ATMO 430 Syllabus
1. Fundamentals (Week 1)
Complex and real numbers
Logarithms and exponentials
Trigonometric and hyperbolic functions
Computer Project 1: Solution of a quadratic equation
2. Differential Calculus (Weeks 2-3)
Derivatives, product, quotient and chain rules
Derivatives of elementary functions
Taylor series representation of functions
Partial and total derivatives
Gradient of a scalar
Divergence and curl of vectors
Computer Project 2: Evaluation of the exponential function
Computer Project 3: Newton's method to obtain the roots of functions
3. Integral Calculus (Weeks 4-5)
Basic techniques of integration
Use of tables of integrals
Fourier series and integrals
Computer Project 4: Integration using the Trapezoid and Simpson's rule
4. Ordinary Differential Equations (Weeks 6-7)
Fundamentals of second order linear differential equations
Series solutions of second order ODEs
Introduction to special functions
Numerical solutions of ODEs
Computer Project 5: Numerical solution of ODEs by Euler's and Runge-Kutta methods
5. Partial Differential Equations (Weeks 8-9)
Fundamentals
Laplace and Poisson's equations
Shallow water equations
Computer Project 6: SOR solution of Poisson's equation
6. Numerical Schemes (Weeks 10-12)
Fundamentals
Advection equation
Subgrid flux terms
Coriolis terms
Pressure gradient and velocity divergence
Spectral techniques
Computer Project 7: Numerical solution of advection equation
7. Statistics (Weeks 13-16)
Basic definitions
Theoretical probability distributions
Hypothesis testing
Time series analysis
Curve fitting, square regression and correlation coefficients
Probabilistic field (ensemble) forecasts
Computer Project 8: Hypothesis testing of meteorological data
Final examination (11:00 am - 1:00 pm, Tuesday, 12 December 2000)
Back to Atmospheric
Sciences Home Page