 COURSE SUMMARY
Course Title:
Differential Equations
Course Code:
18MAT201
Year Taught:
2018
2019
Semester:
3
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Differential Equations' is a course offered at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

Scope and Objectives

To enable students to develop the knowledge of standard concepts of ordinary differential equations and apply analytical techniques to compute solutions to various differential equations.

Syllabus

Unit I: Ordinary Differential Equations

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

Equations of first order but of higher degree:

Equations solvable for dy/dx, y, x, equations in Clairaut’s form, equations reducible to Clairaut’s form.
Part I: 4.1-4.11

Unit II: Equations of Second order

Linear homogeneous differential equations with constant coefficients, Euler- Cauchy equation, Linear Nonhomogeneous Differential Equations: 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

Unit III: Systems of first order linear equations

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

Partial Differential Equations
Review of partial differential equations (order, degree, linear, nonlinear).

Unit IV:

Formation of equations by eliminating arbitrary constants and arbitrary functions.

Solutions of partial differential equations: General, 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 p = dz/dx and q = dz/dy.
Part III: 1.1 – 1.5, 2.3-2.12, 3.1-3.2, 3.7-3.8, 3.10-3.18

Unit V:

Classification of partial differential equations of second order. Homogeneous linear partial differential equations with constant coefficient of higher order.Non-homogeneous linear partial differential equations of higher order.
Part III: 8.1, 4.1-4.12

Textbook

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.