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**The GE Differential Equations Course for Semester III, Delhi University has been taught by Mr. Dheeraj Suri. The Video Lectures are based upon the books prescribed by the University of Delhi. The Duration of Video Lectures is approximately 35 Hours.**

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**Demo Lectures**

**Demo Lectures****Demo PDF of Study Material**

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**Exam Pattern**

**The Question Paper of 75 Marks**

**Part**

**Course Content**** of Our ****Video Lectures**

**Course Content****of Our****Video Lectures****Lectures are Updated as per the Latest Syllabus for 2021**

**Lectures are Updated as per the Latest Syllabus for 2021****Unit 1 : ****Ordinary Differential Equations & Applications**

**Unit 1 :****Ordinary Differential Equations & Applications****Unit 2 : ****Explicit Methods of Solving Higher Order Linear Differential Equations**

**Unit 2 :****Explicit Methods of Solving Higher Order Linear Differential Equations****Unit 3 : ****First Order & Second Order Partial Differential Equations**

**Unit 3 :****First Order & Second Order Partial Differential Equations****End of Syllabus**

**End of Syllabus****Course Description**

**Course Objectives:** This course includes a variety of methods to solve ordinary and partial differential equations with basic applications to real life problems. It provides a solid foundation to further in mathematics, sciences and engineering through mathematical modeling.

**Course Learning Outcomes:** This course will enable the students to learn:

(i) To analyze real-world scenarios to recognize when ordinary (or systems of) or partial differential equations are appropriate for creating an appropriate model.

(ii) Explicit methods of solving higher-order linear differential equations.

(iii) To solve first and second order PDE using method of characteristics, separation of variables, and reducing to suitable canonical form.

**Course Contents:**

**Unit 1: Ordinary Differential Equations and Applications**First order exact differential equations, Integrating factors and rules to find integrating factors. Linear equations and Bernoulli equations, Orthogonal trajectories and oblique trajectories, Basic theory of higher order linear differential equations, Wronskian and its properties; Solving differential equation by reducing its order.

**Unit 2. Explicit Methods of Solving Higher-Order Linear Differential Equations**

Linear homogenous equations with constant coefficients, Linear non-homogenous equations, The method of undetermined coefficients, The method of variation of parameters, The Cauchy-Euler equation; Simultaneous differential equations.

**Unit 3. First and Second Order Partial Differential Equations**

Partial differential equations: Basic Concepts and definitions. Mathematical problems, First order equations: Classification, Construction, Geometrical interpretation. Method of characteristics, General solutions of first order partial differential equations. Canonical forms and method of separation of variables for first order partial differential equations. Classification of second order partial differential equations. Reduction to canonical forms. Second order partial differential equations with constant coefficients, General solutions.

**References:**

1. Kreyszig, Erwin. (2011). Advanced Engineering Mathematics (10th ed.). Wiley India.

2. Myint-U, Tyn and Debnath, Lokenath (2007). Linear Partial Differential Equations for Scientist and Engineers (4th ed.). Birkkäuser Boston. Indian Reprint.

3. Ross, Shepley. L. (1984). Differential Equations (3rd ed.). John Wiley & Sons. **Additional reading:**

Sneddon I. N. (2006). Elements of Partial Differential Equations. Dover Publications.