| Course Name | Differential Equations |
| Course Code | 25MAT337 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | Electives: Mathematics |
| Campus | Mysuru |
Equations of First Order and First Degree: Review of Ordinary Differential Equations (order – degree – linear – nonlinear – implicit and explicit form of solution – general solutions – particular solution – singular solution) – Exact Equations – Integrating Factors – Equations Solvable by Separation of Variables – Homogeneous Equations – Linear Equations – Rules for determining Integrating Factors
(Sections: 1.1-1.9, 2.1-2.24)
Equations of First Order and of Higher Degree: Equations Solvable for , Equations Solvable for y, Equations Solvable for x, Clairaut’s Form, Orthogonal Trajectories of a Given Family of Curves
(Sections: 4.1-4.17, 3.1-3.5)
Linear Equations of Higher Order: Solution of Linear homogeneous differential equations with constant coefficients – Euler-Cauchy equation – Solution of Linear Non-homogeneous Equations – Method of undetermined coefficients – Method of variation of parameters – Operator Methods for Finding Particular Integrals – Solution of simultaneous linear differential equations with constant coefficients
(Sections: 5.1-5.27, 6.1-6.11, 7.1-7.4, 8.1-8.3)
Partial Differential Equations: Review of Partial Differential Equations (order, degree, linear, nonlinear) – Formation of equations by eliminating arbitrary constants and arbitrary functions. – Particular and Complete integrals – Lagrange’s Linear Equation – Charpit’s Method – Methods to Solve the First Order Partial Differential Equations of the Forms f(p,q) = 0, f(z,p,q) = 0, f1(x,p) = f2(y,q) and Clairut’s Form z = px + qy + f(p,q) where (Sections: 1.1 – 1.12, 2.1-2.15, 3.1-3.18)
OBJECTIVE: To enable students to develop the knowledge of standard concepts of ordinary and partial differential equations and apply analytical techniques to compute solutions to various differential equations.
Course Outcomes
| COs | Description |
| CO1 | To exhibit the basic concepts of differential equations into problems. |
| CO2 | To solve basic application problems described by first order differential equations. |
| CO3 | To solve basic application problems described by second order linear differential equations with constant coefficients. |
| CO4 | To create and analyze mathematical models using higher order differential equations. |
| CO5 | To illustrate the concepts of Lagrange’s linear equation and Charpit’s method to solve partial differential equations. |
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO2 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO3 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO4 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO5 | 3 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
Text books:
1. M.D. Raisinghania, Ordinary and Partial Differential Equations, 18th edition, S.Chand, 2016.
References:
DISCLAIMER: The appearance of external links on this web site does not constitute endorsement by the School of Biotechnology/Amrita Vishwa Vidyapeetham or the information, products or services contained therein. For other than authorized activities, the Amrita Vishwa Vidyapeetham does not exercise any editorial control over the information you may find at these locations. These links are provided consistent with the stated purpose of this web site.
