Ordinary Differential Equations
Teacher
MR. Sasi Bhusan Padhi
Category
Core Courses
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Course Name : Ordinary Differential Equations
Code(Credit) : CUTM1514(3-2-1)
Course Objectives
- To understand most of the physical phenomena from Science and Engineering which are modeled by differential equations
- To develop the ability to apply differential equations to significant applied and/or theoretical problems.
Learning Outcomes
Upon successful completion of this course, students will be able to:
- Learn fundamental concepts of ODE theories and where and how such equations arise in applications to scientific and engineering problems.
- Be competent in solving linear/non-linear 1st & higher order ODEs using analytical methods to obtain their exact solutions.
- Find power series solutions of 2nd order differential equations.
Course Syllabus
Module-I ( T-5 hrs-P-4 hrs-P-2 hrs )
Introduction to ordinary differential equations, First order and first degree differential equation, Variable separation method, Homogeneous differential equation, Non-homogeneous equation of first degree.
Practice-1 : Solving One dimensional heat flow equations using Python
Practice-2 : Solving Predator-Prey Equations using Python
Project-1 : Study on different types of first order and first degree ordinary differential equations used in mathematical models
Module-II ( T-6 hrs-P-4 hrs-P-2 hrs )
Exact differential equations, Non-exact differential equations, Integrating factors.
Practice-3 : Solving Growth model (exponential case only) using Python
Practice-4 : Solving Decay model (exponential case only) using Python
Project-2 : Study of Non-exact differential equations and their solutions
Module-III ( T-4 hrs-P-4 hrs-P-2 hrs )
Linear equation, Bernoulli's equation, Introduction to Second and Higher order Linear Homogeneous and Non-homogeneous equations with constant and variable coefficients.
Practice-5 : Solving Oxygen debt model using Python
Practice-6 : Solving Mixing Concentrations problems using Python
Project -3 : Applications of first order differential equations to Decay models
Module-IV ( T-4 hrs-P-4 hrs-P-0 hrs )
Complimentary function and Particular integral, Finding particular integrals for the differential equations containing the Exponential functions, Trigonometric functions (Sine and Cosine) using inverse operator method.
Practice-7 : Solving Escape velocity Problem using Python
Practice-8 : Solving Free Damped Motion of a Spring System using Python
Module-V ( T-4 hrs-P-4 hrs-P-2 hrs )
Finding particular integrals for the differential equations containing Power functions, Product of exponential function with other functions, Functions in the form xV(x) using inverse operator method, Solving second order linear equations using variation of parameters method.
Practice-9 : Solving Free Undamped Motion of a Spring System using Python
Practice-10 : Solving RL circuit problems using Python
Project -4 : Study on Variation of parameter method for solving second order differential equations
Module-VI ( T-4 hrs-P-2 hrs-P-2 hrs )
Solving second order linear equations using Method Of Undetermined Coefficients, Linear equations reducible to constant coefficient form, Euler-Cauchy equation, Legendre’s equation.
Practice-11 : Euler Method for solving Second order differential equation using Python
Practice-12 : Solving Forced Vibration of a Spring System using Python
Project -5 : Study on Method Of Undetermined Coefficients for solving second order differential equations
Module-VII ( T-3 hrs-P-0 hrs-P-2 hrs )
Power series solution, Power series solutions of second order differential equations.
Project -6 : Study on Power series solutions
Text Book:
- Sinha Roy and S. Padhy, A Course of Ordinary and Partial Differential Equations, Kalyani Publishers, New Delhi.
Chapters: 1, 2(2.1 to 2.7), 4(4.1 to 4.8), 7(7.1 to 7.3)
Reference Books:
- Differential Equations and their Applications: Martin Braun, Springer International.
- Advanced Differential Equations: M. D. Raisinghania, S. Chand & Company Ltd., New Delhi.
- A First Course in differential Equations with Modeling Applications: G. Dennis Zill, Cengage Learning India Pvt. Ltd.
- Text Book of Differential Equations : N.M. Kapoor
- Introductory course in Differential Equations : D.A. Murray
- Differential Equations: S. L. Ross, John Wiley & Sons, India, 2004.
Session Plan
Session 1
Introduction to Differential equations
Session 2
First order and first degree ODE
https://www.youtube.com/watch?v=DL-ozRGDlkY
https://www.slideshare.net/vishalgohel12195/differential-equations-of-first-order-64305185
Session 4
Solution of a Homogeneous differential equation
Session 5
Solution of a Non-homogeneous differential equation of first degree
Session 6 & 7
Practice-1
Solving One dimensional heat flow equations using Python
Session 8 & 9
Practice-2
Solving Predator-Prey Equations using Python
Session 10 & 11
Project-1 : Study on different types of first order and first degree ordinary differential equations used in mathematical models
Session 13
Non-exact Differential Equations (Case-1)
https://www.youtube.com/watch?v=eP9UZGwbVZM&pbjreload=101
https://www.slideshare.net/SIDDHI31/exact-non-differential-equation
Session 14
Non-exact Differential Equations (Case-2)
https://www.youtube.com/watch?v=eP9UZGwbVZM&pbjreload=101
https://www.slideshare.net/SIDDHI31/exact-non-differential-equation
Session 15
Non-exact Differential Equations (Case-3)
https://www.youtube.com/watch?v=eP9UZGwbVZM&pbjreload=101
https://www.slideshare.net/SIDDHI31/exact-non-differential-equation
Session 16
Non-exact Differential Equations (Case-4)
https://www.youtube.com/watch?v=eP9UZGwbVZM&pbjreload=101
https://www.slideshare.net/SIDDHI31/exact-non-differential-equation
Session 17
Non-exact Differential Equations (Case-5)
https://www.youtube.com/watch?v=eP9UZGwbVZM&pbjreload=101
https://www.slideshare.net/SIDDHI31/exact-non-differential-equation
Session 18
Session 21 & 22
Practice-3
Growth model (exponential case only) using Python
Session 23 & 24
Practice-4
Decay model (exponential case only) using Python
Session 25 & 26
Project-2 : Study of Non-exact differential equations and their solutions
Session 27 & 28
Practice-5
Solving Oxygen debt model problems using Python
Session 29 & 30
Practice-6
Solving Mixing Concentrations problems using Python.
Session 31 & 32
Project-3
Application of first order differential equation to Decay models
Session 33
Second and higher order linear homogeneous differential Equation with constant coefficients
https://www.youtube.com/watch?v=u-ympqH2SBs
https://www.slideshare.net/virajpatel777701/second-order-homogeneous-linear-differential-equations
Session 34
Case-1. Distinct real roots
Case-2. Repeated real roots
Case-3. Conjugate complex roots
https://www.youtube.com/watch?v=jDeLOAbQ8IY
Session 35
Non-homogeneous differential Equation with constant coefficients
Session 36
Finding particular integral for an exponential function using inverse operator method
https://www.youtube.com/watch?v=r6mkGRLpm_w
https://www.slideshare.net/sumanmathews/inverse-differential-operator
Session 37
Finding particular integral for Trigonometric functions (Sine and Cosine) using inverse operator method
https://www.youtube.com/watch?v=r6mkGRLpm_w
https://www.slideshare.net/sumanmathews/inverse-differential-operator
Session 38 & 39
Practice-7
Solving Escape velocity Problem using Python
Session 40 & 41
Practice-8
Solving Free Damped Motion of a Spring System using Python
Session 42
Finding particular integral for a power function using inverse operator method
https://www.youtube.com/watch?v=r6mkGRLpm_w
https://www.slideshare.net/sumanmathews/inverse-differential-operator
Session 43
Finding particular integral when exponential function is multiplied with another function using inverse operator method
https://www.youtube.com/watch?v=r6mkGRLpm_w
https://www.slideshare.net/sumanmathews/inverse-differential-operator
Session 44
Finding particular integral when the function is of the form xV(x) using inverse operator method
Session 45
Solving second order linear equations using variation of parameters method
Session 46 & 47
Practice-9
Solving Free Undamped Motion of a Spring System using Python
Session 48 & 49
Practice-10
Solving RL circuit problems using Python
Session 50 & 51
Project-4
Study on Variation of parameter method and Method of undetermined coeffeciants for solving second order differential equations
Session 52
Solving second order linear equations using method of undetermined coefficients
Session 53
Equations reducible to linear equations with constant coefficients
Session 55
Session 56 & 57
Practice-11
Euler Method for solving Second order differential equations using Python
Session 58 & 59
Practice-12
Solving Forced Vibration of a Spring System using Python
Session 60 & 61
Project-5
Study on Method Of Undetermined Coefficients for solving second order differential equations
Session 64
Power series solution to second order differential equations
http://www.math.mcgill.ca/gantumur/math315w14/downloads/power.pdf
Session 65 & 66
Project -6
Study on Power series solutions
Case Studies
Case Studies
Our Main Teachers
MR. Sasi Bhusan Padhi works as an Assistant Professor, Department of Mathematics, Centurion University of Technology and Management. He has received M.Sc degree in Mathematics from Berhampur University in the year 2001 with Gold Medal. He has 17 years of teaching experience in different Graduate and Post Graduate colleges. Now he is doing research in […]