Lectures related to Problem Solving Techniques

Linear Equations: Solutions and Operations

Covers the solution of linear equations and operations with matrices and vectors.

Transporters: a proxy for parallel transport

Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.

Linear Equations: Vectors and Matrices

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Linear Equations: Matrix Notation & Solutions

Covers matrix notation for linear equations, solutions, and geometric interpretations.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Forkas Lemma: Theorem of the Alternatives

Explores the Forkas Lemma and the Theorem of the Alternatives in linear equation systems.

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Linear Combinations: Vectors and Matrices

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Gaussian Process-Based Model Predictive Control

Explores Gaussian Process-Based Model Predictive Control for HVAC systems using Gaussian processes, Bayesian statistics, and non-linear equations.

Ordinary Differential Equations

Covers the extension of ordinary differential equations to n-dimensional space.

Analytical Study of Space

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Decomposition of a Vector

Covers the decomposition of a vector in a base and its applications in speed and distance calculations.

Linear Algebra: Operations and Applications

Explores operations and applications of linear algebra in solving equations and transformations.

Ordinary Differential Equations

Covers the approximation of a system of differential equations using a method based on time intervals.

Matlab: Interactive Mode and Project Steps

Introduces Matlab basics, error handling, and billiards project concepts.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Energy System Optimization

Explores energy system optimization, including heat, cost, and CO2 emissions.

Vectors in Space: Properties and Interpretations

Explores properties and interpretations of vectors in space, including mixed product and linear dependence.

Systems of Linear Equations and Matrices

Covers the definition and solution of linear equations with real coefficients in 2D and 3D space.