Mathematics 1B

Learning Outcomes

• Students who have succeeded in this course should be able to:
  
  Define the key concepts associated with:
  
• differential equations,
  
• convergence of sequences,
  
• Taylor polynomials and series,
  
• vectors in two and three dimensions,
  
• determinants, eigenvalues and eigenvectors,
  
• curves and surfaces.
  
  Use techniques from the course (including the use of computer-based tools where appropriate) to:
  
• solve elementary first or second order differential equations.
  
• prove simple statements using the principle of mathematical induction,
  
• test sequences or series for convergence,
  
• find Taylor polynomials and use them to solve problems involving limits or approximation,
  
• describe and solve geometric problems using vectors,
  
• find the eigenvalues and eigenvectors of small matrices,
  
• parameterise and analyse curves in Cartesian and polar coordinates,
  
• analyse surfaces by finding their slopes and relative extrema.
  
  Describe and interpret:
  
• the solutions of differential equations in a variety of contexts,
  
• infinite sequences and series, their limits and applications,
  
• the connection between vectors and the geometry of lines and planes,
  
• curves and surfaces and their key properties.
  
  Identify the appropriate method of solution for differential equations.
  
  Synthesise appropriate techniques from different sections of the course, for example combining techniques of sequences and differential equations to determine long term behaviour, or combining vector geometry with curves and surfaces.

University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Prerequisites

Restrictions

For further information see Mathematics and Statistics .