Functional Analysis and Applications

Metric Spaces and Banach Fixed Point Theorem.- Banach Spaces.- Hilbert Space.- Fundamental Theorems.- Differential and Integral Calculus in Banach Spaces.- Optimisation Problems.- Operator Equations and Variational Methods.- Finite Element and Boundary Element Methods.- Variational Inequalities and Applications.- Spectral Theory with Application.- Frame and Basis Theory in Hilbert Spaces.- Wavelet Theory.- Wavelet Method for Partial Dierential Equations and Image Processing.- Wavelet Frames.- Gabor Analysis.

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• Análise funcional e transforma
• Cálculo diferencial e equações
• Modelação matemática
• Matemática para engenheiros
• Optimização
• Algoritmos e estruturas de dados

Functional Analysis;Optimization Theory and Algorithms;Operator Equations;Finite Elements Methods;Boundary Elements Methods;Variational Inequalities;Inverse Problems and Regularization;Frames and Wavelet Theory;Numerical Methods;Gabor Analysis;Image Processing;partial differential equations