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Last updated:

December 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course covers the same material as 18.03 with more emphasis on theory.

Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.

Course Curriculum

    • Modeling and Terminology Unlimited
    • Linear Differential Equations Unlimited
    • Existence and Uniqueness of Solutions: Uniqueness Unlimited
    • Existence and Uniqueness of Solutions: Picard Iterates Unlimited
    • Extension of Solutions Unlimited
    • Qualitative Analysis Unlimited
    • Approximate Numerical Solutions Unlimited
    • Homogeneous 2nd Order Linear ODE’s with Constant Coefficients Unlimited
    • Some Instructions on Plotting Functions in MATLAB® Unlimited
    • Inhomogeneous 2nd Order Linear ODE’s Unlimited
    • Theory of 2nd Order Linear and Nonlinear ODE’s Unlimited
    • Extra Topics Unlimited
    • Fourier Trigonometric Series Unlimited
    • The Dirac Delta Function Unlimited
    • The Laplace Transform: Solving IVP’s Unlimited
    • Properties of the Transform Unlimited
    • Convolution Unlimited
    • Extra Topics Unlimited
    • Compartment Models and Introduction to Linear Algebra Unlimited
    • Eigenvalues, Eigenvectors and Eigenspaces Unlimited
    • Homogeneous Linear Systems: Real Eigenvalues Case Unlimited
    • Theory of General Linear Systems of ODE’s Unlimited
    • Supplementary Notes on Jordan Normal Form Unlimited
    • The Fundamental Theorem Unlimited
    • Autonomous Systems and Interacting Species Models Unlimited
    • Stability of Linear and Nonlinear Autonomous Systems Unlimited
    • Conservative Systems and Lyapunov Functions Unlimited

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Massachusetts Institute of Technology