Assignments & Practice Problems

PRACTICE PROBLEMS

• Practice Problem1: The Real Number System 

• Practice Problem2:  Convergence of sequences and monotone sequences

• Practice Problem3: Cauchy criterion, Subsequence

• Practice Problem4: Limits and Continuity

• Practice Problem5: Maxima/Minima, Intermediate Value Property

• Practice Problem6: Differentiability, Rolle's Theorem

• Practice Problem7: Mean Value Theorem, Cauchy Mean Value Theorem, L'Hospital Rule

• Practice Problem8: Fixed Point Iteration Method, Newton's Method

• Practice Problem9: Tests for maxima and minima, Curve sketching (figures)

• Practice Problem10: Taylor's Theorem

• Practice Problem11: Series: Definition, Necessary and sufficient conditions, absolute convergence

• Practice Problem12: Comparison, Limit comparison and Cauchy condensation tests

• Practice Problem13: Ratio and Root tests, Leibniz's Test

• Practice Problem14: Power Series, Taylor Series

• Practice Problem15: Riemann Integration -I

• Practice Problem16: Riemann Integration -II

• Practice Problem17: Fundamental Theorems of Calculus, Riemann Sum

• Practice Problem18: Improper Integrals (figures)

• Practice Problem19: Area of a region between curves; Polar Coordinates (figures)

• Practice Problem20: Area in Polar coordinates, Volume of a solid by slicing (figures)

• Practice Problem 21: Washer and Shell methods, Length of a plane curve (figures)

• Practice Problem 22: Areas of surfaces of revolution, Pappus Theorem

• Practice Problem 23: Review of Vectors, Equations of lines and planes, Quadric surfaces (figures)

• Practice Problem 24: Calculus of Vector Valued Functions I : Parametric representations of curves (figures)

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

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

• Practice Problem 27:  Functions of several variables : Differentiability and Chain Rule

• Practice Problem 28: Directional derivative, gradient and tangent plane

• Practice Problem 29:  Mixed Partial Derivatives, Mean Value Theorem and Extended Mean Value theorem

• Practice Problem 30:  Maxima, Minima, Second Derivative Test

• Practice Problem 31:  Method of Lagrange Multipliers

• Practice problem 32: Double integral

• Practice problem 33: Change of variables in double integrals, Polar coordinates

• Practice problem 34: Triple integral, Change of variables, Cylindrical and Spherical coordinates

• Practice problem 35: Parametric surfaces, surface area and surface integrals

• Practice problem 36: Line integrals

• Practice problem 37: Green's  Theorem

• Practice problem 38: Stokes' Theorem

• Practice problem 39: Divergence Theorem

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