EM1030 Differential Equations

EM1030

Differential Equations

2

Core

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.

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

• ● 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 Inc.