Lectures related to Vibrational Mechanics: Modes and Equations

Applications of Trigonometric Functions

Covers various applications of trigonometric functions, such as calculating values using inverse trigonometric functions.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Solving Cauchy Problems: Differential Equations and Solutions

Demonstrates the process of solving a Cauchy problem for a differential equation with specific initial conditions.

Mathematical Exercises: Functions and Equations

Covers mathematical exercises on functions, equations, and trigonometric functions.

Absolute Value

Covers the concept of absolute value and its properties, including graphical interpretation and equation solving.

Implicit Functions Theorem

Explores the Implicit Functions Theorem, demonstrating how to find solutions to equations like x²+y²=1 through implicit differentiation and function properties.

Vibratory Mechanics: Continuous Systems

Explores vibratory mechanics in continuous systems, covering separation of variables, boundary conditions, and harmonic solutions.

General Solutions of Differential Equations

Explores general solutions of differential equations with a focus on x

Resolution Sequence: Defining a Procedure

Explains the systematic procedure for solving flow sheets and stream calculations.

Linear Differential Equations: Methods and Solutions

Covers methods for solving first-order linear ordinary differential equations.

Mathematical Functions and Limits

Covers mathematical functions, limits, and their applications.

Exercises on Linear Equations

Covers exercises on linear equations, including solving equations and finding variable values.

Differential Equations: General Solutions and Methods

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

Linear Equations Resolution

Covers the resolution of linear equations, focusing on trigonometric equations and elementary concepts.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Forced Harmonic Oscillator: Resonance

Explores the forced harmonic oscillator, damping, and resonance phenomenon, focusing on the amplitude of oscillations in resonance.

Quadratic Equation: Programming Solutions

Covers the programming of a script to calculate the solutions of quadratic equations.

Non-linear Equations: Dichotomy Method

Explores non-linear equations using the dichotomy method for finding zeros with tolerance.

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

Linear Algebra: Identical Applications

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.