BINF690 Numerical Methods in Bioformatics
Course syllabus for Fall 2016:
Lecture 1, Aug 29, 2016
Numerical methods in science. Programming and implementation of numerical methods.
- Read Chapters 1-3
- 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
- Send me the plot V=V(t) and your code implementing Euler algorithm.
- Explain what will happen with the droplet at t>10 min.
- 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. The homework is due Sep 12.
Lecture 2, Sep 12, 2016
Taylor series and error propagation
- Prove the expression for the error propagation for the function f(x,y)=x/y.
- 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)
- Read Chapter 4
The homework is due Sep 19.
Lecture 3, Sep 19, 2016
Roots of equations
- Solve problems 5.12 and 6.4
- Read Chapters 5 and 6
The homework is due Sep 26.
Lecture 4, Sep 26, 2016
Linear algebraic equations
- Solve problem 9.9
- Read Chapter 9
The homework is due Oct 3.
Lecture 5, Oct 3, 2016
- Solve problem 14.8. In addition, use the code to solve this problem numerically.
- Prove numerical expression for the 2nd order derivative d2f/dxdy
- Read Chapters 13 and 14
The homework is due Oct 11.
Lecture 6, Oct 11, 2016
Lecture 7, Oct 17, 2016
- Solve problem 17.7 (5th textbook edition) or 17.6 (6th or 7th editions)
- Read Chapters 17 and 18
The homework is due Oct 24.
Lecture 8, Oct 24, 2016
- 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.
- Compute the integral for the 3rd order interpolating polynomial in the
1/3 Simpson method
- Read Chapters 21 and 22.
The homework is due Oct 31.
Lecture 9, Oct 31, 2016
Ordinary differential equations
- 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.
- Read Chapters 25.
The homework is due Nov 7.
Lecture 10, Nov 7, 2016
Boundary value and eigenvalue problems
- Solve problems 27.11 and 27.12.
- Read Chapters 27.
The homework is due Nov 14.
Lecture 11, Nov 14, 2016
Numerical methods: Molecular dynamics
- Read lecture notes.
- Find an error in section IV.
The homework is due Nov 21.
Lecture 12, Nov 21, 2016
Numerical methods: Monte Carlo algorithm
- Read lecture notes.
- Compute average energy at different temperatures using MC.
The homework is due Nov 28.
Lecture 13, Nov 28, 2016
Lecture 14, Dec 5, 2016
Advanced numerical techniques