Numerical Analysis for Geophysicists

0341.2008

General Information

Lecturer:	Prof. Moshe Reshef Kaplun Building, Room 212
Teaching Assistant:	Pavel Sinitsyn Kaplun Building, Room 602 Reception hours: Coordinate by pavelsin@post.tau.ac.il.
Lectures Schedule:	Sunday, 12:00 - 15:00 Tuesday, 12:00 - 13:00
Final Grade:	25% - Homework 25% - Final Project 50% - Final Exam

Course Syllabus

The course focuses on elementary and advanced numerical methods for scientific computing.
Main programming language is C.
Visualization will be done with gnuplot or Matlab.

Roots of equations
Numerical interpolation
Systems of linear equations
Numerical integration
Ordinary differential equations (ODE)
Partial differential equations (PDE)
Special functions

Course Timeline

Week #	Topics	Exercise
1	Root finding: bisection, newton-raphson, secant, synthetic division	Exe1 - Basic Programming & Visualization (pdf) Data for exercise (zip)
2	Class programming exercise and root finding (cont.)
3	Solving Linear Systems: gauss-Jordan, gauss elimination, LU decomposition, Crout algorithm, Cholesky decomposition, partial pivoting, Jacob iterative method, Gauss-Seidel, matrix inversion, bonded systems	Exe2 - Root finding (pdf)
4	Cramer method Interpolation: linear, Vandermonde matrix, horner method, direct method, lagrange	Exe3 - Linear equations (pdf)
5	Neville method, newton method, splines, cubic splines, natural spline	Exe4 - Basic interpolation (pdf)
6	Hermite interpolation	Exe5 - Advanced interpolation (pdf)
7	B-spline Numerical integration: Trapezoid rule, simpson method, close/open interval integration	Exe6 - Numerical integration (pdf)
8	Richardson extrapolation / Romberg method, quadrature, gauss-quadrature, Newton-Cotes, Orthogonal polynomials: Legendre, lagrange etc. Numerical Derivatives: backward/forward/central difference
9	Roundoff/truncation errors ODE: single/multi step methods in IVP, forward Euler method, implicit method, backward euler, global/local errors, runga-kutta
10	predictor-corrector, leap-frog BVP: shooting	Exe7 - Numerical derivatives and ODE (pdf)
11	Collocation PDE: elliptic (laplace)/parabolic (heat/diffusion)/hyperbolic (waves) equations, boundary conditions: dirichlet/neuman, Courant condition/CFL	Exe8 - High order ODE (pdf)
12
13		Final Project - Acoustic Waves and Heat/Diffusion equations (pdf)

Exercise Submission & Guidelines

pavelsin@post.tau.ac.il

Grades Table

(xlsx)

Grading Policy:

Programming exercises will be graded according to the following criterions.

Code (40%) - The C code is written properly, divided into functions with meaningful names.
Documentation (20%) - Each C file starts with a credit (see example below), code is documented incluing functions and their parameters.
Compliation (10%) - The C code compiles without errors.
Program Execution (30%) - The program runs, performs necessary tasks, without errors.

Some Examples:

How a C program should look like (my_simple_program.cpp)
3D plotting with GnuPlot (gnuplot_3D_example.pdf)
Plotting with Matlab (matlab_plot.m)
Other Materials from Old Site:
- Usefull C routines:
  - C Demo program Demo_Prog1.c
  - Allocating 2d-array 2d_alloc.c
  - Drawing a polynom (remember to compile with -lm) draw_poly.c
  - Drawing 3D data make3Ddata.c
  - LU Decomposition (LU.c)
  - Spline (spline.c)
  - ODE (ode2.c)
- Introduction to Linux working environment

Relevant Books & References

Numerical Recipes in C (Official Website)
A first course in numerical analysis - Ralston & Rabinowitz
Numerical methods for scientists and engineers, Hamming
Introduction to numerical analysis, Hildebrand

Other Useful Material

C/C++ Development
- Complete IDE for Windows - Microsoft Visual Studio Community (2015) , Installetion Instructions for Eclipse or MobaXterm
- Complete IDE for Linux - Eclipse
- Complete IDE for MacOSX - Xcode
- Code editor for all platforms - Microsoft Visual Studio Code or Eclipse
- C Programming Tutorial
Linux and Windows:
- File transfer between Linux and Windows - WinSCP
- Open Linux terminal from Windows - PuTTY
The Linux Shell:
- What is the Shell, useful commands - LinuxCommand
- Linux for Beginners - UNIX Tutorial
Simple Text Editors in Linux Shell:
- pico / nano
- emacs (reference card)
Plotting in Linux/Windows:
- gnuplot website
- Version 5.0 Download
- Tutorials and Manual