Select and implement methods for interpolation and understand their consequences for convergence of model results as discretization is refined.
Carry out a few simple methods for numerical integration
Implement procedures for numerical differentiation
Write programs to solve systems of equations, both linear and non-linear
Computational thinking is becoming widely recognized as a skill necessary for every educated person in a technologically advanced society.
We will focus on just a subset of computational thinking which concerns creating models of the physical world – something that engineers frequently need to do. Because of that choice, this course covers many topics normally viewed as within the domain of mathematics such as algebra and calculus, but the solution procedures are algorithmic rather than symbolic.
The major themes of the course are:
Representation — How do you encode information about the world in a computer? How do your choices in representation affect the ease with which you can solve problems?
Decomposition — How do you break a large and diverse problem into many simpler parts?
Discretization — How do you break up space and time into a large number of relatively small pieces? What are the alternative ways of doing this? What are the consequences of discretization procedures for accuracy and speed?
Verification — How do you build confidence in the results of a model?
What is Computational Thinking? (representation, discretization, error, decomposition, verification)Interpolation (building simple surrogates for more complex functions)Integration (processes for numerical quadrature)Randomness (generating and using pseudorandom variables in models)Differentiation (numerical derivatives)Solving equations (Gaussian elimination for linear systems, Newton-Raphson for non-linear systems)
Q: Is computational thinking about thinking like a computer does?
A: No. It’s about using computers to expand your own thinking.