Semester:

2

Course Code:

EM1030

Course Name:

Differential Equations

Credit Value:

2 (Notional hours: 100)

Prerequisites:

None

Core/Optional

Core

Hourly Breakdown

Lecture hrs.

Tutorial hrs.

Assignment hrs.

Independent Learning & Assessment hrs.

24

6

-

70

Course Aim: To introduce analytical solving techniques for differential equations with constant coefficients and interpret the solutions.

Intended Learning Outcomes:

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

➢      solve higher order ordinary differential equations with constant coefficients.

➢      analyze the solution of a second order ordinary differential equation with constant coefficients.

➢      apply matrix methods and Laplace transform in solving systems of ordinary differential equations with constant coefficients.

➢      obtain analytical solutions of first order linear partial differential equations using method of characteristics.

➢      classify second order linear partial differential equations and solve the wave equation, the Laplace equation and the heat equation.

Course Content:

➢      Second Order Ordinary Differential Equations: Spring mass damper equation: forced oscillations and resonance.

➢       Laplace Transform: Definition, existence and properties; Laplace transform of standard functions, derivatives and integrals; solve ordinary differential equations with constant coefficients; discontinuous forcing functions; convolution.

➢      Boundary Value Problems: boundary value problem of a second order differential equation with constant coefficients using direct calculation; Euler Bernoulli equation and Macaulay’s Bracket method.

➢      Systems of ODEs: converting higher-order differential equations to a system of first-order differential equations; eigenvalue eigenvector method; matrix exponential method.

➢      First order linear partial differential equations: Partial differential equations as a mathematical model and Classification; Method of characteristics.

➢      Second order linear partial differential equations: classification: hyperbolic, parabolic and elliptic equations; Fourier series; method of separation of variables: wave equation, heat equation, Laplace equation on rectangular domains with homogeneous boundary conditions.

Teaching /Learning Methods:

Classroom lectures, tutorial discussions and in-class assignments

Assessment Strategy:

Continuous Assessment 50%

Final Assessment 50%

Details: Tutorials/Assignments/Quizzes 20% Mid Semester Examination 30%

Theory (%)

50%

Practical (%)

-

Other (%)

-

Recommended Reading:

➢      R.K. Nagle, E.W. Saff, A.D. Snider, Fundamentals of Differential Equations, 8th edition, (2012), Pearson Education.

➢      E. Kreyszig, Advanced Engineering Mathematics, 9th edition, (2010), John Wiley &sons Inc.

➢      Jiří Lebl, Differential Equations for Engineers, Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org).

➢      Walter A. Strauss, Partial Differential Equations, 2nd edition,(2007), John Wiley and Sons In