| Course Name | Real Analysis |
| Course Code | 25MAT301 |
| Campus |
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. |
|
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 |
– |
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