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Numerical analysis and modelling for scientists and engineers

Numerical analysis is a multidisciplinary subject which is recognized as an integral part in many areas including: mathematics, computer science, physics, commerce, engineering, biology, e.t.c.

Participants will get a comprehensive introduction to either Python or SageMath after which they will use either of these programming languages to find numerical solutions to applied scientific problems. While analytic/symbolic methods will not be our main focus, we will nonetheless use the Python Sympy library or SageMath Symbolic Toolbox to find analytic solutions to symbolic expressions.

This numerical analysis course targets students and professionals in mathematics, engineering, finance, economics, biology amnong others. Those who have an interest in mathematical modelling and simulation are highly encouraged to apply.

Dates Monthly: Starts every Third Monday
Duration: 2 week (10 days)
Time 0830Hrs - 1630Hrs EAT (Mon - Fri)
Delivery Classroom (online also available)
Charges KES 125,500 ($1,250)
The course can be customized to fit your specific needs in terms of course content, date, time and venue (including online sessions). Please talk to us for the customization.
  1. Getting started with Python
    • About Python
    • Python Editors
    • Python Modules
    • Structure of Python commands
    • Creating variables and arrays
    • Working with strings
    • Input and output functions
    • Accessing Python help
  2. Arithmetic operations and built-in functions
    • Real Numbers
    • Complex Numbers
    • Lists
    • Tuples
    • Round functions
    • Mathematical functions
    • Tuples
  3. Python functions and program control flow
    • Introduction
    • Scripts
    • User defined functions
    • Program control flow
  4. Vectors and matrices with NumPy library
    • Introduction
    • Creating scalars and arrays
    • Sequences
    • Subscripting arrays
    • Special matrices
    • Restructuring matrices
    • Operations on matrices
  5. Symbolic mathematics with SymPy library
    • Introduction
    • Polynomials and function simplification
    • Solutions of equations
    • Limits
    • Series expansion
    • Series summation
    • Symbolic operations on matrices
    • Differentiation and Integration
    • Ordinary differential equations
    • Transforms
    • Vector differential calculus
    • Vector integral calculus
  6. Vectors and matrices with Numpy library
    • Introduction to plotting with Matplotlib library
    • Introduction
    • The plot and fplot functions
    • Titles and axes labels (x and y)
    • Creating multiple graphs
    • Adding annotations / text to graphs
    • X and Y axes properties
    • Additional options
  7. Direct solutions of linear systems of equations
    • Introduction
    • Elementary row operations
    • Elementary row operation applications
    • LU factorization
    • Solutions of linear systems with Python built-in functions
  8. Iterative and conjugate gradient methods
    • Introduction
    • Vector norms
    • Matrix norms
    • Iterative techniques
    • Conjugate gradient methods
  9. Equations with multiple roots
    • Introduction
    • Closed domain methods
    • Open domain methods
    • Other methods
    • Equations with multiple roots
  10. Solutions of systems of non-linear equations
    • Introduction
    • Fixed point iteration
    • Newton’s method
    • Quasi-Newton methods: Broyden method
    • Steepest gradient techniques: Steepest descent
    • Homotopy and continuation methods: Continuation algorithm
  11. Numerical differentiation
    • Introduction
    • Direct polynomial fit
    • Newton difference methods
    • Three point formulas
    • Five point formulas
    • Richardson extrapolation
    • Second derivative mid-point formula
  12. Numerical integration
    • Introduction
    • Direct polynomial fit
    • Newton-Cotes formulas
    • Composite rules
    • Romberg integration
    • Gaussian quadrature
    • Double integration
  13. Curve fitting and interpolation
    • Introduction
    • Least square regression
    • Linearizing nonlinear data
    • Polynomial interpolation
    • Interpolation using Splines
  14. Initial value problems
    • Introduction
    • Single step methods
    • Adaptive Runge-Kutta methods
    • Multi-step methods
    • Predictor-corrector methods
    • Extrapolation method
    • Systems of ordinary differential equations
    • Higher order ordinary differential equations
  15. Boundary value problems
    • Introduction
    • Shooting method
    • Finite difference method
    • Rayleigh-Ritz method

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