Week - 1 |
Definition of sequence, Convergence of sequence, Monotone sequences, Subsequences |
Week - 2 |
Cauchy sequence, Geometric sequence, Accumulation points, Series, Convergence of series |
Week - 3 |
Geometric series, Positive series , Comparison theorems, Ratio test, Root test, Leibniz theorem, Absolute convergence |
Week - 4 |
Continuity and Limit |
Week - 5 |
Continuous functions on compact intervals, Intermediate value theorem |
Week - 6 |
Function sequences and function series, Power series |
Week - 7 |
Derivative |
Week - 8 |
Derivative, Properties of derivatives |
Week - 9 |
Local maximum and local minimum, Rolle's theorem, Mean value theorem
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Week - 10 |
Derivatives of function and power series |
Week - 11 |
Inverse functions, Exponential function, Logarithms, General exponentials Trigonometric functions, Hyperbolic functions |
Week - 12 |
Inverse functions, Exponential function, Logarithms, General exponentials Trigonometric functions, Hyperbolic functions |
Week - 13 |
Indeterminate forms, Sketching the graph of a function |