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NumPy for scalars and linear algebra on n-dimensional arrays; Computing eigenspace, Solving
dynamical systems on coupled ordinary differential equations, Functional programming
fundamentals using NumPy; Symbolic computation and SymPy: Differentiation and integration of
functions, Limits, Solution of ordinary differential equations, Computation of eigenvalues,
Solution of expressions at multiple points (lambdify), Simplification of expressions, Factorization,
Collecting and canceling terms, Partial fraction decomposition, Trigonometric simplification,
Exponential and logarithms, Series expansion and finite differences, Solvers, Recursive equations.
UNIT – III: Document Generation with Python and LaTeX (12 Hours)

Pretty printing using SymPy; Pandas API for IO tools: interfacing Python with text/csv, HTML,
LaTeX, XML, MSExcel, OpenDocument, and other such formats; Pylatex and writing document
files from Python with auto-computed values, Plots and visualizations.

PRACTICAL (30 Hours)

 Software labs using IDE such as Spyder and Python Libraries.
 Installation, update, and maintenance of code, troubleshooting.
 Implementation of all methods learned in theory.
 Explore and explain API level integration and working of two problems with standard
Python code.

SUGGESTED READINGS:

1. Farrell, Peter (2019). Math Adventures with Python. No Starch Press. ISBN Number: 978-
1-59327-867-0.
2. Farrell, Peter et al. (2020). The Statistics and Calculus with Python Workshop. Packet
Publishing Ltd. ISBN: 978-1-80020-976-3.
3. Saha, Amit (2015). Doing Math with Python. No Starch Press. ISBN: 978-1-59327-640-9
4. Morley, Sam (2022). Applying Math with Python (2nd ed.). Packet Publishing Ltd. ISBN:
978-1-80461-837-0
5. Online resources and documentation on the libraries, such as:
 https://matplotlib.org
 https://sympy.org
 https://pandas.pydata.org
 https://numpy.org
 https://pypi.org
 https://patrickwalls.github.io/mathematicalpython/

Math.424 Integral Equations and Calculus of Variations 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is:
 To describe the methods to reduce Initial value problems associated with linear differential
equations to various integral equations.
 To Categorize and solve different integral equations using various techniques.
 To solve the singular integral equations and derivation of Hilbert-Schmidt theorem.
 To know the variational problems, extremum of a functional and necessary conditions for
the extremum of a functional.

LEARNING OUTCOMES:

After the completion of the course, students are able to

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