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-Kutte methods.
• Fourier Series.
• 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.]