Mathematical Physics I (Practical)

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Study Materials

• Gnuplot in Action understanding data and Graphs - Phillipp K. Janert.
• Scientific Computing in Python - Abhijit Kar Gupta.
• Physics in Laboratory including python Programming (Semester I) - Mandal, Chowdhury, Das, Das.
• Introduction to Numerical Analysis - S.S. Sastry.
• Numerical Methods - Arun Kr Jalan & Utpal Sarkar.
• Numerical Mathematical Analysis - J. B. Scarborough.
• Elementary Numerical Analysis - K.E. Atkinson.
• An Introduction to computational Physics - T.Pang.
• Learning with Python-how to think like a computer scientist - J. Elkner, C. Meyer, and A. Downey.
• Gnuplot 5 - Lee Phillips.
• Python Programming - Satyanarayana, Radhika Mani, Jagdesh.
• Python 2.1 Bible - Dave Brueck, Stephen Tanner.
• Computatioal Physics problem solving with Computers - Landau, Paez, Bordeianu.

Topics

• Introduction to programming in python:
• Introduction:
• Using the python interpreter as a calculator.
• Variable and data types (int, float, complex, list, tuple, string, the type() function).
• Basic mathematical operations.
• Compound statements in python:
• Conditionals: if: elif: else:
• Loops for:, while:
• User defined functions def: [return statement, default values for arguments, keyword arguments]
• Importing modules with math and cmath as examples.
• Basic idea of namespaces-local and global.
• Python scripts, I/O operations (including opening and writing to files).
• The python iterables data type:
• List:
• Defining lists,reading and changing elements from lists, slicing (with discussion on the difference between ll=mm and ll=mm[:], concatenation, list comprehension.
• built in functions involving lists: range(), len(), sum(), min(), max().
• list methods: append(), extend(), count(), index(), sort(), insert(), pop(), remove(), reverse().
• Tuples: Contrast and compare with lists, packing/unpacking using tuples (including a,b=b,a to swap variables).
• Strings: defining strings, the use of single, double or triple quotes as string delimiters, len(), indexing, slicing, string concatanation, some string methods: strip(), split(), join(), find(), count(), replace(), string formatting in python (using the % operator).
• Problems and applications:
• Problem 0: Observe and interpret the result of the following two scripts
• i=0; a=1; while a>0: i=i+1; a=a/2; print i;
• i=0; a=1; b=1; while a+b>b: i=i+1; a=a/2; print i;
• Problem 1: Root finding for a single variable (basic theory and algorithm).
• Bisection method.
• Newton-Raphson Method.
• Problem 2: Sorting of lists (algorithm, flowchart and code).
• Bubble sort.
• Selection sort.
• Problem 3: ODE in one and two dimensions using Euler algorithm (output to be saved in data files and gunuplot to be used to plot graphs).
• Capacitor charging/discharging.
• Simulating a half-wave rectifier with a capacitor filter.
• Particle dynamics in 1D.
• Problem 4: Matrix operations using list of lists.