This course introduces various case studies drawn from different areas of
science to illustrate the use of computers as a problem-solving tool. Each integrates physical principles and
mathematical models, as well as numerical techniques and computer implementations, into a coherent perspective.
HW assignment (30%): both hand-written and computational.
Project (70%)
SCHEDULE
Software for Applied/Computational Mathematics: MATLAB, LaTex
Introduction to Mathematical Modeling
Image as Matrix
Tools: Linear Algebra. Singular value decomposition.
Applications: Histogram processing for image enhancement.
Filtering for image enhancement and restoration.
Linear signal/image compression. Image segmentation. (*) Compressed Sensing.
Topics: Image sampling and quantization
Dynamical Systems:
Nondimensionalization
- Phase Space
- Stability of Fixed Points
- Basin of Attraction
Chaos and Fractals:
Poincare Section
- Bifurcation
- Fractal Dimensions and Correlation Dimension