NAM COLLEGE KALLIKKANDY
Re-accredited by NAAC with ‘A’ Grade
Aided & Affiliated to Kannur University
Kannur, Kerala 670693
DEPARTMENT OF MATHEMATICS
Tools & Libraries
Python 3
NumPy
Matplotlib
PuLP
Syllabus — Theory (12 hrs) + Practical (18 hrs)
Unit 1 — Python Foundations for Mathematics
Theory: 3 h | Practical: 2 h | Total: 5 h
Python syntax, data types, control structures and functions
Introduction to NumPy: arrays, array operations, broadcasting
Mathematical functions in NumPy: linspace, arange, trig, exponential
Plotting with Matplotlib: line plots, scatter, subplots, annotations
Writing and organising mathematical programs in Python
Practical
Array manipulations · Plotting mathematical functions · Writing reusable Python functions for iterative algorithms
Unit 2 — Numerical Methods I: Root Finding
Theory: 3 h | Practical: 5 h | Total: 8 h
Errors in numerical computation; convergence criteria
Bisection Method — derivation, algorithm, convergence rate
Regula Falsi (False Position) Method — theory and comparison
Newton-Raphson Method — derivation from Taylor series, quadratic convergence
Comparison of methods: speed, stability, conditions for convergence
Practical
Implement all three root-finding algorithms · Plot iteration convergence graphs · Compare methods on test equations
Unit 3 — Numerical Integration
Theory: 3 h | Practical: 5 h | Total: 8 h
Concept of numerical quadrature; Newton-Cotes formulae
Trapezoidal Rule — derivation, error analysis
Simpson's 1/3 Rule — derivation, even-interval requirement
Simpson's 3/8 Rule — derivation, applicability conditions
Comparative accuracy and error estimation
Practical
Implement Trapezoidal, Simpson's 1/3 and 3/8 rules · Visualise area under the curve · Error comparison with exact integrals
Unit 4 — LPP: Graphical Method
Theory: 3 h | Practical: 6 h | Total: 9 h
Introduction to Linear Programming Problems (LPP)
Formulation of LPP: objective function and constraints
Graphical method — feasible region, corner-point theorem
Maximisation and minimisation problems
Special cases: unbounded solutions, infeasibility, multiple optima
Practical
Define and solve LPP using PuLP · Plot feasible region and constraints · Highlight corner points and optimal solution
Schedule Overview
| U1 | Python & NumPy foundations | 5 h | |
| U2 | Root finding methods | 8 h | |
| U3 | Numerical integration | 8 h | |
| U4 | LPP graphical method | 9 h |
Assessment Pattern — Total 100 Marks
Assignment 40 marks
Problem solving (numerical methods)15
Problem solving (integration + LPP)15
Report / documentation quality10
Practical Exam 60 marks
Program writing & execution30
Output correctness & plots15
Viva voce10
Lab record / documentation5
Minimum pass mark: 50/100. Candidates must score at least 20/40 in the Assignment and 30/60 in the Practical Exam separately.
Grading Criteria for Certification
| Grade | Score (out of 100) | Percentage | Descriptor |
|---|---|---|---|
| A+ | 90 – 100 | 90% and above | Outstanding |
| A | 80 – 89 | 80 – 89% | Excellent |
| B+ | 70 – 79 | 70 – 79% | Very Good |
| B | 60 – 69 | 60 – 69% | Good |
| C | 50 – 59 | 50 – 59% | Pass |
| F | Below 50 | < 50% | Fail — re-assessment required |