Department of Mathematics
MATH133 - Mathematics
IB (Advanced)
Unit Syllabus
Calculus:
- Review of functions of a real variable.
- Introduction to differential equations;
modelling with differential equations.
- First order ordinary differential equations:
separation of variables, homogeneous equation, linear equation;
applications.
- Second order linear ordinary differential
equations with constant coefficients: homogeneous case, method
of undetermined coefficients, lifting of the trial function,
initial and boundary conditions; applications.
- Functions of two variables: partial
derivatives, total derivative, linearization of the derivative,
tangent planes and normals, stationary points, change of variables,
polar coordinates, constrained optimization; exact first order
ordinary differential equations.
- Real sequences, recurrence relations,
series, relationship with integrals, power series, Taylor and
Maclaurin series; applications to differential equations.
Algebra:
- Vector spaces, subspaces, linear combination,
linear independence, basis and dimension.
- Row space, column space, nullspace,
rank of a matrix.
- Modelling with matrices in science and
finance.
- Eigenvalues and eigenvectors, diagonalization
of matrices; applications.
- Congruences.
- Elementary group theory.
