Engineering_Mathematics_ODE_AnthonyChen.pptx

This original educational presentation, prepared by Anthony Chen, provides a clear and concise introduction to Ordinary Differential Equations (ODEs), a fundamental topic in engineering mathematics.
It covers definitions, classifications, common solution methods, and an example solution using separation of variables. The presentation uses original diagrams, colorful backgrounds, and step-by-step explanations to make learning more engaging and accessible.

1. Engineering Mathematics – Ordinary Differential Equations Prepared by Anthony Chen | Original diagrams and explanations

2. Introduction to ODEs Definition: An equation involving functions and their derivatives with respect to one independent variable. Order: Determined by the highest derivative present. Linear vs. Nonlinear: Depends on whether the dependent variable and its derivatives appear linearly. Applications: Electrical circuits, mechanical vibrations, population models, heat transfer, etc.

3. Classification of ODEs Order: 1st, 2nd, higher-order Linearity: Linear or nonlinear Homogeneous vs. Nonhomogeneous Initial Value Problem (IVP) vs. Boundary Value Problem (BVP)

4. Common Solution Methods Separation of Variables Integrating Factor (for linear first-order ODEs) Characteristic Equation (for linear constant-coefficient ODEs) Laplace Transform Numerical Methods (Euler's, Runge-Kutta)

5. Example – dy/dx = 0.5y Solution using separation of variables: y = Ce^(0.5x)

6. Author’s Note All diagrams are original and created by Anthony Chen For educational purposes only Prepared specifically for SlideShare upload