This module investigates numerical linear algebra through singular value decomposition (SVD) and its applications. Key topics include:
Students will learn to apply SVD techniques to real-world data-driven problems.
This module delves into the properties of positive definite matrices, emphasizing their significance in optimization and stability analysis. Students will explore applications in various fields, focusing on:
Through practical examples, students will gain insights into how these matrices influence computational methods.
This module focuses on one-dimensional applications of linear algebra concepts, particularly through difference matrices. Key topics include:
Students will learn to apply these concepts to practical problems, enhancing their analytical skills.
This module examines network applications using incidence matrices. It covers topics such as:
Students gain practical insights into solving network-related problems using linear algebra techniques.
This module explores the applications of least squares in linear estimation. It introduces key concepts such as:
Students will gain hands-on experience in applying these techniques to solve estimation problems.
This module addresses dynamic applications of linear algebra, focusing on eigenvalues and their roles in solving differential equations. Key topics include:
Students will learn how to apply these concepts to real-world dynamic systems.
This module provides an overview of applied linear algebra theory. Students will explore:
Through examples and exercises, students will solidify their understanding of applied linear algebra principles.
This module contrasts discrete and continuous systems, focusing on differences and derivatives. Key topics include:
Students will learn to analyze and apply these concepts to various engineering problems.
This module investigates boundary value problems, specifically focusing on Laplace's equation. Students will cover:
Through hands-on exercises, students will apply these concepts to real-world scenarios.
This module explores solutions of Laplace's equation using complex variables. Key areas of focus include:
Students will develop skills in applying complex variable methods to Laplace's equation.
This module discusses Delta functions and Green's functions, emphasizing their applications in solving differential equations. Key topics include:
Students will learn to apply these mathematical concepts to solve real-world problems.
This module addresses initial value problems, focusing on the wave equation and heat equation. Students will explore:
Through practical exercises, students will apply these methods to real-world scenarios.
This module examines solutions of initial value problems using eigenfunctions. Key topics include:
Students will learn how to apply eigenfunction techniques to solve initial value problems effectively.
This module covers numerical linear algebra techniques, focusing on orthogonalization and the QR decomposition. Key areas include:
Students will gain practical skills in applying these numerical methods to real-world challenges.
This module investigates numerical linear algebra through singular value decomposition (SVD) and its applications. Key topics include:
Students will learn to apply SVD techniques to real-world data-driven problems.
This module covers numerical methods in estimation, focusing on recursive least squares and covariance matrices. Key areas include:
Students will gain skills in applying these concepts to real-world estimation problems.
This module explores dynamic estimation methods, emphasizing the Kalman filter and square root filter. Key topics include:
Students will learn to apply these filters to optimize dynamic estimation tasks.
This module focuses on finite difference methods for equilibrium problems. It covers key concepts such as:
Students will learn to apply these methods to various engineering problems.
This module extends the study of finite difference methods to stability and convergence. Key topics include:
Students will develop skills in assessing the stability and convergence of numerical solutions.
This module covers optimization and minimum principles, focusing on the Euler equation. Key topics include:
Students will learn to apply these principles to optimize various engineering and scientific problems.
This module focuses on finite element methods for solving equilibrium equations. Key areas include:
Students will learn to apply finite element methods to solve complex equilibrium problems.
This module investigates spectral methods for dynamic equations, emphasizing their applications. Key topics include:
Students will learn to apply spectral methods to a range of dynamic systems.
This module explores Fourier expansions and convolution, focusing on their applications. Key topics include:
Students will gain practical skills in applying these techniques to solve problems.
This module focuses on fast Fourier transform (FFT) and circulant matrices. Key topics include:
Students will learn to apply FFT techniques to enhance computation efficiency.
This module covers discrete filters, focusing on lowpass and highpass filters. Key topics include:
Students will learn to design and apply filters in various contexts.
This module investigates filters in both time and frequency domains. It covers key concepts such as:
Students will gain insights into designing effective filters for various applications.
This module explores filter banks and perfect reconstruction. Students will learn about:
Practical examples will illustrate the use of filter banks in real-world scenarios.
This module covers multiresolution techniques, focusing on wavelet transform and scaling functions. Key topics include:
Students will gain practical skills in applying wavelet techniques to solve complex problems.
This module explores splines and orthogonal wavelets, specifically Daubechies construction. Key areas include:
Students will learn to apply these techniques in various data-driven contexts.
This module examines applications of wavelet techniques in signal and image processing, focusing on compression. Key topics include:
Students will gain hands-on experience applying wavelet techniques to achieve efficient compression.
This module covers network flows and combinatorics, focusing on the Max Flow = Min Cut theorem. Key areas include:
Students will learn to apply combinatorial techniques to optimize network flows.
This module introduces the simplex method in linear programming, covering essential concepts such as:
Students will learn to apply the simplex method to solve linear programming challenges.
This module covers nonlinear optimization, focusing on algorithms and theory. Key topics include:
Students will gain insights into applying nonlinear optimization techniques to complex problems.