Details of MA1101 (Autumn 2025)
| Level: 1 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA1101 | Mathematics I | Somnath Basu |
| Syllabus |
|---|
| Part I: Combinatorics Permutations, combinations, binomial theorem.
Part II: Set theory & Logic Standard Operations: unions & intersections, various laws, complementation, cartesian product, symmetric difference. Relations: various relations, equivalence classes, partition. Mappings: injective, surjective, bijective, inverse of a function, examples, characteristic functions, step functions. Logical quantifiers: Examples from set theory. Negations: Contrapositive statements involving various quantifiers. Negations: Contrapositive statements involving various quantifiers. Part III: Number Systems Construction of Z and Q from N. Part IV: Calculus Basic notions: limit, continuity, differentiability, chain rule, Leibniz rule. Mean Value Theorems: Rolle's Theorem (statement only), Mean Value Theorem, Taylor's Theorem of order 2, L'Hospitals rule. Applications of derivatives: monotone function, maxima and minima. Integration: Integrals as Anti-derivatives, Properties of indefinite integral. Methods of Integration: Substitution Method, Integration using trigonometric identities, Integration using Partial Fractions, Integration by Parts; Integrals of some special functions or special form; Definite integral as the limit of a Riemann sum (Summation of a series with the help of Integration) ; Fundamental Theorem of Integral Calculus (First/second Form for definite integral, NO PROOFs) ; Properties of definite integral; The Fundamental Theorem Integral Calculus (Second/first Form for indefinite integral, NO PROOFs) ; Application of integral: Area under Simple Curves, Area between Two Curves. |
| References |
|---|
| Suggested Texts:
1. Apostol, T.M., Calculus I, Wiley India Pvt Ltd. 2. Apostol, T.M., Calculus II, Wiley India Pvt Ltd. 3. Artin, M., Algebra, Prentice-Hall of India, 2007. 4. Barnard, S. and Child, J.M., Higher Algebra, Macmillan, 1936. 5. Bartle, R.G., Sherbert, D.R., Introduction to Real Analysis, John Wiley & Sons, 1992. 6. Denlinger, C.G., Elements of Real Analysis, Jones & Bartlett Learning, 2010. 7. Halmos, P.R., Naive Set Theory, Springer 8. Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010. 9. Piskunov, N., Differential and Integral Calculus: Volume 1, CBS, 1996. 10. Polya, G., How to Solve It, Princeton University Press, 2004. 11. NCERT Mathematics Textbook for Class 12 - Part 1 and 2, 2019. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | MP | 1 | Not Allowed |
| 4 | MP | 3 | Not Allowed |
| 5 | MR | 1 | Not Allowed |
| 6 | MR | 3 | Not Allowed |
| 7 | MS ( Mathematical Sciences ) | 1 | Core |
| 8 | RS | 1 | Not Allowed |
| 9 | RS | 2 | Not Allowed |