EM211

On successful completion of the course, the students should be able to;

1. Identify and derive the mathematical models of many physical problems as differential equations.
2. Solve first order separable, linear and exact differential equations and reducible forms.
3. Solve higher order linear ordinary differential equations analytically using Doperators,method of undetermined coefficients and Laplace transformations and analyze the solution of such second order equations.
4. Apply matrix methods and Laplace transform in solving systems of linear systems ofordinary differential equations.

1. Introduction: Differential Equations as a mathematical model and classification.
2. First order ordinary Equations: Separable, linear, exact, reducible forms.
3. Higher order ordinary linear equations with constant coefficients: D-operators, undetermined coefficients; bracket method; solution behaviors.
4. Linear Systems: Eigenvalue and eigenvector method; decoupling; matrix exponential method.
5. Laplace Transforms: Laplace transform of functions and derivatives, solving ordinary differential equations and linear systems, convolution.

1. R.K. Nagle, E.W. Saff, A.D. Snider,Fundamentals of Differential Equations, 8th edition, (2012), Pearson Education.
2. E. Kreyszig, Advanced Engineering Mathematics,9th edition, (2006), John Wiley &sons Inc.
3. Philip Franklin,Differential Equations for Engineers,5th edition, (1980), Dover Publications.