based
Modeling, Simulation and Neural Control of Quadrotor Helicopter, Berlin, Germany: LAP-LAMBERT, August 2010, ISBN-13: 978-3838392981.
[2] A. Samad, M Yasir Amir, A Shaikh, “Sentry Gun with Face Detection”, Berlin, Germany: LAP- LAMBERT, June 2011, ISBN-13: 978-3845402031.
[3] M Yasir Amir, Basics of Classical and Neural Control, Berlin, Germany: LAP-LAMBERT, September 2011, ISBN-13: 978-3846507568.
[4] M Yasir Amir, Noman Ovais, Wireless Electrical Power Measurement and Monitoring System, Berlin, Germany: LAP LAMBERT Academic, 20 February 2013, ISBN 978-3659351785.
MS Thesis Supervised
1. Robust Integral of Sign of Error based Control of Twin Rotor System
2. Terminal Sliding Mode Control of Twin Rotor System
Important UG FYPs Supervised:
Design and fabrication of I) Quadrotor Helicopter, II) Development of Battery Electric
Vehicle, III) CNC Lathe Machine, IV) Sentry Gun with Face Detection and Target Locking, V)
Cell phone charger using EM-Waves and Solar Energy, VI) Self balancing Wheeled Inverted
Pendulum SEGBOT like robot , VII) Atmospheric water generator, VIII) Solar thermal power
generation using Seebeck effect.
Other Projects: a. Design of High Speed, Controlled Impedance, Minimum Cross Talk, Analog, Digital
and Mixed Signal Test Boards of up to 36 layer, using PGAs, BGAs, SOICs and other
SMT components for customers including Intel, Xilinx, Altera, Cypress, AMD etc.
b. Manny short term projects such as designing reconfigurable PV cell array, controlled rectifier, line following robot, super-capacitor based regenerative braking, EMF detector for paranormal applications etc.
c. Design and Fabrication of 8085 microprocessor based hand held computer with
Alphanumeric display and 8KB RAM. (1998 during my holidays after HSSC-I)
d. Obstacle Avoiding Robot using infra-red. (1999 after HSSC)
e. Secure Voice Communication System using Encryption.(B.E Final Year Project)
f. Fabricated many small hobby projects such as short range voice communication system, AF Amplifiers etc. using SM.
Membership: Pakistan Engineering Council (Elect/20302)
Computer Skills: Microsoft Windows, MS Office, MS Project, Latex.
Assembly, C, C++, MATLAB-Simulink, EAGLE, ORCAD, PCAD, EWB, Multisim,
Proteus (ISIS, ARES)
Other Skills: Jeep 4x4 electrical wiring and brake/ suspension/steering repair and maintenance hands
on experience.
Personal: Married Muslim, Age 39+ years
Language Skills: English/ Urdu (Read, Write and