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Department of Mathematics
MATH235 - Mathematics
IIA
Unit Syllabus
Calculus:
- Functions of several variables, open
sets, limits and continuity.
- Differentiation, partial derivatives,
total derivatives, consequences of differentiability, conditions
for differentiability, gradients and directional derivatives.
- Implicit and inverse function theorems.
- Higher order derivatives, iterated partial
derivatives, Taylor's theorem, stationary points, constrained
maxima and minima.
- Double integrals, Fubini's theorem,
mean value theorem, triple integrals.
- Change of variables, planar transformations,
the Jacobian, triple integrals.
Algebra:
- Real inner product spaces, angles and
orthogonality, orthogonal and orthonormal bases, orthogonal projections.
- Brief discussion of applications to
real Fourier series.
- Matrices, change of basis, orthogonal
matrices, eigenvalues and eigenvectors, orthonormal diagonalization.
- Applications to least squares approximation
and to quadratic forms.
- Linear transformations, kernel and range,
inverse linear transformations, matrices of linear transformations,
change of basis, eigenvalues and eigenvectors.
- Complex vector spaces, unitary matrices,
unitary diagonalization.
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