Integrated B.Tech. - M.Tech. 4th semester in Computational Mathematics
Department of Mathematics,
National Institute of Technology Agartala.
Course instructor: Supriyo Dutta.
Teaching Assistant: Md. Samsur Rahaman.
Meetings: Wednesday 11 am - 1 pm Lab, Friday 11 am to 1 pm Theory.
First Class 8-th January 2025.
Class test 1: 7-th February 2025
Mid-term: Date will be announced by Exam Section
Lab Examination: 23-rd April 2025 (Wednesday)
Class test 2: Will be announced soon.
End-term: Date will be announced by Exam Section
The theory syllabus for the mid term exam is upto the 14-th February class.
Fundamental Concepts of Python: Introduction to Python, history, unique features of Python, literals, variables and identifiers operators expressions and data types.
Control Structures: Selection control, iterative control.
Lists: List structures, lists (sequences), iterating over lists
Functions: Program routines, calling value-returning functions, calling non value-returning functions, parameter passing, variable scope, dictionaries and sets, recursion, Python built in function, Python user defined functions, Python packages functions, defining and calling function, the anonymous functions, loops and statement in Python, yield and generators, Python modules and packages.
Text Files: Using text files, string passing, Python exceptions handling, handling an exception try, , except, else, try-finally clause, argument of an exception, , Python standard exceptions, raising an exception, user defined exceptions.
Python Regular Expressions: Regular expressions, the match function, , the search function, matching vs searching, search and replace, , extended regular expressions.
Literals, variables and identifiers, operators, expressions and data types, selection control, iterative control, list structures, lists (sequences), , iterating over lists, program routines, calling value-returning functions, calling non value-returning functions, parameter passing, variable scope, dictionaries and sets, recursion, yield and generators, using text files, string passing, exception handling.
We are not following the syllabus for Lab. These topics will be taught in theory classes. We select a number of different practical problems.
You may consult to the course instructor or teaching assistant to get a soft copy of these books.
John V. Guttag. Introduction to Computation and Programming Using Python with Application to Computational Modelling and Understanding Data. The MIT Press. 2021.
Kenneth A. Lambert, Martin Osborne. Fundamentals of Python: First Programs. Course Technology, Cengage Learning. 2012
Mark Summerfield. Programming in Python 3: A Complete Introduction to the Python Language. Pearson Education. 2010
You may download and install
Python from https://www.python.org/ , if Python is not per-installed in your computer.
Anaconda from https://www.anaconda.com/ . We shall use Jupyter notebook regularly, which is included in Anaconda.
You are restricted to use Jupyter Notebook with Anaconda.
Solve the problems given in the class. In the next class, bring print outs of all the programs and collect signature of your course instructor.
Your example will be different from the example of your instructors and friends. If same example are found both of you shall get deducted marks.
Consider the following problems.
Problem 1: Using the Symbolic Python (Sympy) do the following:
i) Integrate a given integrable function.
ii) Find partial derivative of a function with more than one variable.
You can chose your functions independently.
Instructor's solution (10th January 2025)
Problem 2: Using the Symbolic Python (Sympy), Numerical Python(Numpy), and Scientific Python (Scipy) do the following:
i) Given two matrices A and B, find A + B, A - B, A*B
ii) Given a square matrix A find its determinant. if A is invertible, find its inverse.
iii) Given a square matrix, calculate its eigenvalues and eigenvectors.
Instructor's solution (15th January 2025):
Problem 3: Using Python do the following:
i) Determine if a given number is prime.
ii) Generate Fibonacci series.
Instructor's solution (22nd January 2025):
Problem 4: Using the Numerical Python(Numpy), Scientific Python (Scipy) and Matplotlib do the following:
i) Plots a 3D parametric curve.
#Parameters:
# param_func: A function that defines the curve as a function of t (returns [x(t), y(t), z(t)]).
# t_range: Tuple defining the parameter range (t_min, t_max).
# num_points: Number of points to evaluate the curve.
ii) Plots a conic section given the general equation:
ax^2 + bxy + cy^2 + dx + ey + f = 0
with parameters:
# a, b, c, d, e, f: coefficients of the conic equation
# xlim, ylim: limits for x and y axes (tuple, e.g., (-5, 5))
# grid_size: number of points for the grid in each dimension
Instructor's solution (29nd January 2025)
Problem 5: Using the Numerical Python(Numpy), Scientific Python (Scipy) and Matplotlib draw a given continuous 3-dimensional surface
Instructor's solution (5th February 2025)
Problem 6: Using Pandas and OS do the following:
i) Find a file in the file system of your computer.
ii) Import a .xlsx file as a dataframe
iii) Manipulate data in a dataframe.
iv) Export dataframe in an .xlsx file.
Instructor's solution (12th February 2025):
Problem 7: Using Pandas represent the frequency distributions with bar diagram, histogram and pi diagram.
Instructor's solution (19th February 2025):
Problem 8:
Instructor's solution (5th March 2025):
Problem 9:
Instructor's solution (12th March 2025):
Problem 10:
Instructor's solution (19th March 2025):
Problem 11:
Instructor's solution (26th March 2025):
Problem 12:
Instructor's solution (2rd April 2025):
Problem 13:
Instructor's solution (9th April 2025):
Final Lab exam 16th April 2025 (tentative).
Theory classes before Mid-term
Lecture 1 (8th January 2025): Introduction to computer and programing languages. Declarative and Imperative knowledge.
Lecture 2 (17th January 2025): How to print in Python. Algebraic operations on numbers and strings. Lecture note is under preparation.
Lecture 3 (24th January 2025): Variables in Python, if-else conditions, nested if-else statements, use of and, or in if else condition.
Lecture 4 (31th January 2025): Enumeration on string elements, input from user, while loop.
Lecture 6 (7th February 2025): Range, For loop, class test.
Lecture 7 (14th February 2025): Exhaustive enumeration and finding positive square root of a positive number.
Lecture 7 (21th February 2025)
After Mid-term
Lecture 8 (7th March 2025)
Lecture 9 (21th March 2025)
Lecture 10 (28th March 2025)
Lecture 11 (4rd April 2025)
Lecture 12 (11th April 2025)
Lecture 13 (25th April 2025)
Coming soon.
For old question papers find the previous course websites.
Class test - 1 question paper dated 07.02.2025
Class test - 2 question paper
Lab Examination question paper dated 23.04.2025
End Term question paper