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September 21, 2023

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Description

18.03 Differential Equations (Spring 2010, MIT OCW). Taught by Professor Arthur Mattuck, this course is a study of Ordinary Differential Equations (ODEs), including modeling physical systems. 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 (ODEs) deal with functions of one variable, which can often be thought of as time. Topics covered in this course include: Solution of first-order ODEs by analytical, graphical and numerical methods; Linear ODEs; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems; and Nonlinear autonomous systems. (from ocw.mit.edu)

Course Curriculum

  • Lecture 01 – The Geometrical View of y’= f(x,y) Unlimited
  • Lecture 02 – Euler’s Numerical Method for y’=f(x,y) and its Generalizations Unlimited
  • Lecture 03 – Solving First-order Linear ODEs Unlimited
  • Lecture 04 – First-order Substitution Methods: Bernoulli and Homogeneous ODEs Unlimited
  • Lecture 05 – First-order Autonomous ODEs Unlimited
  • Lecture 06 – Complex Numbers and Complex Exponentials Unlimited
  • Lecture 07 – First-order Linear with Constant Coefficients Unlimited
  • Lecture 08 – Continuation; Applications to Temperature, RC-circuit, Growth Models Unlimited
  • Lecture 09 – Solving Second-order Linear ODEs with Constant Coefficients Unlimited
  • Lecture 10 – Continuation: Complex Characteristic Roots Unlimited
  • Lecture 11 – Theory of General Second-order Linear Homogeneous ODEs Unlimited
  • Lecture 12 – Continuation: General Theory for Inhomogeneous ODEs Unlimited
  • Lecture 13 – Finding Particular Solutions to Inhomogeneous ODEs Unlimited
  • Lecture 14 – Interpretation of the Exceptional Case: Resonance Unlimited
  • Lecture 15 – Introduction to Fourier Series Unlimited
  • Lecture 16 – Continuation: More General Periods Unlimited
  • Lecture 17 – Finding Particular Solutions via Fourier Series Unlimited
  • Lecture 19 – Introduction to the Laplace Transform Unlimited
  • Lecture 20 – Derivative Formulas Unlimited
  • Lecture 21 – Convolution Formula Unlimited
  • Lecture 22 – Using Laplace Transform to Solve ODEs with Discontinuous Inputs Unlimited
  • Lecture 23 – Use with Impulse Inputs; Dirac Delta Function Unlimited
  • Lecture 24 – Introduction to First-order Systems of ODEs Unlimited
  • Lecture 25 – Homogeneous Linear Systems with Constant Coefficients Unlimited
  • Lecture 26 – Continuation: Repeated Real Eigenvalues, Complex Eigenvalues Unlimited
  • Lecture 27 – Sketching Solutions of 2×2 Homogeneous Linear System with Constant Coefficients Unlimited
  • Lecture 28 – Matrix Methods for Inhomogeneous Systems Unlimited
  • Lecture 29 – Matrix Exponentials; Application to Solving Systems Unlimited
  • Lecture 30 – Decoupling Linear Systems with Constant Coefficients Unlimited
  • Lecture 31 – Nonlinear Autonomous Systems Unlimited
  • Lecture 32 – Limit Cycles: Existence and Nonexistence Criteria Unlimited
  • Lecture 33 – Relation Between Nonlinear Systems and First-order ODEs Unlimited

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