Course

Lab Exercises:
Programming: Review of basic python programming techniques –conditionals, branching and looping, arrays, functions, printing and saving. (Ref. 1) [2 weeks]
Differential Equations: Program to solve elementary differential equations using first order forward Euler method: Projectile motion or simple harmonic oscillations. [2 weeks]
Linear Algebra and Array Operations:
One and higher dimensional arrays, indexing; column and row vectors, transposition; vector and matrix operations using for loops and built-in vector operations (a selection from): addition, scalar multiplication; inner product of vectors, orthogonality, angle between vectors, norm, unit vectors, multiplication of matrices, unit matrix. [2 weeks]
Further array operations: submatrices – slicing, reshaping, rearranging, and resizing, conversion of 1D to 2D arrays and vice versa; selected examples from symmetric matrices, transposition and index switching operations. [1 week]
Determinants, determinants of matrices of given set column or row vectors using built-in functions, volume of a parallelopiped, other properties. [1 week]
Solution to simultaneous linear equation using row reductions and built-in functions. [1 week]
Special matrices, Orthogonal matrices in 2D, rotations in 2D and their properties; rotation of a vector in 2D; general transformation of a vector. Instructor demonstrations of transformation of a square: rotations, general deformation, demonstrations of pure compression and pure elongation in certain directions – the idea of eigenvectors. [1 week]
Finding eigenvalues and eigenvectors of a matrix using built-in functions, properties of eigenvectors; non-degenerate and degenerate cases for 3×3 matrices. [1 week]

Description: Building upon the first course on computing using python, this course further trains students on the use of python programming skills and python libraries to practice numerical calculation on some of the topics covered in single variable and multivariate calculus, differential equations, and linear algebra. These topics are to be covered a theory class in a course taken earlier or done concurrently.

On successful completion of the course, students shall be
CO1: familiar with basic computer terminology and start using ide as a versatile scientific calculator, use variables, basic data types, input/output data
CO2: Use standard programming constructs including branching, selection, repetition, functions, composition, modules, aggregated data (arrays, lists, etc.)
CO4: Apply basic programming skills to perform basic numerical computing for differentiation, integration, solving elementary matrix operations, basic linear algebra calculations.
CO5: learn, identify and use basic data structures for different purposes.

Skills and Employability: Entire course contents with tutorials and assignments help build foundations and develops computational thinking, programming skills – design and implementation of software for scientific, engineering and industrial computing applications in universities, industries and research labs/organizations.

Evaluation Pattern: As in the rules for Assessment Procedure (R.14)

1. Svein Linge, Hans Petter Langtangen, Programming for Computations – Python, 2E (2020, Springer)
   https://personal.math.ubc.ca/~pwalls/math-python/ (sequences and series, numerical differentiation, numerical integration, linear algebra)
2. Hans Petter Langtangen, A Primer on Scientific Programming with Python, 5E, Springer, 2016.
3. D.J. Pine, Introduction to Python for Science & Engineering (2019, Taylor & Fransis) (linear least-squares fit)
4. Tony Gaddis, Starting Out with Python, 3E, Pearson, 2015.Book contains flowcharting and pedagogical program development in an introductory Python book.
   C. Hill, Learning Scientific Programming with Python, 2E (2020, CUP). (Reference for Array methods, Linear Algebra)
5. Mahendra Verma, Practical Numerical Computing Using Python: Scientific & Engineering Applications, Self-Published
   https://notebook.community/hasan2014/assignment-bank/01_Predator-Prey-Model
   https://scientific- python.readthedocs.io/en/latest/notebooks_rst/3_Ordinary_Differential_Equations/02_Examples
   /Lotka_Volterra_model.html