Lectures related to Properties of Laplace Transform

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Understanding Microcontrollers: Functions

Introduces the fundamentals of functions in microcontroller programming, emphasizing naming rules and step-by-step development.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Products and Convolution of Transforms

Covers the definition and properties of convolution of two functions and explores radioactive material decay rates.

Complex Analysis: Holomorphic Functions

Explores holomorphic functions in complex analysis and the Cauchy-Riemann equations.

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.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

Definitions and Notations

Covers the definitions and notations related to functions.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

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Convexity Criteria

Covers the study of functions, focusing on convexity criteria within closed subintervals.

Python Crash Course

Provides a Python crash course covering basic arithmetics, complex numbers, strings, lists, dictionaries, and more.

Wirtinger Derivatives

Covers Wirtinger derivatives in complex variables, discussing their definition, application, and properties as independent variables.

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.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Python Modules and Functions

Covers Python libraries, modules, scoping, functions, lambdas, and practical examples.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Laplace Transforms: Applications and Convergence Properties

Introduces Laplace transforms, their properties, and applications in solving differential equations.