Dmitri Klimov, Professor
School of Systems Biology
           


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Courses
BINF690 Numerical Methods in Bioinformatics
BINF740 Introduction to Biophysics
BINF739/BIOL691 Molecular Modeling for Biologists
BINF741 Introduction to Computer Simulations of Biomolecules

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BINF690 Numerical Methods in Bioformatics


Course syllabus for Fall 2017:

Lecture 1, Aug 28, 2017

Numerical methods in science. Programming and implementation of numerical methods.


Homework

  1. Read Chapters 1-3
  2. Solve problem 1.15 in the 5th textbook edition. In the 6th or 7th editions the problem 1.15 appears as 1.13. In addition to solving this problem as it is stated in the book, you also need to
    1. Send me the plot V=V(t) and your code implementing Euler algorithm.
    2. Explain what will happen with the droplet at t>10 min.
    3. Obtain analytical solution and compare it with the numerical one.

Assignment (c) is optional, but I will give extra point if it is done correctly.

Lecture 2, Sep 11, 2017

Taylor series and error propagation


Homework:

  1. Prove the expression for the error propagation for the function f(x,y)=x/y.
  2. Solve problems 4.5 and 4.8 (5th edition) or 4.4 and 4.10 (6th edition) or 4.6 and 4.11 (7th edition)
  3. Read Chapter 4

Lecture 3, Sep 18, 2017

Roots of equations


Homework:

  1. Solve problems 5.12 and 6.4
  2. Read Chapters 5 and 6

Lecture 4, Sep 25, 2017

Linear algebraic equations


Homework:

  1. Solve problem 9.9
  2. Read Chapter 9

Lecture 5, Oct 2, 2017

Optimization


Homework:

  1. Solve problem 14.8. In addition, use the code to solve this problem numerically.
  2. Prove numerical expression for the 2nd order derivative d2f/dxdy
  3. Read Chapters 13 and 14

Lecture 6, Oct 10, 2017

Midterm exam


Lecture 7, Oct 16, 2017

Curve fitting


Homework:

  1. Solve problem 17.7 (5th textbook edition) or 17.6 (6th or 7th editions)
  2. Read Chapters 17 and 18

Lecture 8, Oct 23, 2017

Numerical integration


Homework:

  1. Solve problem 21.5. In addition, (a) compute integral using trapezoidal rule (n=5); (b) compute integral using Romberg integration (n1=5, n2=10); (c) compare numerical results with analytical integration.
  2. Compute the integral for the 3rd order interpolating polynomial in the 1/3 Simpson method
  3. Read Chapters 21 and 22.

Lecture 9, Oct 30, 2017

Ordinary differential equations


Homework:

  1. Solve problem 25.9 (5th edition) or 25.5 (6th or 7th editions). In addition, (a) use 4th order RK method to solve the problem; (b) plot all solutions.
  2. Read Chapters 25.

Lecture 10, Nov 6, 2017

Boundary value and eigenvalue problems


Homework:

  1. Solve problems 27.11 and 27.12.
  2. Read Chapters 27.

Lecture 11, Nov 13, 2017

Numerical methods: Molecular dynamics


Homework:

  1. Read lecture notes.
  2. Find an error in section IV.

Lecture 12, Nov 20, 2017

Numerical methods: Monte Carlo algorithm


Homework:

  1. Read lecture notes.
  2. Compute average energy at different temperatures using MC.

Lecture 13, Nov 27, 2017

Applications


Lecture 14, Dec 4, 2017

Advanced numerical techniques