B.Sc. Hons

B.Sc. Hons Applied Mathematics, with distinction and a 90% aggregate.

Funding

  • Harry Crossley Foundation Honours Research Fellowship
  • UCT Council Senior Entrance Merit Scholarship
  • Hyman Liberman Scholarship
The Hyman Liberman Scholarship is awarded in each year to the student with the highest overall B.Sc. results in the preceding year.

Courses

These courses were selected from the departments of Applied Mathematics, Physics, Statistics, Mechanical Engineering and Electrical Engineering.

Advanced Mathematical Physics A Existence and stability of soliton solutions
Singular perturbation expansion
Adiabatic approximations
Topological solitons
Vortices in ferromagnets
Grob-Pitaevski, Maxwell and Chern-Simons vortices
Magnetic monopoles, instantons
Advanced Mathematical Physics BInverse Scattering Transform for the non-linear Schrodinger, KdV and sine-Gordon
NLS as a Hamiltonian system
Infinite sequences of integrals of motion
The Riemann problem
Applications to solitons of the principle of chiral fields
Reduction group
Applications to the two-dimensional Toda lattices
Continuum MechanicsTensor algebra and analysis
Configurations and kinematics of continuous media
Deformation and strain tensors
Balance of mass, linear and angular momentum, and energy: the stress tensor
Constitutive theory
Linear elasticity
Ideal fluids and Newtonian fluids
Viscous Newtonian fluids and Navier-Stokes
Quantum MechanicsHilbert spaces
Schrodinger's Equation in coordinate and momentum space
Uncertainty principle
Linear harmonic oscillator by Dirac's method
Rotation Groups
Creation/annihilation operations
Spin
Time-dependent perturbation
Radiative decays
Gauge invariance
Supersymmetry
Pauli, Dirac and Klein-Gordon equations
Relativistic corrections to the hydrogen atom
Zeeman and Stark effects
Operations Research A & B
Linear progamming, the dual problem
Integer programming
Pareto frontiers
Call center simulations
Queue modelling
Memoryless processes
Exponential and Poisson distributions
Decision ModellingDecision trees
Criteria weighting methods
Quantifying preferences
Utility curves
Expected utility
Non-linear optimisation
Optimisation problems
Gradient descent
Quadratic programming
Karush-Kuhn-Tucker equations
Digital Signal ProcessingDigital Signal Processing
    Discrete Time Fourier Transform
    Z-Transform
    Continuous time systems
    Converting discrete and continous time
    DFT and FFT
    Filter design
Radar Signal Processing
    Analytic representation and sampling of signals
    Linear radar system model
    Transmit pulse waveforms
Image Processing
    Multidimensional signal processing
    The human visual system
    Image formation in digital and optical systems
    Edge detection methods
Electronic CircuitsDiode and Zener junctions and circuit analysis
AC models of Bipolar Junction Transistors (BJT's)
T-equivalence, Ebers-Moll model
Basic follower, amplifier circuit configurations
Common-emitter biasing
Midpoint collector feedback
Miller's theorem, feedback in amplifiers
Transistor high frequency behaviour
Differential amplifiers (long-tailed pair)
Darlington and cascode connections
Wilson and other current mirrors
Operational Amplifiers
Frequency dependence and bode plots
Slew rate, bias current, offset voltage
Linear opamp circuits
    Optional inverter
    Inverting amplifier
    Follower with gain
    Universal adder-subtractor
    Differential amplifiers and CMRR
    Transimpedance amplifier
Opamp applications
    Integrators and (stable) differentiators
    FET-switched inverters and set-able integrators
    Rectification and peak detection
    Hysteretic comparators and relaxation oscillators
    Synchronous detection
    Bootstrapping impedances
    Lab Project: Voltage Controlled Oscillator
Filters
    s-domain analysis of opamp circuits
    Stabilisation with lead-lag network
    Wein-bridge oscillator and inductorless design
    Bessel, Chebyshev and Butterworth filters
    Sallen and Key filter realisation
    Multiple feedback bandpass filter
    State variable filter and notch filters

ċ
Graham Poulter,
17 Mar 2010, 13:11
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