Lectures related to Solutions of Differential Equations

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Differential Equations: Initial Conditions and Solutions

Discusses ordinary differential equations, focusing on initial conditions and methods for finding solutions.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.