Lectures related to Course Overview: Projects and Exams

Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.

Explores geometric transformations, invariant properties, and mean relationships in modern geometry.

Explores the historical and practical applications of geometry in architecture, emphasizing key geometric principles in architectural design.

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Explores the evolution of projective geometry and its applications in architectural representation.

Explores the parabolic heat equation evolution and numerical solution methods.

Covers the fundamentals of projective geometry and its applications in architecture.

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Explores the radiation impedance of a piston on a screen using COMSOL Multiphysics, focusing on resistance, mass, and impedance expressions.

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Explores characteristic curves and solutions in partial differential equations, emphasizing uniqueness and existence in various scenarios.

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Explores biomechanical modeling of the musculoskeletal system using differential equations and finite element modeling.

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.

Covers the application of finite difference methods to solve partial differential equations.

Covers the classification and solutions of partial differential equations, including Laplace transform and separation of variables techniques.