23UMATC34 Differential Equations and Applications Syllabus:

23UMATC34 Differential Equations and Applications Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives of the Course

  • Knowledge about the methods of solving Ordinary and Partial Differential Equations.
  • The understanding of how Differential Equations can be used as a powerful tool in solving problems in science.

UNIT-I:

Equations of the First Order and Higher Degree- Equations Solvable for p- Equations Solvable for x – Equations Solvable for y – Clairaut’s Equation- Linear equations of Second and Higher Order with constant coefficients.

UNIT-II:

Simultaneous Equations, Euler’s Homogeneous Linear Differential Equations– Legendre’s Linear Equations

UNIT-III:

Method of Variation of Parameters- Method of undetermined Coefficients. Total differential Equation

UNIT-IV:

Formation of PDE – Complete Integral – Particular Integral – Singular Integral – Equation’s Solvable by direct Integration – Solving equations of the types: f(p, q) = 0, f(x, p, q) = 0, f(y, p, q) = 0, f(z, p, q) = 0, f(x, p) = f(y, p), Z = p x + q y + f(p, q), Equations Reducible to standard form

UNIT-V:

Lagranges Linear Equation, Charpits Method

Recommended Text

  • P.Kandasamy, K.Thilagavathy [2004], “Mathematics for B.Sc” Vol-III, S.Chand & Company Ltd., New Delhi-55.

Reference Books

  • A. Murray, Introductory course in Differential Equations, Orient and Longman
  • T. H.Piaggio, Elementary Treaties on Differential Equations and their applications, C.B.S Publisher & Distributors, Delhi,1985.
  • Horst R. Beyer, Calculus and Analysis, Wiley, 2010.
  • Braun, M. Differential Equations and their Applications. (3rd Edn.), Springer- Verlag, New York. 1983.
  • Boyce, W.E. and R.C.DiPrima. Elementary Differential Equations and Boundary Value Problems. (7th Edn.) John Wiley and Sons, Inc., New York. 2001.
  • Sundrapandian, V. Ordinary and Partial Differential Equations, Tata McGraw Hill Education Pvt.Ltd. New Delhi, 2013
  • Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, 1984.
  • I. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International Edition, 1967.
  • G.F. Simmons, Differential equations with applications and historical notes, 2ndEd, Tata Mcgraw Hill Publications, 1991.