## MA3356 Syllabus - Differential Equations - 2021 Regulation Anna University

MA3356

DIFFERENTIAL EQUATIONS

LTPC

3104

COURSE OBJECTIVES:
• To acquaint the students with Differential Equations which are significantly used in engineering problems.
• To introduce the basic concepts of PDE for solving standard partial differential equations.
• To acquaint the knowledge of various techniques and methods of solving ordinary differential equations.
• To understand the knowledge of various techniques and methods of solving various types of partial differential equations.
• To understand the finite methods for time dependent partial differential equations.

UNIT I

ORDINARY DIFFERENTIAL EQUATIONS

9+3

Higher order linear differential equations with constant coefficients – Particular integrals: Operator methods, Method of variation of parameters, Methods of undetermined coefficients– Cauchy’s and Legendre’s linear equations – Simultaneous first order linear equations with constant coefficients.

UNIT II

PARTIAL DIFFERENTIAL EQUATIONS

9+3

Formation of partial differential equations – Singular integrals -- Solutions of standard types of first order partial differential equations - Lagrange’s linear equation -- Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and nonhomogeneous types.

UNIT III

NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

9+3

Explicit Adams-Bashforth Techniques, Implicit Adams-Moulton Techniques, Predictor-Corrector Techniques, Finite difference methods for solving two-point linear boundary value problems, Orthogonal Collocation method.

UNIT IV

FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS

9+3

Laplace and Poisson’s equations in a rectangular region: Five point finite difference schemes, Leibmann’s iterative methods, Dirichlet and Neumann conditions – Laplace equation in polar coordinates: finite difference schemes.

UNIT V

FINITE DIFFERENCE METHOD FOR TIME DEPENDENT PARTIAL DIFFERENTIAL EQUATION

9+3

Parabolic equations: explicit and implicit finite difference methods, weighted average approximation - Dirichlet and Neumann conditions – First order hyperbolic equations – method of characteristics, different explicit and implicit methods; Wave equation: Explicit scheme- Stability of above schemes.

TOTAL: 60 PERIODS

COURSE OUTCOMES: Upon successful completion of the course, students will be able to:
1. Apply various methods of solving differential equation which arise in many application problems.
2. Understand how to solve the given standard partial differential equations.
3. Understand the knowledge of various techniques and methods for solving first and second order ordinary differential equations.
4. Solve the partial and ordinary differential equations with initial and boundary conditions by using certain techniques with engineering applications.
5. Familiar with various methods to solve time dependent partial differential equations.

TEXT BOOKS:
1. Grewal. B.S, “Higher Engineering Mathematics”, 44th Edition, Khanna Publications, New Delhi, 2018.
2. Gupta S.K., “Numerical Methods for Engineers” (Third Edition), New Age Publishers, New Delhi , 2015.
3. M K Jain , S R K Iyengar , R K Jain, “Computational Methods for Partial Differential Equations”, New Age Publishers, New Delhi , 1994.

REFERENCES:
1. Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2012.
2. Peter V. O’Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, 2012.
3. Saumyen Guha and Rajesh Srivastava, “Numerical methods for Engineering and Science”, Oxford Higher Education, New Delhi, 2010.
4. Burden, R.L., and Faires, J.D., “Numerical Analysis – Theory and Applications”, Cengage Learning, India Edition, New Delhi, 2009. Publishers,1993.
5. Morton K.W. and Mayers D.F., “Numerical solution of partial differential equations”, Cambridge University press, Cambridge, 2002.