T.Y.B.Sc.

This page was last updated on 1-Jul-2025

A.Y. 2025-26

Syllabus for the academic year 2025-26. Download

Lecture Notes for Multiple Integrals. (GNCUSMA501) Download
eNotes for Multivariable Calculus 2 (GNCUSMA501). Download
GNCUSMA501 Practical 1. Download
GNCUSMA502 Practical 2. Download
GNCUSMA502 Practical 3. Download
GNCUSMA502 Practical 4. Download
GNCUSMA502 Practical 5. Download
GNCUSMA502 Practical 6. Download
GNCUSMA502 Practical 7. Download

Lecture Notes for Groups and Subgroups. (GNCUSMA502) Download
GNCUSMA502 Practical 1-7. Download

GNCUSMA503 (Topology of Metric Spaces) All Practical 1-7. Download

A.Y. 2024-25

Syllabus for the academic year 2024-25. Download

Practical of Multivariable Calculus 2

Evaluation of double and triple integrals. Download
Changes variables in double and triple integrals. Download
Line integral of scalar and vector fields. Download
Green's theorem, conservative field and applications. Download
Evaluation of surface integrals. Download
Stoke's and Gauss divergence theorem. Download
Miscellaneous theory questions. Download
Multivariable calculus 2 question paper held in October 2023. Download
Multivariable calculus 2 question paper held in April 2024. Download

Practical of Group Theory

All Practical. Download

A.Y. 2023-24

Practical for Semester 6

Practical for Basic Complex Analysis

Practical for Ring Theory

Practical for Topology of Metric Spaces and Real Analysis

Practical for Graph Theory and Combinatorics

Practical for Semester 5

Practical for Multivariable Calculus II
Practical for Group Theory

Syllabus for Academic Year 2023-24

A.Y. 2022-23

For Graph Theory, Download
Ring Theory Practical 1, Download

Multivariable Calculus II Practical 1, Download
Multivariable Calculus II Practical 2, Download
Multivariable Calculus II Practical 3, Download
Multivariable Calculus II Practical 4, Download
Multivariable Calculus II Practical 5, Download
Multivariable Calculus II Practical 6, Download
Multivariable Calculus II Practical 7, Download
eNotes for Multivariable Calculus II, Download

Syllabus for the Academic Year 2022-23, Download

A.Y. 2021-22

Lecture recordings for Basic Complex Analysis

Lecture 15: Cauchy integral theorem (02/02/2022; 11.00 a.m.)
Lecture 13, 14: Practical 1 and integration of complex valued functions (29/01/2022; 10.20 a.m., 11.10 a.m.)
Lecture 11, 12: Stereographic projection and practical 2 (22/01/2022; 10.00 a.m.,)
Lecture 10: Stereographic projection (19/01/2022; 11.00 a.m.)
Lecture 9: Problems on singularities (15/01/2022; 10.00 a.m.)
Lecture 8: Singularities (12/01/2022; 11.00 a.m.)
Lecture 6, 7: Analytic functions and Cauchy-Riemann equations (08/01/2022; 10.00 a.m.)
Lecture 5: Recording NA
Lecture 3, 4: Functions, limits, continuity and derivatives-Part 1 and Part 2 (18/12/2021; 10.00 a.m.)
Lecture 2: Forms of complex numbers (15/12/2021; 11.00 a.m.)
Lecture 1: Introduction to complex number system (01/12/2021; 11.00 a.m.)

Introduction to Complex Analysis:

Practical 1: Limits, Continuity and Derivatives of Functions of a Complex Variables
Practical 2: Stereographic Projections, Analytic Functions, Finding Harmonic Conjugates
Practical 3: Contour Integral, Cauchy Integral Formula, Mobius Transformation
Practical 4: Taylor' Series, Trigonometric, Exponential, Hyperbolic Functions
Practical 5 and 6: Power Series, Radius of Convergence, Laurent Series; Isolated Singularities, Cauchy Residue Theorem
Practical 7: Miscellaneous Practical

More study materials available in the library

Lecture recordings for Multivariable Calculus II

Lecture 27: Green's theorem (22/09/2021; 11.00 a.m.)
Lecture 26: Conservative vector field in R and Green's theorem (15/09/2021; 11.00 a.m.)
Lecture 24, 25: Fundamental theorem of calculus and conservative vector fields (04/09/2021; 10.00 a.m., 10.50 a.m.)
Lecture 23: Line integrals of vector fields (01/09/2021; 11.00 a.m.)
Lecture 21, 22: Line integrals of scalar field (28/08/2021; 10.00 a.m., 10.50 a.m.)
Lecture 20: Parametrization of curves (25/08/2021; 11.00 a.m.)
Lecture 18, 19: Line integrals (21/08/2021; 10.00 a.m., 10.50 a.m.)
Lecture 17: Invertible affine transformations (18/08/2021; 11.00 a.m.)
Lecture 16 Change of variable in R3 (11/08/2021; 11.00 a.m.)
Lecture 14, 15: Change of variable, Jacobian of transformation (07/08/2021; 10.00 a.m., 10.50 a.m.)
Lecture 13: Leibnitz's rule, introduction to coordinate system in R2 (04/08/2021; 11.00 a.m.)
Lecture 12: Triple integration, Leibnitz's rule (28/07/2021; 11.00 a.m.)
Lecture 10, 11: Triple integration, sketching solids and finding limits (24/07/2021; 10.00 a.m., 10.50 a.m.)
Lecture 9: Triple integration (17/07/2021; 9.45 a.m.)
Lecture8: Reversing the order of integration, finding area (13/07/2021; 11.00 a.m.)
Lecture 7: Sketching regions and identifying the types of regions (10/07/2021; 11.00 a.m.)
Lecture 6: Region of Type II, Reversal of order of integration (07/07/2021; 9.30 a.m.)
Lecture 5: Fubini's theorem and types of region (type 1) (03/07/2021; 11.00 a.m.)
Lecture 4: Fubini's theorem and examples (30/06/2021; 11.00 a.m.)
Lecture 3: Riemann integration and examples (26/06/2021; 11.00 a.m.)
Lecture 2: Riemann criterion, continuity and integrability (23/06/2021; 11.00 a.m.)
Lecture 1: Introduction, Reimann integration (19/06/2021; 11.00 a.m.)

Multivariable Calculus II Practical Sheets:

Syllabus for A.Y. 2021-22

A.Y. 2020-21

Lecture recordings for Sem 6:

Lecture 21: Residue, pole and residue theorem (09/04/2021; 1.00 p.m. to 1.50 p.m.)
Lecture 20: Laurent series examples (01/04/2021; 10.00 a.m. to 10.50 a.m.)
Lecture 19: Trigonometric and hyperbolic functions, Laurent series, removable and essential singularities (30/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 18: Maclaurin series and exponential functions (26/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 17: Taylor's series (23/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 16: Cauchy integral theorem and formula (19/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 15: Linear fractional transformations and complex integrals (16/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 14: Harmonic functions and analyticity (12/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 13: Singularities, regular points, zeros; harmonic functions (09/03/2021, 12.00 p.m. to 12.50 p.m.)
Lecture 12: Analytic and singularity (05/03/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 11: Analytic and entire functions (02/03/2021; 12.10 p.m. to 1.00 p.m.)
Lecture 10: Differentiability numerical (26/02/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 9: Differentiability and Cauchy-Riemann equations (23/02/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 8: Limits involving infinity, differentiability of real valued functions and its interpretation (16/02/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 7: Limits, continuity and boundedness (12/02/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 6: Limits and continuity of complex functions, epsilon-delta definition (09/02/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 5: Functions of complex numbers, components and limits (29/01/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 4: Recording unavailable (19/01/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 3: Domains and regions in complex plane, circles and disks in complex plane, introduction to functions (12/01/2021; 12.00 p.m. to 12.50 p.m.)
Lecture 2: Polar representation, Euler formula, De-Moivre's formula, roots of unity and it's geometry (8th Jan 2021; 12.00 p.m. to 12.50 p.m.)
Lecture 1: Introduction to complex numbers, the set of complex numbers as a vector space, algebra of complex numbers, Argand's diagram (5th Jan 2021; 12.00 p.m. to 12.50 p.m.)

Introduction to Complex Analysis:

Practical 1: Limits, Continuity and Derivatives of Functions of a Complex Variables
Practical 2: Stereographic Projections, Analytic Functions, Finding Harmonic Conjugates
Practical 3: Contour Integral, Cauchy Integral Formula, Mobius Transformation
Practical 4: Taylor' Series, Trigonometric, Exponential, Hyperbolic Functions
Practical 5 and 6: Power Series, Radius of Convergence, Laurent Series; Isolated Singularities, Cauchy Residue Theorem
Practical 7: Miscellaneous Practical
QP 33539*: University Exam April 2018
Sem VI Practical Descriptive held in April 2019

*Question Paper based on older syllabus. Unit 2 and 3 questions are of current (revised) syllabus

More study materials available in the library

Syllabus for A.Y. 2020-21

Lecture Recordings for Semester 5:

Find here the lecture recordings for Surface Integrals:

Lecture 33 (21st December 2020; 1.15 p.m. to 2.00 p.m.)
Lecture 32 (18th December 2020; 12.00 p.m. to 1.15 p.m.)
Lecture 31 (15th December 2020; 1.00 p.m. to 1.55 p.m.)
Lecture 30 (8th December 2020; 1.00 p.m. to 2.15 p.m.)

Find here the lecture recordings for Line Integrals:

Lecture 29 (3rd December 2020; 12.00 p.m. to 1.10 p.m.)
Lecture 28 (1st December 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 26 and 27 (27th November 2020; 12.00 p.m. to 1.50 p.m.)
Lecture 25 (24th November 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 24 (20th November 2020; 12.00 p.m. to 12.50 p.m.)

Find here the lecture recordings for Multiple Integrals:

Lecture 23 (10th November 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 22 (6th November 2020; 12.00 p.m. to 12.50 p.m.)
Lecture 21 (3rd November 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 20 (27th October 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 19 (20th October 2020; 1.05 p.m. to 1.55 p.m.)
Lecture 18 (16th October 2020; 11.05 a.m. to 11.55 a.m.)
Lecture 17 (13th October 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 16 (9th October 2020; 12.00 p.m. to 12.50 p.m.)
Lecture 15 (6th October 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 14 (29th September 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 13 (25th September 2020, 1.20 p.m. to 2.10 p.m.)
Lecture 12 (15th September 2020; 1.00 p.m. to 1.50 p.m.)
(Lecture 11 is unavailable due to technical issues)
Lecture 10 (8th September 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 9 (3rd September 2020; 12.15 p.m. to 1.05 p.m.)
Lecture 8 (1st September 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 7 (1st September 2020; 12.10 p.m. to 1.00 p.m.)
Lecture 6 (25th August 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 5 (21st August 2020; 12.15 p.m. to 1.05 p.m.)
Lecture 4 (18th August 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 3 (14th August 2020; 12.15 p.m. to 1.05 p.m.)
Lecture 2 (11th August 2020; 1.00 p.m. to 1.50 p.m.)
Lecture 1 (7th August 2020; 12.15 p.m. to 1.05 p.m.)

Multiple Integrals

Integral Calculus Practical:

A.Y. 2019-20

NOTE

Owing to the Novel Covid 19 pandemic all exams stand postponed until further notice. All students are required to regularly visit the college and university website for further details and contact your teachers for clarification, if any required. Do not beleive and spread rumours.