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Basic Details:

  • Course Code: EM 1030
  • Credits: 2
  • Compulsory/Optional: Chemical, Computer, Civil, Mechanical, Manufacturing

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:

Spring mass damper equation: forced oscillations and resonance.

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 problem of a second order differential equation with constant coefficients using direct calculation; Euler Bernoulli equation and Macaulay’s Bracket method.

Converting higher-order differential equations to a system of first-order differential equations; eigenvalue eigenvector method; matrix exponential method.

Partial differential equations as a mathematical model and Classification; Method of characteristics.

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.

Time Allocation (Hours):

Lectures
0
Tutorials
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