PRACTICE PROBLEMS
1 
The
Real Number System 

2 
Convergence
of a Sequence, Monotone Sequences 

3 
Cauchy
Criterion, Bolzano  Weierstrass Theorem 

4 
Continuity
and Limits 

5 
Existence
of Maxima/Minima, Intermediate Value Property 

6 
Differentiability,
Rolle's Theorem 

7 
Mean
Value Theorem, Cauchy Mean Value Theorem, L'Hospital
Rule 

8 
Fixed
Point Iteration Method, Newton's Method 

9 
Tests
for maxima and minima, Curve sketching 

10 
Taylor's
Theorem 

11 
Series:
Definition, Necessary and sufficient conditions, absolute convergence 

12 
Comparison,
Limit comparison and Cauchy condensation tests 

13 
Ratio
and Root tests, Leibniz's Test 

14 
Power
Series, Taylor Series 

15 
Integration,
Riemann's Criterion for integrability (Part I) 

16 
Integration,
Riemann's Criterion for integrability (Part II) 

17 
Fundamental
Theorems of Calculus, Riemann Sum 

18 
Improper
Integrals 


Uniform
Continuity (Not for Examination) 

19 
Area
of a region between curves; Polar Coordinates 

20 
Area
in Polar Coordinates, Volume of a Solid by Slicing 

21 
Washer
and Shell Methods, Length of a plane curve 

22 
Areas
of Surfaces of Revolution; Pappus's Theorems 

23 
Review
of vectors, equations of lines and planes, Quadric Surfaces 

24 
Calculus
of Vector Valued Functions I: Parametric curves 

25 
Calculus
of Vector Valued Functions II: Tangent, Normal and Curvature 

26 
Functions
of several variables : Sequences, continuity and partial derivatives 

27 
Functions of several variables : Differentiabilty
and Chain Rule 

28 
Directional
derivative, gradient and tangent plane 

29 
Mixed Partial Derivatives, Mean Value Theorem and Extended
Mean Value theorem 

30 
Maxima, Minima, Second Derivative Test 

31 
Method of Lagrange Multipliers 

32 
Double integral 

33 
Change
of variables in double integrals, Polar coordinates 

34 
Triple
integral, Change of variables, Cylindrical and Spherical coordinates 

35 
Parametric surfaces, surface area and surface integrals 

36 
Line
integrals 

37 
Green's
Theorem 

38 
Stokes'
Theorem 

39 
Divergence
Theorem 