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Week - 1 |
Riemann integral: Riemann–Darboux lower and upper sums |
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Week - 2 |
Riemann integral: Definite integral of a function, properties of the definite integral |
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Week - 3 |
Fundamental theorem of differential and integral calculus; Indefinite integral and its properties |
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Week - 4 |
Riemann integrability: Sets of measure zero, integrability theorem |
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Week - 5 |
Improper integrals: Classification of improper integrals |
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Week - 6 |
Improper integrals: Convergence tests |
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Week - 7 |
Improper integrals: Gamma function, Stirling formula |
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Week - 8 |
Applications of the integral: Mean value theorem, Taylor theorem with integral remainder |
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Week - 9 |
Some special integrals: Basel problem |
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Week - 10 |
Some special integrals: Real Riemann zeta function |
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Week - 11 |
Concept of transcendental functions and transcendence of some elementary functions |
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Week - 12 |
Irrationality of the number e, irrationality of the number pi |
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Week - 13 |
Fourier series: Basic concepts |
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Week - 14 |
Fourier series: Convergence and applications |