Differential Equations

0( 0 REVIEWS )
1 STUDENTS

Direction fields, existence and uniqueness of solutions – Numerical methods – Linear equations, models – Solution of linear equations, integrating factors – Complex numbers, roots of unity – Complex exponentials; sinusoidal functions – Linear system response to exponential and sinusoiAutonomous equations; the phase line, stability – Linear vs. nonlinear – Modes and the characteristic polynomial – Good vibrations, damping conditions – Related Mathlet: Damped vibrations – Exponential response formula, spring drive – Related Mathlet: Harmonic frequency response: Variable input frequency – Complex gain, dashpot drive – Operators, undetermined coefficients, resonance – Frequency response – LTI systems, superposition, RLC circuits – Engineering applications

Fourier series – Operations on fourier series – Periodic solutions; resonance – Step functions and delta functions – Step response, impulse response – Convolution – Laplace transform: basic properties – Application to ODEs – Second order equations; completing the squares – The pole diagram – The transfer function and frequency response – Linear systems and matrices – Eigenvalues, eigenvectors – Complex or repeated eigenvalues – Qualitative behavior of linear systems; phase plane – Normal modes and the matrix exponential – Nonlinear systems – Linearization near equilibria; the nonlinear pendulum – Limitations of the linear: limit cycles and chaos

Course Curriculum

Course Reviews

N.A

ratings
  • 5 stars0
  • 4 stars0
  • 3 stars0
  • 2 stars0
  • 1 stars0

No Reviews found for this course.

FreeVideoLectures.com All rights reserved.

Setup Menus in Admin Panel