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Lecture 1 |
The Real Number System | |
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Lecture 2 |
Convergence of a Sequence, Monotone Sequences | |
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Lecture 3 |
Cauchy Criterion, Bolzano - Weierstrass Theorem | |
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Lecture 4 |
Continuity and Limits | |
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Lecture 5 |
Existence of Maxima, Intermediate Value Property, Differentiabilty | |
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Lecture 6 |
Rolle's Theorem, Mean Value Theorem | |
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Lecture 7 |
Cauchy Mean Value Theorem, L'Hospital Rule | |
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Lecture 8 |
Fixed Point Iteration Method, Newton's Method | |
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Lecture 9 |
Sufficient Conditions for Local Maximum, Point of Inflection | |
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Lecture 10 |
Taylor's Theorem | |
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Lecture 11-13 |
Infinite Series, Convergence Tests, Leibniz's Theorem | |
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Lecture 14 |
Power Series, Taylor Series | |
| Lecture 15 - 16 | Riemann Integration | |
| Lecture 17 | Fundamental Theorems of Calculus, Riemann Sum | |
| Lecture 18 | Improper Integrals | |
| Uniform Continuity (Not for Examination) | ||
| Lecture 19 | Area Between Two Curves; Polar Coordinates | |
| Lecture 20 | Area in Polar Coordinates,Volume of Solids | |
| Lecture 21 | Washer and Shell Methods, Length of a plane curve | |
| Lecture 22 | Areas of Surfaces of Revolution; Pappus's Theorems | |
| Lecture 23 | Review of vectors, equations of lines and planes; sequences in R^3 | |
| Lecture 24 | Calculus of Vector Valued Functions | |
| Lecture 25 | Principal Normal; Curvature | |
| Lecture 26 -27 | Functions of Several Variables : Continuity and Differentiability | |
| Lecture 28 | Directional Derivatives, Gradient, Tangent Plane | |
| Lecture 29 | Mixed derivative Theorem, MVT, Extended MVT | |
| Lecture 30 | Maxima, Minima, Second Derivative Test | |
| Lecture 31 | Lagrange Multiplier Method | |
| Lecture 32 | Double integrals | |
| Lecture 33 | Change of Variable in a Double Integral, Triple Integrals | |
| Lecture 34 | Change of Variables in a Triple Integral, Area of a Parametric Surface | |
| Lecture 35 | Surface Area, Surface Integrals | |
| Lecture 36 | Line Integrals, Green's Theorem | |
| Lecture 37 | Green's Theorem (contd.), curl, Divergence | |
| Lecture 38 | Stokes' Theorem | |
| Lecture 39 | The Divergence Theorem |