Lectures related to Quantum Field Theory: Spectral Density

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Mathematics: Basics and Applications

Covers the basics of mathematics and its applications in architecture.

Linear Differential Equations: Constant Coefficients and Solution Methods

Covers linear differential equations with constant coefficients and introduces the method of good choice for finding particular solutions.

Fourier Transform and Residue Calculus

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Integration of Entire Series

Covers the integration of entire series term by term, demonstrating the convergence radius and providing examples.

Polynomial Functions: Integration and Coefficients

Covers the integration of polynomial functions and determining coefficients using linear algebra.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

Polynomial Division: Terms and Factors

Covers polynomial division, terms, factors, and integration methods.

Polynomials: Theory and Applications

Covers the theory of polynomials, including definitions, properties, and applications.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Polynomial, Exponential, Logarithmic Functions

Covers polynomial, exponential, and logarithmic functions, differentiability, compositions, and limits.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.