EE1060 Differential Equations and Transform Techniques

Welcome to the official webpage of EE1060: Differential Equations and Transform Techniques.

This course explores the role of differential equations in modeling continuous-time systems, focusing on both analytical and numerical solution techniques for ordinary differential equations. Students will learn about first- and second-order differential equations, phase plane analysis, and matrix exponentials. Additionally, the course covers the application of transform techniques like Fourier Series, Fourier Transforms, and Laplace Transforms to solve differential equations, and introduces discrete-time system modeling using difference equations and the Z-transform. These foundational topics will support students as they progress to more advanced areas in Electrical Engineering.

Course Contents: Role of Differential equations in modeling of Continuous Time (CT) Systems, Linear Ordinary Differential Equations, Complex Arithmetic, First and Second Order Differential Equations - Analytical Solution Techniques, Numerical and Matrix Methods for Solving Ordinary Differential Equations, Analysis of Systems of Differential Equations - Critical Points, Phase Plane Analysis, Matrix Exponentials. LTI systems, Convolution, Transform Techniques and their role in solving Differential Equations - Fourier Series, Fourier Transforms, and Laplace Transforms. Discrete-time System Modeling, Difference equations, solution of difference equations, Z-transform and its role in solving difference equations, Existence and Convergence of Transforms

Instructor

• Name : Seshadri Sravan Kumar V

• Email : seshadri@ee.iith.ac.in

• Office : 603, Electrical Engineering

Class Timings

• Class timings : Slot A (Monday 09:00 - 09:55, Wednesday 11:00 - 11:55 and Thursday 10:00 - 10:55)

• Venue: EE-GF-004, Electrical Engineering

Evaluation Pattern

• Quizzes : 40% (Top 4 scores will be considered)

• Exams : 60% (25% for Mid-Term and 35% for Final Exam)

References

• W. E. Boyce, R. C. DiPrima, D. B. Meade, “Elementary Differential Equations and Boundary Value Problems”, 9th edition, Wiley, 1997.

• Brad G. Osgood, “Lectures on Fourier Transform and Its Applications”, IASPark City Mathematics Series American Mathematical Society (AMS), 2019.

• Charles Henry Edwards, David E. Penney, “Differential Equations and Boundary Value Problems: Computing and Modeling”, 4th edition, Pearson, 2000.

• George F. Simmons, “Differential Equations with Applications and Historical Notes”, 2nd edition, CRC Press, 2016.

• Ruel V. Churchill, “Fourier Series and Boundary Value Problems”, McGraw-Hill, 1941.

• Gustav Doetsch, “Introduction to the Theory and Application of the Laplace Transformation”, Springer, 2012.

• Morris Tenenbaum, Harry Pollard, “Ordinary Differential Equations”, Dover Books on Mathematics, Dover Publications, 1985.

Teaching Assistants

Credit to the following undergraduate students who have volunteered to serve as Teaching Assistants for the course.