Lectures related to Zero of a function

Homogeneous Linear Second-Order Differential Equations

Covers the solution of homogeneous linear second-order differential equations with constant coefficients and explores various cases of real and complex roots.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Discussion of Function f

Covers the discussion of the function f(x) = |2x-1| -x²+1 on a given domain and its continuity, zeros, and derivatives.

Integration of Rational Functions

Covers the integration of rational functions, including the decomposition into partial fractions and the use of complex zeros.

Polynomial Functions: Integration and Coefficients

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

Hadamard Factorization and Zeros of Zeta

Completes the proof of Hadamard Factorization and uses it to derive an expression for the zeta function in terms of its zeros.

Logarithmic Derivative of Zeta

Explores the behavior of the zeta function and its explicit formula.

Quantum Field Theory: Spectral Density

Covers the concept of spectral density in Quantum Field Theory.

Polynomial, Exponential, Logarithmic Functions

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

Bisection Method: Example

Focuses on using the bisection method to approximate function roots with precision.

Viète Relations: Polynomial Roots and Coefficients

Explores Viète's identities, relating polynomial roots and coefficients to solve equations.

Complex Numbers: Exponential Formulas

Covers the activation process of a home connection and explores exponential formulas, Euler's formula, and complex equations.

Convergence of Parametrized Series

Explores the convergence of a series parameterized by alpha and its conditions for convergence.

Mathematics: Basics and Applications

Covers the basics of mathematics and its applications in architecture.

Integration of Entire Series

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

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Fourier Transform and Residue Calculus

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Bernoulli convolutions: The dimension of Bernoulli convolutions

Explores the dimension of Bernoulli convolutions, discussing fair tosses and polynomial roots.

Important Examples: Operations and Multiplication

Covers important examples related to operations and multiplication in real vector spaces.