Lectures related to Periodic continued fraction

Powers and Roots: Understanding Irrational Equations

Delves into powers and roots, emphasizing irrational equations and the disjunction of cases.

Covers the Inverse Laplace Transform and its applications in finding projections from the Laplace domain to the time domain.

Groups and Numbers: Hidden Subgroup Problem

Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.

Roots of Real Numbers

Explores the properties and applications of roots of real numbers through practical examples.

Partial Fraction Expansion

Introduces Partial Fraction Expansion as a valuable tool for analyzing stable LTI systems.

Balanced Realization: SISO Case

Covers the concept of balanced realization in the SISO case, focusing on system observability and controllability.

Heterogeneous Catalysis: Kinetics and Mechanisms

Explores heterogeneous catalysis, focusing on reaction mechanisms, kinetics, and ammonia synthesis.

Response of overdamped 2nd order system to step

Covers the response of an overdamped second-order system to a step input.

Trigonometric Equations: Sinus and Cosinus

Covers the resolution of simple trigonometric equations involving sinus and cosinus functions.

Beam Geometry and Internal Forces

Covers the definition of beam geometry and internal forces diagrams.

System Equivalence

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

Thermal Analysis of Foundry: Chvorinov Theory

Explores foundry casting conditions, defects reduction, and Chvorinov's thermal analysis theory in the foundry process.

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Decimal Writing: Fractions and Division

Explains the conversion between decimal and fractional writing, including division with remainder and a trick for periodic numbers.

Sampling from Rough Energy Landscapes

Explores challenges and strategies for sampling from rough energy landscapes, focusing on Monte Carlo integration and tuning algorithms.

Diagonalization: Examples

Explores examples of diagonalization in linear algebra, focusing on eigenvalues and eigenvectors.

Shor Algorithm: Measurement Process Analysis

Explores the analysis of the measurement process in the Shor Algorithm.

Chemical Equilibria and Reactivity

Covers atomic structure, isotopes, molar mass, and chemical reactions.