This repository contains my lecture notes and solved exercises from MIT 18.03: Differential Equations (Spring 2010) and the textbook Elementary Differential Equations (6th Edition) by Edwards & Penney. Differential equations are fundamental for Linear Systems Theory, Control Systems, Signal Processing, State Estimation, and Dynamical System Modeling in Robotics and Engineering
- First-Order Differential Equations: Analytical, graphical, and numerical solutions.
- Second-Order Linear ODEs: Constant coefficients, undetermined coefficients, variation of parameters.
- Complex Numbers & Exponentials: Oscillations, damping, resonance, sinusoidal signals.
- Laplace Transform Methods: Convolution, delta functions, solving differential equations.
- Linear Systems of ODEs: Eigenvalues, eigenvectors, matrix exponentials.
- Nonlinear Autonomous Systems: Phase plane analysis, stability of critical points.
- 📁 Lecture_Notes – Summarized theoretical concepts from MIT 18.03 lectures.
- 📁 Exercises – Solved problems from Edwards & Penney and lecture problem sets.
Differential equations form the mathematical foundation for modeling dynamic systems in physics, engineering, and control theory. Mastering these concepts is essential for understanding Linear Systems Theory, system behavior, stability, and real-world applications in robotics and automation.
- MIT Course Website: MIT 18.03 - Differential Equations
- Textbook: Elementary Differential Equations - Edwards & Penney (6th Edition)
📧 Email: [email protected]
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