Singapore University of Social Sciences

Numerical Methods and Advanced Calculus (MTH217)


MTH217 considers more advanced techniques to solve various problems in applied mathematics, and prepares students for higher level 3 studies in applied mathematics.

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.


  • Functions of Several Variables.
  • Classification of stationary points.
  • Numerical Methods for Ordinary Differential Equations.
  • Systems of differential equations.
  • Fourier Series.
  • Fourier series for even and odd functions, and for any periodic functions.
  • Differential Equations.
  • Heat transfer problems.
  • Vector Calculus.
  • Coordinate systems.
  • Multiple Integrals.
  • The scalar line integral, area integrals, volume integrals.

Learning Outcome

  • Use functions of several variables.
  • Solve optimization points of functions of several variables.
  • Identify appropriate numerical methods to solve a class of differential equations.
  • Calculate and contrast exact and numerical solutions to a class of differential equations.
  • Describe Fourier series of functions and periodic functions.
  • Solve partial differential equations by separating variables.
  • Determination of vector calculus problems in 3 dimensions.
  • Identify force problems using potential fields.
  • Solve multiple integrals, including area, centre of mass and inertial multiple integrals.
  • 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 numerical methods and advanced calculus using Mathcad.
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