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Related lectures (30)

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Periodic Functions: Integrals and Approximations

Discusses periodic functions, integrals, and approximations using trigonometric polynomials and proofs of related theorems.

Numerical Methods: ODE RK Schemes

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Real Functions of Real Variables: Properties and Domains

Covers the properties of real functions, domains, and types of functions, including periodicity.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

The Mathematical Pendulum

Explores the mathematical pendulum, small oscillations, harmonic oscillator, and integration of the equation of motion.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Calculus of Variations and Euler's Elastica

Explores variational methods, Euler's Elastica, numerical and analytical methods, and the buckling of slender structures.

Decision Trees: Classification

Explores decision trees for classification, entropy, information gain, one-hot encoding, hyperparameter optimization, and random forests.