Mathematics for Mechanical Engineering (MEng2.6)
The syllabus for this part of the second year course covers:
[topics recently removed from the syllabus are included below in square brackets]
Systems of linear differential equations. Normal modes, natural oscillation frequencies.
Double integrals, Jacobians. Line integrals, Green's theorem in the plane.
Vector calculus: grad,div and curl; directional derivatives.
Numerical solutions of ordinary differential equations. [Picard iteration.] Euler's Method. Runge-Kutta methods.
Partial Differential Equations (PDEs). Solution by separation of variables. Hyperbolic, elliptic and parabolic equations.
Numerical solution of parabolic PDEs. Finite Difference Methods. [Solution of large numbers of sparse simultaneous equations.] Explicit and Crank-Nicolson methods, [Jacobi and Gauss-Seidel methods.]
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