Lectures related to Euler's criterion

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Residues Theorem Applications

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Residues Theorem

Explores the Residues Theorem and the classification of holomorphic functions.

RSA Cryptography: Primality Testing and Quadratic Residues

Explores RSA cryptography, covering primality testing, quadratic residues, and cryptographic applications.

Green Functions and Electrostatics

Explores Green functions, complex analysis, and electrostatics, including EM waves and residue theorem.

Green Functions and Complex Analysis

Covers EM fields of moving charged particles and Green functions.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Residue Theorem: Cauchy's Integral Formula and Applications

Covers the residue theorem, Cauchy's integral formula, and their applications in complex analysis.

Fourier Analysis: Inversion Formula

Explores the Fourier inversion formula and the importance of the integral on the half-circle being zero for the method to work.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Analyse IV: Laurent Series and Singularities

Covers Laurent series, singularities, and meromorphic functions, addressing convergence, holomorphicity, and residue theorem applications.

Chinese Remainders & RSA

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Residues and Singularities

Covers the calculation of residues, types of singularities, and applications of the residue theorem in complex analysis.

Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Analyzing Poles and Residues

Covers the analysis of poles and residues in complex functions, focusing on the calculation of singularities, poles, and residues.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.