Differential Equations

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Course Format This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include: - **Lecture Videos** by Professor Arthur Mattuck. - **Course Notes** on every topic. - **Practice Problems** with **Solutions**. - **Problem Solving Videos** taught by experienced MIT Recitation Instructors. - **Problem Sets** to do on your own with **Solutions** to check your answers against when you're done. - A selection of **Interactive Java® Demonstrations** called _Mathlets_ to illustrate key concepts. - A full set of **Exams with Solutions**, including practice exams to help you prepare. Content Development Haynes Miller  Jeremy Orloff  Dr. John Lewis  Arthur Mattuck

Separable Equations | MIT 18.03SC Differential Equations, Fall 2011.
Exploration of the Amplitude and Phase: First Order Applet.
Lec 1 | MIT 18.03 Differential Equations, Spring 2006.
Exploration of the Isoclines Applet.
Direction Fields | MIT 18.03SC Differential Equations, Fall 2011.
Lec 2 | MIT 18.03 Differential Equations, Spring 2006.
Exploration of the Euler's Method Applet.
Euler's Method | MIT 18.03SC Differential Equations, Fall 2011.
Lec 3 | MIT 18.03 Differential Equations, Spring 2006.
Linear Equations | MIT 18.03SC Differential Equations, Fall 2011.
Solutions of First-order Linear Equations | MIT 18.03SC Differential Equations, Fall 2011.
Lec 6 | MIT 18.03 Differential Equations, Spring 2006.
Complex Numbers and Euler's Formula | MIT 18.03SC Differential Equations, Fall 2011.
Lec 8 | MIT 18.03 Differential Equations, Spring 2006.
Sinusoidal Functions | MIT 18.03SC Differential Equations, Fall 2011.
Lec 7 | MIT 18.03 Differential Equations, Spring 2006.
First-order Constant Coefficient Linear ODE's | MIT 18.03SC Differential Equations, Fall 2011.
Sinusoidal Inputs | MIT 18.03SC Differential Equations, Fall 2011.
Lec 5 | MIT 18.03 Differential Equations, Spring 2006.
Exploration of the Phase Lines Applet.
Lec 9 | MIT 18.03 Differential Equations, Spring 2006.
Autonomous Equations and Phase Lines | MIT 18.03SC Differential Equations, Fall 2011.
Homogeneous Constant Coefficient Equations: Any Roots | MIT 18.03SC Differential Equations.
Homogeneous Constant Coefficient Equations: Real Roots | MIT 18.03SC Differential Equations.
Lec 10 | MIT 18.03 Differential Equations, Spring 2006.
Exploration of the Damped Vibrations Applet.
Damped Harmonic Oscillators | MIT 18.03SC Differential Equations, Fall 2011.
Lec 11 | MIT 18.03 Differential Equations, Spring 2006.
Lec 12 | MIT 18.03 Differential Equations, Spring 2006.
Lec 13 | MIT 18.03 Differential Equations, Spring 2006.
Forced Oscillations | MIT 18.03SC Differential Equations, Fall 2011.
Gain and Phase Lag | MIT 18.03SC Differential Equations, Fall 2011.
Undetermined Coefficients | MIT 18.03SC Differential Equations, Fall 2011.
Lec 14 | MIT 18.03 Differential Equations, Spring 2006.
Pure Resonance | MIT 18.03SC Differential Equations, Fall 2011.
Exploration of the Amplitude and Phase: Second Order II Applet.
Frequency Response | MIT 18.03SC Differential Equations, Fall 2011.
Lec 15 | MIT 18.03 Differential Equations, Spring 2006.
Lec 16 | MIT 18.03 Differential Equations, Spring 2006.
Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011.
Exploration of the Fourier Coefficient Applet.
Manipulating Fourier Series | MIT 18.03SC Differential Equations, Fall 2011.
Lec 17 | MIT 18.03 Differential Equations, Spring 2006.
Linear ODE's with Periodic Input | MIT 18.03SC Differential Equations, Fall 2011.
Step and Delta Functions | MIT 18.03SC Differential Equations, Fall 2011.
Unit Step and Impulse Response | MIT 18.03SC Differential Equations, Fall 2011.
Lec 21 | MIT 18.03 Differential Equations, Spring 2006.
Exploration of the Convolution Accumulation Applet.
Convolution and Green's Formula | MIT 18.03SC Differential Equations, Fall 2011.
Lec 19 | MIT 18.03 Differential Equations, Spring 2006.
Lec 20 | MIT 18.03 Differential Equations, Spring 2006.
Laplace Transform: Basics | MIT 18.03SC Differential Equations, Fall 2011.
Partial Fractions and Laplace Inverse | MIT 18.03SC Differential Equations, Fall 2011.
Laplace: Solving ODE's | MIT 18.03SC Differential Equations, Fall 2011.
Pole Diagrams | MIT 18.03SC Differential Equations, Fall 2011.
Lec 24 | MIT 18.03 Differential Equations, Spring 2006.
Linear Systems of Equations | MIT 18.03SC Differential Equations, Fall 2011.
Lec 25 | MIT 18.03 Differential Equations, Spring 2006.
Lec 26 | MIT 18.03 Differential Equations, Spring 2006.
Linear Systems: Complex Roots | MIT 18.03SC Differential Equations, Fall 2011.
Linear Systems: Matrix Methods | MIT 18.03SC Differential Equations, Fall 2011.
Lec 27 | MIT 18.03 Differential Equations, Spring 2006.
Phase Portraits | MIT 18.03SC Differential Equations, Fall 2011.
Trace-Determinant Diagram | MIT 18.03SC Differential Equations, Fall 2011.
Lec 28 | MIT 18.03 Differential Equations, Spring 2006.
Lec 29 | MIT 18.03 Differential Equations, Spring 2006.
Matrix Exponentials | MIT 18.03SC Differential Equations, Fall 2011.
Lec 30 | MIT 18.03 Differential Equations, Spring 2006.
Lec 33 | MIT 18.03 Differential Equations, Spring 2006.
Lec 31 | MIT 18.03 Differential Equations, Spring 2006.
Linearization | MIT 18.03SC Differential Equations, Fall 2011.
Lec 32 | MIT 18.03 Differential Equations, Spring 2006.