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Week - 1 |
Properties of real numbers: Algebraic properties, order properties |
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Week - 2 |
Properties of real numbers: Completeness property; Sequences and series: Concept of a sequence |
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Week - 3 |
Sequences and series: Convergence of a sequence |
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Week - 4 |
Sequences and series: Subsequences, accumulation points |
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Week - 5 |
Sequences and series: Concepts of limit inferior and limit superior |
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Week - 6 |
Sequences and series: Concept of a series and convergence of a series |
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Week - 7 |
Sequences and series: Series with positive terms, alternating series, absolute convergence |
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Week - 8 |
Limits and continuity |
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Week - 9 |
Continuous functions on compact intervals: Intermediate value theorem, minimum–maximum theorem |
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Week - 10 |
Derivative and its properties |
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Week - 11 |
Fermat's theorem, Rolle's theorem, mean value theorem |
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Week - 12 |
Functions that are continuously differentiable up to a certain order and functions that are infinitely differentiable; Applications of the derivative |
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Week - 13 |
Function sequences and function series: Pointwise convergence, uniform convergence, power series, binomial series; Definition of elementary functions via series (exponential and logarithmic functions, trigonometric and inverse trigonometric functions) |
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Week - 14 |
Taylor theorem, analytic functions, differentiation of function sequences and series |