Dmitri Klimov, Professor

School of Systems Biology

School of Systems Biology

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BINF690 Numerical Methods in Bioinformatics

BINF741 Introduction to Computer Simulations of Biomolecules

**Course syllabus for Fall 2016:**

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

Homework

- 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.

**Taylor series and error propagation**

Homework:

- 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.

**Roots of equations**

Homework:

- Solve problems 5.12 and 6.4
- Read Chapters 5 and 6

The homework is due Sep 26.

**Linear algebraic equations**

Homework:

- Solve problem 9.9
- Read Chapter 9

The homework is due Oct 3.

**Optimization**

Homework:

- Solve problem 14.8. In addition, use the code to solve this problem numerically.
- Prove numerical expression for the 2nd order derivative d
^{2}f/dxdy - Read Chapters 13 and 14

The homework is due Oct 11.

**Midterm exam**

**Curve fitting**

Homework:

- 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.

**Numerical integration**

Homework:

- 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.

**Ordinary differential equations**

Homework:

- 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.

**Boundary value and eigenvalue problems**

Homework:

- Solve problems 27.11 and 27.12.
- Read Chapters 27.

The homework is due Nov 14.

**Numerical methods: Molecular dynamics**

Homework:

- Read lecture notes.
- Find an error in section IV.

The homework is due Nov 21.

**Numerical methods: Monte Carlo algorithm**

Homework:

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

The homework is due Nov 28.

**Applications**

**Advanced numerical techniques**