Course Title: Ordinary and Partial Differential Equations
Type of Course: Compulsory, Theory, Non-departmental
Offered to: EEE
Pre-requisite Course(s): None
Ordinary Differential Equations: Degree and order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solution of general linear equations of second and higher order with constant coefficients. Solution of homogeneous linear equations. Solution of differential equations of the higher order when dependent and independent variables are absent. Solution of differential equations by the method based on factorization of operators. Frobenius method.
Partial Differential Equations: Introduction. Solutions of linear and nonlinear partial differential equations of first order. Linear equations of higher order. Equations of the second order with variable coefficients. Wave equations. Particular solutions with boundary and initial conditions.
To provide the basic concept of differential equations, their solution along with their physical significance.
To establish sufficient knowledge to deal with various type of differential equations for solving engineering problems.
To provide the basic properties of singularities and series solution techniques with engineering applications.
Fundamental concepts of Pre-Calculus, Differential, and Integral calculus; and preliminary knowledge to solve algebraic, transcendental equation.
| CO No. | CO Statement (3-4) |
Corresponding PO(s)* | Domains and Taxonomy level(s) | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) |
|---|---|---|---|---|---|
| 1 | Understand differential equations to solve 1st and higher order linear differential equations. | PO(b) | C2 | Lectures, Homework | Written exams; assignment |
| 2 | Apply the appropriate (different techniques) methods to solve the linear and non-linear differential equations. | PO(a) | C3 | Lectures, Homework | Written exams; assignment |
| 3 | Classify the singular points and able to obtain series solution | PO(a) | C5 | Lectures, Homework | Written exams; assignment |
| 4 | Interpret rigorous knowledge to solve linear and non-linear partial differential equations of Physical Models. | PO(b) | C3 | Lectures, Homework | Written exams; assignment |
Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Weekly schedule: For Ordinary Differential Equations
| Week | Topics |
|---|---|
| Week-1 | Degree and order of ordinary differential equations, Formation of differential equations. |
| Week-2 | Formation of differential equations, Solution of first order differential equations by various methods (separable form and reducible to separable form). |
| Week-3 | Solution of first order differential equations by various methods (homogeneous form and reducible to homogeneous form). |
| Week-4 | Solution of first order differential equations by various methods (linear differential equation and Bernoulli’s differential equation). |
| Week-5 | Solution of first order differential equations by various methods (exact differential equation, non-exact differential equation and integrating factor by inspection). |
| Week-6 | Class Test |
| Week-7 | Classification of solutions of differential equations, Application of first order differential equations. |
| Week-8 | Solution of general linear equations of second and higher order with constant coefficients (homogeneous and non-homogeneous). |
| Week-9 | Solution of general linear equations of second and higher order with constant coefficients (non-homogeneous). |
| Week-10 | Solution of homogeneous linear equations (Cauchy-Euler equations). |
| Week-11 | Solution of differential equations of the higher order when dependent and independent variables are absent, Solution of differential equations by the method based on factorization of operators. |
| Week-12 | Frobenius method (introduction and solution of type-I problems: roots of indicial equations unequal and not differing by an integer). |
| Week-13 | Frobenius method (solution of type-II problems: roots of indicial equations unequal, differing by an integer and making a coefficient of y indeterminate; solution of type-III problems: roots of indicial equations unequal, differing by an integer and making a coefficient of y infinite; solution of type-IV problems: roots of indicial equations equal). |
| Week-14 | Class Test |
Weekly schedule: For Partial Differential Equations
| Week | Topics |
|---|---|
| Week-1 | Introduction to partial differential equations. |
| Week-2 | Introduction to partial differential equations. |
| Week-3 | First order Linear partial differential equations. |
| Week-4 | First order Linear partial differential equations. |
| Week-5 | First order Non-linear partial differential equations. |
| Week-6 | First order Non-linear partial differential equations. |
| Week-7 | Class Test |
| Week-8 | Linear equations of higher order. |
| Week-9 | Linear equations of higher order. |
| Week-10 | Second order PDE with variable coefficient. |
| Week-11 | Wave equations. |
| Week-12 | Particular solutions with boundary and initial conditions. |
| Week-13 | Particular solutions with boundary and initial conditions. |
| Week-14 | Class Test |
Class Participation: Class participation and attendance will be recorded in every class.
Continuous Assessment: Continuous assessment for any of the activities such as quizzes, assignment, presentation etc. The scheme of the continuous assessment for the course will be declared on the first day of classes.
Final Examination: A comprehensive term final examination will be held at the end of the term following the guideline of academic council.
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
Elementary Differential Equations by Earl D. Rainville and Phillip E. Bedient.
A First Course in Differential Equations with Modeling Applications by Dennis G. Zill.
Ordinary and Partial Differential Equations by M.D. Raisinghania
Elements of Partial Differential Equations by Ian Naismith Sneddon
Differential Equations with Applications by M. M. K. Chowdhury.
Advanced Engineering Mathematics by Erwin Kreyszig (Wiley).
Introduction to Partial Differential Equations and Boundary Value Problems by Rene Dennemeyer
Besides going through relevant topics of the textbook, it is strongly advised that the students follow the class Lectures and discussions regularly for a thorough understanding of the topics.