| Course Name | Real Analysis |
| Course Code | 25MAT301 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 5 |
| Credits | 4 |
| Campus | Mysuru |
Review: Sets and Functions – Mathematical Induction – Finite and Infinite Sets.
The Real Numbers: The Algebraic and Order Properties of R – Absolute Value and the Real Line – The Completeness Property of R – Applications of the Supremum Property – Intervals.
Chapter-1 (Sec.1.1-1.3), Chapter-2 (Sec.2.1-2.5)
Sequences and Series: Sequences and Their Limits – Limit Theorems – Monotone Sequences – Subsequences and the Bolzano-Weierstrass Theorem – The Cauchy Criterion – Properly Divergent Sequences – Introduction to Infinite Series – Absolute Convergence of Infinite series – Tests for Absolute convergence – Tests for Non-absolute convergence.Chapter-3 (Sec.3.1-3.7), Chapter-9 (Sec.9.1-9.3)
Limits and Continuous Functions:Limits of Functions – Limit Theorems – Some Extensions of the limit concept – Continuous Functions – Combinations of Continuous Functions – Continuous Functions on Intervals – Uniform Continuity. Chapter-4 (Sec.4.1-4.3), Chapter-5 (Sec.5.1-5.4)
Differentiation: The Derivative – The Mean Value Theorem – L’Hospital’s Rules – Taylor’s Theorem. Chapter-6 (Sec.6.1-6.4)
The Riemann Integral: Riemann Integral – Riemann Integrable Functions – The Fundamental Theorem – Approximate Integration.Chapter-7 (Sec.7.1-7.4)
Course Objectives:
Course Outcomes:
| COs | Description |
| CO1 | Explain the concept of Absolute value and the concept of supremum |
| CO2 | Explain concept of Convergence, Divergence and Oscillatory sequence |
| CO3 | Explain the concept of continuous function, discontinuity, uniformly continuous. |
| CO4 | Apply Taylor’s theorem and Maclaurin’s theorem to solve problems |
| CO5 | Apply the concept Riemann integral to analyze problems. |
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 1 | – | 1 | 3 | 3 | – | 2 | – | – | – | – | 1 | 2 | – |
| CO2 | 1 | – | 2 | 3 | 2 | – | 2 | – | – | – | – | 1 | 2 | – |
| CO3 | 1 | – | 2 | 3 | 2 | – | 3 | – | – | – | – | 2 | 2 | – |
| CO4 | 2 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 1 | 2 | – |
| CO5 | 2 | – | 1 | 3 | 2 | – | 3 | – | – | – | – | 3 | 2 | – |
TEXTBOOKS:
1) Robert Gardner Bartle, Donald R. Sherbert, Introduction to Real Analysis, 4th Edition, John Wiley & Sons, 2011.
REFERENCES:
1) Tom M. Apostol, Mathematical Analysis, 2nd Edition, Narosa publishing house, New Delhi,1989.
2) Rudin. W, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill International Editions, 1976.
3) H.L. Royden and P.M. Fitzpatrick, Real Analysis, 4th Edition. Pearson Education Asia Limited, 2010.
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