PRACTICE PROBLEMS
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1 |
The
Real Number System |
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2 |
Convergence
of a Sequence, Monotone Sequences |
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3 |
Cauchy
Criterion, Bolzano - Weierstrass Theorem |
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4 |
Continuity
and Limits |
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5 |
Existence
of Maxima/Minima, Intermediate Value Property |
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6 |
Differentiability,
Rolle's Theorem |
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7 |
Mean
Value Theorem, Cauchy Mean Value Theorem, L'Hospital
Rule |
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8 |
Fixed
Point Iteration Method, Newton's Method |
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9 |
Tests
for maxima and minima, Curve sketching |
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10 |
Taylor's
Theorem |
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11 |
Series:
Definition, Necessary and sufficient conditions, absolute convergence |
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12 |
Comparison,
Limit comparison and Cauchy condensation tests |
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13 |
Ratio
and Root tests, Leibniz's Test |
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14 |
Power
Series, Taylor Series |
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15 |
Integration,
Riemann's Criterion for integrability (Part I) |
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16 |
Integration,
Riemann's Criterion for integrability (Part II) |
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17 |
Fundamental
Theorems of Calculus, Riemann Sum |
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18 |
Improper
Integrals |
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Uniform
Continuity (Not for Examination) |
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19 |
Area
of a region between curves; Polar Coordinates |
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20 |
Area
in Polar Co-ordinates, Volume of a Solid by Slicing |
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21 |
Washer
and Shell Methods, Length of a plane curve |
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22 |
Areas
of Surfaces of Revolution; Pappus's Theorems |
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23 |
Review
of vectors, equations of lines and planes, Quadric Surfaces |
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24 |
Calculus
of Vector Valued Functions I: Parametric curves |
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25 |
Calculus
of Vector Valued Functions II: Tangent, Normal and Curvature |
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26 |
Functions
of several variables : Sequences, continuity and partial derivatives |
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27 |
Functions of several variables : Differentiabilty
and Chain Rule |
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28 |
Directional
derivative, gradient and tangent plane |
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29 |
Mixed Partial Derivatives, Mean Value Theorem and Extended
Mean Value theorem |
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30 |
Maxima, Minima, Second Derivative Test |
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31 |
Method of Lagrange Multipliers |
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32 |
Double integral |
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33 |
Change
of variables in double integrals, Polar coordinates |
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34 |
Triple
integral, Change of variables, Cylindrical and Spherical coordinates |
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35 |
Parametric surfaces, surface area and surface integrals |
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36 |
Line
integrals |
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37 |
Green's
Theorem |
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38 |
Stokes'
Theorem |
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39 |
Divergence
Theorem |