Ordinary Differential Equation

Type of Course:

• Compulsory Yes (Cohort BA (H) Mathematics)
• Elective Yes (Cohort BA (H) other than Mathematics)

Course Coordinator and Team: Kranti Kumar (cc) and Nikhil Sharma

Email of course coordinator: kranti[at]aud[dot]ac[dot]in

Pre-requisites: Mathematics at XII grade level

Aim: Differential Equations is a subject that is most widely used by academics (Mathematicians and others) as well as professionals and hence is a most desirable area of study.The present course on Ordinary Differential Equations has been designed to introduce various techniques to solve First and higher order linear differential equations as well as a system of equations. The course has an added attraction of the compulsory lab component where using Mathematica, one can plot the graphs of the curves represented by the solutions of the differential equations. This helps students to visualise the geometry behind a differential equation. The students who are interested in only solutions and not the techniques by which a differential equation is solved also have the option of using Mathematica commands to solve them..

Brief description of modules/ Main modules:

• First Order Differential Equations
• Linear differential equations
• Series solution
• Laplace Transform
• Total and Simultaneous differential Equations
• Lab work using MATHEMATICA

Refererences:

MAIN REFERENCES:

• M. L. Abell and J. P. Braselton, Differential Equations with MATHEMATICA, Elsevier Academic Press, 3rd edition, 2004.
• S. L. Ross, Differential Equations, John Wiley and Sons, India, 3rd Edition, 2004.

ADDITIONAL REFERENCES:

• Belinda Barnes and G. R. Fulford, Mathematical Modeling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Taylor and Francis, 2nd edition, 2009.
• William E Boyce and Richard C DiPrima, Elementary Differential equations and Boundary Value problems, John Wiley and sons, 8th edition, 2005.
• C. H. Edwards and D. E. Penny, Differential Equations and Boundary Value Problems: Computing and Modeling, Pearson Education, India, 2005.

Tentative Assessment schedule with details of weightage: