Differential Equations 18.03 MIT
Online Free Online Course by
World Mentoring Academy
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Details
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal
with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients
and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear
systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams. Find lecture notes, study materials, and more courses at http://ocw.mit.edu.
Resources: OpenCourseware from MIT, UC Berkeley, Stanford along with many of the World's finest University's.
Language: English
Professors: Joshua Coleman, Michael Williams
Units: 32
Lesson content
- Lec 1 The Geometrical View of y'=f(x,y): Direction...
- Lec 2 Euler's Numerical Method for y'=f(x,y) and its Generalizations.
- Lec 3 Solving First-order Linear ODE's; Steady-state and Transient Solutions.
- Lec 4 First-order Substitution Methods: Bernouilli and Homogeneous ODE's
- Lec 5 First-order Autonomous ODE's: Qualitative Methods, Applications.
- Lec 6 Complex Numbers and Complex Exponentials.
- Lec 7 First-order Linear with Constant Coefficients
- Lec 8 Continuation
- Lec 9 Solving Second-order Linear ODE's
- Lec 10 Complex Characteristic Roots
- Lec 11 Theory of General Second-order Linear Homogeneous ODE's
- Lec 12 General Theory for Inhomogeneous ODE's
- Lec 13 Finding Particular Sto Inhomogeneous ODE's
- Lec 14 Interpretation of the Exceptional Case: Resonance.
- Lec 15 Introduction to Fourier Series; Basic Formulas for Period 2(pi).
- Lec 16 More General Periods
- Lec 17 Finding Particular Solutions via Fourier Series
- Lec 19 Introduction to the Laplace Transform; Basic Formulas.
- Lec 20 Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
- Lec 21 Convolution Formula
- Lec 22 Using Laplace Transform
- Lec 23 Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
- Lec 24 Introduction to First-order Systems of ODE's
- Lec 25 Homogeneous Linear Systems with Constant Coefficients
- Lec 26 Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
- Lec 27 Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
- Lec 28 Matrix Methods for Inhomogeneous Systems
- Lec 29 Matrix Exponentials; Application to Solving Systems.
- Lec 30 Decoupling Linear Systems with Constant Coefficients.
- Lec 31 Non-linear Autonomous Systems
- Lec 32 Limit Cycles: Existence and Non-existence Criteria.
- Lec 33 Relation Between Non-linear Systems and First-order ODE's
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