Singapore University of Social Sciences

Further Mathematical Methods and Mechanics (MTH215)


MTH215 focuses on the use of matrix algebra and related structures to model complicated and coupled motions. The powerful techniques of linear algebra and calculus are fully exploited to solve a large class of problems arising from real-life senerios.

Level: 2
Credit Units: 5
Presentation Pattern: Every July
E-Learning: BLENDED - Learning is done MAINLY online using interactive study materials in Canvas. Students receive guidance and support from online instructors via discussion forums and emails. This is supplemented with SOME face-to-face sessions. If the course has an exam component, this will be administered on-campus.


  • Matrices and Determinants.
  • Eigenvalues and Eigenvectors.
  • Simultaneous Differential Equations.
  • Homogeneous and inhomogeneous systems and second-order systems.
  • Non-linear Differential Equations.
  • Analyze and interpret graphical solutions of the models.
  • Damped Vibrations.
  • Forced Vibrations.
  • Normal Modes.
  • Find the normal modes of simple oscillating mechanical systems.
  • Systems of Particles.
  • Apply Newton's law of restitution and conservation laws to solve collision problems.

Learning Outcome

  • Identify simultaneous equations and matrix algebra applications.
  • Solve applications of eigenvalues and eigenvecors.
  • Explain when systems of differential equations can be expressed in matrix form.
  • Calculate solutions of differential equations.
  • Express damped dynamical systems as second order coupled system.
  • Describe when a coupled second order system of differential equations exhibits normal modes.
  • Relate normal modes to initial conditions.
  • Apply centre of mass, momentum and energy conservation of an interacting system of particles.
  • Apply a range of mathematical techniques to solve a variety of quantitative problems.
  • Analyze and solve problems individually and/or as part of a group.
  • Solve a number of problem sets within strict deadlines.
  • Solve problems related to mathematical methods and mechanics using Mathcad.
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