Notes For the Non-Linear Dynamics and Stochastic Differential Equations Course G31.3105, .3106

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  1. Course Outline and Detailed Instructions for G31.3105/6:
    Nonlinear Dynamical Processes, Stocastic Processes, and Time Series
    1. new!Course introduction and detailed notes

  2. Notes On Non-Linear Dynamics
    1. An Introduction to Differential Equations Leading to the kdv Equations
    2. The Center Manifold Theorem, Dimension of Limit Sets, and Relaxation Oscillations


  3. Notes On Stochastic Differential Equations
    1. A Detailed Algebraic Development of the Chapman-Kolmogorov Equation And Its Ancillary Equations
    2. Some Notes On Continuity and Differentiability
    3. An Introduction to the Ito Calculus and Stochastic Differential Equations
    4. Introduction to the Markov Process: Based On Van Kapen up to the Fokkes-Plack Equation
    5. Some Supplemental Notes on the Markov and Diffusion Process: Feb. 25, 1995
    6. An Introduction to Markov Chains
    7. Non-linear Time Series, Stochastic Processes and Dynamical Systems: Some Important Relationships Explored
    8. An Introduction to Stochastic Calculus
    9. An Introduction to Stochastic Processes and Related Subjects


  4. Notes On Spectral Analysis, Kalman Filters, and Wavelets
    1. The Relationship Between Spectral and Autocorrelation Properties
    2. Spectral Analysis of Bivariate Stationary Process
    3. Complex Demodulation
    4. Cross Sepctral Analysis
    5. Estimation of Spectra
    6. General Notes on the Fourier Series Representation of Functions
    7. Some Theoretical Notes on Filters and Linear Transformation
    8. An Introduction to Spectral Analysis: Some Special Examples of Stochastic Processes
    9. Some Results in Time Series Modeling and Analysis

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