Fall
2012
Recommended
reading:
Dynamical
Systems in Neuroscience – The Geometry of Excitability and Bursting
By
Eugene Izhikevich
e-book (available to Brown users)
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HOMEWORKS Please hand in paper
copy in class on due date Matlab assignments: include
printout of code as well as figures Homework 1 - Due
Wednesday September 19 Solutions Homework 2 - Due Monday October 1
Solutions Homework 3 - Due Wednesday October 10 Solutions Homework 4 - Due Friday November 2
Solutions hw4.m Homework 5 - Due Monday November 19 Solutions Homework 6 - Due Wednesday December 5
Solutions |
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FINAL EXAM Thursday 12/20/2012
2:00 PM Barus and Holley 160 |
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Coverage:
all material studied sinde midterm. No
computers or calculators of any kind allowed. |
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Review Session – Wed Dec 12, 2012 |
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Class 37 – Fri Dec 7, 2012 |
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The Lotka-Volterra Predator-Prey Model The
Lorenz system and its strange attractor code |
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Class 36 – Wed Dec 5, 2012 |
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The Poincare-Bendixson Theorem An
Excitatory-Inhibitory Neural-Network Model |
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Class 35 – Mon Dec 3, 2012 |
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The
FitzHugh-Nagumo Model fitzhugh_nagumo.m |
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Class 34 – Fri Nov 30, 2012 |
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Linearization
of Non-Linear Systems (continued) |
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Class 33 – Wed Nov 28, 2012 |
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Linearization
of Non-Linear Systems |
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Class 32 – Mon Nov 26, 2012 |
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Systems of Non-Linear DEs: Examples (continued) Code:
First_Order_System.m |
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Class 31 – Mon Nov 19, 2012 |
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An example of Eigenvector Analysis in Brain Science: The Brain-State-in-a-Box (BSB) Model
(James
Anderson et al. 1977) Systems
of Non-Linear DEs: Examples |
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Class 30 – Fri Nov 16, 2012 |
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Four-Step Study of Systems of Linear DEs |
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Class 29 – Wed Nov 14, 2012 |
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Systems
of Linear DEs: Eigenvector Analysis (continued) |
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Class 28 – Mon Nov 12, 2012 |
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Systems
of Linear DEs: Eigenvector Analysis |
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Class 27 – Fri Nov 9, 2012 |
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Systems
of Linear DEs: Examples (continued) Code:
Linear_First_Order_System.m |
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Class 26 – Wed Nov 7, 2012 |
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Systems
of Linear DEs: Examples |
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Class 25 – Mon Nov 5, 2012 |
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More
examples (continued) |
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Class 24 – Fri Nov 2, 2012 |
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Non-Homogeneous
Linear Differential Equations (continued) More
examples (continued) |
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Class 23 – Wed Oct 31, 2012 |
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Non-Homogeneous
Linear Differential Equations |
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Class 22 – Fri Oct 26, 2012 |
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Simple code – can be used
as template for HWs First-order
DEs with direction field (code) More complicated code,
with various functionalities |
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Class 21 – Wed Oct 24, 2012 |
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Qualitative
Analysis of Differential Equations (continued) Separable
Differential Equations |
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Class 20 – Mon Oct 22, 2012 |
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Introduction
to Differential Equations (continued) Nice Tutorial on
Membrane Equation (courtesy of David
Heeger) Qualitative
Analysis of Differential Equations |
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Class 19 – Fri Oct 19, 2012 |
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Introduction
to Differential Equations (continued) |
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Class 18 – Wed Oct 17, 2012 |
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Introduction
to Differential Equations |
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Class 17 – Mon Oct 15, 2012 |
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MIDTERM EXAM – Sun Oct 14, 2012 Barus and Holley 141 |
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Coverage:
all material studied until exam. No
computers or calculators of any kind allowed. You
will not be asked to compute numerical values of complicated expressions or
expressions that involve exponentials or similar functions. Practice Midterm Exam Solutions |
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Class 16 – Fri Oct 12, 2012 |
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Approximations Approximations (code) |
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Class 15 – Wed Oct 10, 2012 |
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The Poisson Neuron, the Exponential distribution, and
the Poisson distribution (continued) |
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Class 14 – Fri Oct 5, 2012 |
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The Poisson Neuron, the Exponential distribution, and
the Poisson distribution |
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Class 13 – Wed Oct 3, 2012 |
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Class 12 – Mon Oct 1, 2012 |
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Covariances and related notions |
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Class 11 – Fri Sept 28, 2012 |
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Basic Statistics for the Binomial Distribution The case of the forgetful professor |
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Class 10 – Wed Sept 26, 2012 taught by Dahlia Nadkarni |
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Independent RVs, Means, Variances
(continued) |
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Class 9 – Mon Sept 24, 2012 |
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Independent RVs, Means, Variances |
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Class 8 – Fri Sept 21, 2012 |
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Binomial Distribution (continued) birthdays.m (Matlab Example) |
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Class 7 – Wed Sept 19, 2012 taught by Dahlia Nadkarni |
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Class 6 – Mon Sept 17, 2012 |
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Class 5 – Fri Sept 14, 2012 |
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Class 4 – Wed Sept 12, 2012 |
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Example
of Probability on Infinite Discrete Sample Space |
Class 3 – Mon Sept 10, 2012 |
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Class 2 – Fri Sept 7, 2012 |
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Matlab Examples 2. Probability 3. Differential equations 3.1 Linear_System.m 3.2 The Hodgkin-Huxley model |
Class 1 – Wed Sept 5, 2012 |
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o
Organizational
matters (see Information
Sheet). o
Asking whether a
neuron fired in a given millisecond is a random experiment. o
Flipping a coin
(whether fair or biased) is also a random experiment. o
Neuron firing and
coin flipping involve two very different types of randomness. Yet both are captured
adequately in a single mathematical framework. o
General remarks
on applied math, probability and differential equations: conciseness,
generality, explanatory power, predictive power. |
Information Sheet
(includes syllabus)
MWF
2:00-2:50, J. Walter Wilson 301
Instructor
Elie
Bienenstock email:
firstname [at] brown [period] dam [period] edu
Office
Hours: please email me to set appointment
Computer TA
Grader