Mathematics - I

Notes will be updated here periodically. 

Pre-requisites: 

Calculus and Progression (NCERT level)

Course Syllabus: 

[Unit 1a] - Differential Calculus: Continuity and differentiability of a function of single variable, statement of Rolle’s Theorem, Lagrange’s mean value theorem and applications. 

[Unit 1b] - Functions of Several Variables:  Continuity and differentiability, mixed partial derivatives, local maxima and minima for functions of two variables, Lagrange multipliers.

[Unit 2] - Integral Calculus: Definite Integrals as a limit of sums, Applications of integration to area, volume, surface area, and Improper integrals. 

[Unit 3a] - Sequence & Series: Limit of a sequence, monotone and Cauchy sequences and properties of convergent sequences, examples. Infinite series, positive series, tests for convergence and divergence, integral test, alternating series, Leibnitz test.

[Unit 3b] - Functional Series: Pointwise and uniform convergence, basic aspects of Power series, Fourier series.

Course Outcomes: 

Students will be able to understand

1. Single and multi-variable differential calculus and its application in analyzing the curves and finding the extreme values. 

2. Integral calculus and its application in finding the length, area and volume obtained by the curves.

3. Concepts of sequence and series, and various fundamental tests determine convergence behavior.   

4. Power series and Fourier series, and their application.  

Recommended Books: 

Text Books:

1. B S Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th edition, (2017).

2. G.B. Thomas and R.L. Finney, Calculus and Analytic Geometry, Pearson Education, 9th edition, (2007).

3. R.K. Jain and S.R.K Iyenger, Advanced Engineering Mathematics, Narosa Publishing House, 11th edition, (2011).

4. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley, 8th edition, (2006).

Reference Books:

1. Stewart James., Essential Calculus, Thomson Publishers, 6th edition, (2007).

2. J. E. Marsden, A. J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer-Verlag, 3rd edition, (1993).

3. S. R. Ghorpode, B. V. Limaye, A course in Multivariable Calculus and Analysis, Springer, 1st edition, (2009).

Evaluation Scheme: 

Students will be evaluated on a scale of 100 = (0.75*E1+0.5*E2+0.5*E3) where

E1 - 2 Open Book Exams of 50 Marks each for 2 Hr duration

E2 - 1 Quiz (following level of GATE/IES/UPSC) of 30 Marks for 1 Hr duration

E3 - 1 Exam on Self-Learnt Topic of 20 Marks for 1.25 Hrs duration

Note: A minimum of 20 marks are required to pass the course. Also, Highest grade (A) will be allotted to students scoring 85+. The grading will be relative-scaled.

Exam/Test Schedule: 

1. Mid Term Exam (MTE) will held on 03 November 2025 from 10:00 AM to 12:00 PM.

2. Self-Learning Topic Exam will held on 08 December 2025 from 09:45 to 11:00 AM. (syllabus: curve tracing in Cartesian coordinate system; MATLAB curve plotting and level curves) 

3. Quiz will held on 19 December 2025. The time will be announced later. (syllabus: single and multi-variable differential calculus; integration)