Course

Unit 1

Review of differential equations (order, degree, linear, nonlinear, implicit and explicit form of solution, general solutions, particular solution, singular solution). Exactness, nonexact equations reduce to exact form.Part I: 1.1-1.9, 2.12-2.22 (5 hours)Equations solvable for dy/dx, y, x, equations in Clairauts form, equations reducible to Clairauts form. Part I: 4.1-4.11 (4 hours)

Unit 2

Linear homogeneous differential equations with constant coefficients, Euler- Cauchy equation,Linear Nonhomogeneous DifferentialEquations: Wronskian, linear independence, Method of undetermined coefficients. Method of variation of parameters.Part I: 5.1-5.5, 6.1-6.3, 1.12,1.13, 5.26-5.27, 7.1-7.5 (9 hours)

Unit 3

Conversion of nth order differential equation to n first order differential equations, homogeneous linear system with constant coefficients, fundamental matrices, complex eigen values, repeated eigenvalues. simultaneous linear differential equations with constant coefficients, simultaneous linear differential equations with variable coefficients, Part I: 8.1-8.3, 2.1- 2.7(8 hours) Review of partial differential equations (order, degree, linear, nonlinear).

Unit 4

Formation of equations by eliminating arbitrary constants and arbitrary functions. General, particular and complete integrals.Lagranges linear equation, Charpits 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 Clairuts form z = px + qy + f(p,q) where p= ?z/?x and q= ?z/?y. Part III: 1.1 1.5, 2.3-2.12, 3.1-3.2, 3.7-3.8, 3.10-3.18 (13 hours)

Unit 5

Homogeneous linear partial differential equations with constant coefficient of higher order. Non-homogeneous linear partial differential equations of higher order, method of separation of variables.Part III: 4.1-4.12 (13 hours)

Text Books / References

Textbooks:

1. M.D. Raisinghania, Ordinary and Partial Differential Equations, S.Chand, 18th edition, 2016.

References:

1. William E. Boyce and Richard C.DiPrima, Elementary differential equations and boundary value problems, Wiley india, 9th edition, 2012
2. Nita H, Shah, Ordinary and Partial Differential Equations: Theory and Applications, PHI learning, 2nd edition, 2015.
3. Dennis Zill, A First Course in Differential Equations, Cengage Learning, 9th edition, 2009.

Course Outcomes: After successful completion of the course, students will be able to:

• CO1: Understand and apply the first order differential equations to some problems
• CO2: Understand the solutions of the higher order ODE with various methods.
• CO3: Understand the formation of the first order PDE.
• CO4: To learn the solutions of higher order PDE

CO-PO Mapping: