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Good Books for reference:
Good Books for reference:
Calculus and Analytic Geometry (Thomas, G.B.and Finney, R.L.), 9th edition.
Calculus, Vol I and II (Tom M Apostol).
Syllabus for Calculus
Syllabus for Calculus
Finite, countable and uncountable sets
Real number system as a complete ordered field
Archimedean property
Sequences and series
Convergence
Lecture 2 What are sequences?
Lecture 3 Behaviour of sequences.
Lecture 4: Epsilon N definition of Limits of sequences
Lecture 5: Recursive definition of sequences.
Lecture 6: What are subsequences?
Lecture 7: Nondecreasing sequences.
Lecture 8: Bounded sequences
Lecture 9: Bounded and Nondecreasing sequences are convergent
Lecture 10: Properties of Limits of sequences
Lecture 11: Frequently arising Limits
Lecture 12: Introduction to series.
Lecture 13: Checking the convergence of a series by the sequence of partial sums
Lecture 14: Geometric series
Lecture 15: Some Problems based on geometric series
Lecture 16: Telescopic series
Lecture 17: nth term test for checking the divergence of a series.
Lecture 18: Some noteworthy points regarding convergence of series.
Lecture 19: The integral test for checking the convergence of series of positive terms
Lecture 20: Problems based on integral test.
Lecture 21: p test for checking convergence/divergence of a series
Lecture 22: Comparison tests ( Direct comparison test and limit comparison test ).
Lecture 23: Problems on Limit comparison test (LCT) and Direct comparison test (DCT)
Lecture 24: Ratio test
Lecture 25: Nth root test.
Lecture 26: Alternating series
Limits
Continuity
Uniform continuity
These contents would be covered soon.
Differentiability
Mean value theorems
Lecture 1: What is a function?
Lecture 2: min-max theorem for continuous functions.
Lecture 3: Local and Global extreme values.
Lecture 4: First derivative theorem for local extreme values.
Lecture 5: Problems on finding extreme values of functions.
Lecture 6: All critical and boundary points may not be the points of local extreme values.
Lecture 7: How to find out if a critical/boundary point is a point of local extreme value?
Lecture 8: Problems on finding extreme values revisited
Lecture 9: Rolle’s theorem
Lecture 10: The mean value theorem
Lecture 11: Concave up and concave down graphs
Lecture 12: Point of inflection
Lecture 13: Cartesian graphing using first and second derivatives I
Lecture 14: Cartesian graphing using first and second derivatives-II
Lecture 15: Cartesian graphing using first and second derivatives-III
Riemann integration
Improper integrals
Functions of two or three variables
Continuity
Directional derivatives
Partial derivatives
Total derivative
Maxima and minima
Saddle point
Method of Lagrange’s multipliers
Double and Triple integrals and their applications
Lecture 1: Introduction to multiple integrals
Lecture 2: Double integrals over the Bounded non rectangular regions
Lecture 3: Reversing the order of integration
Line integrals and Surface integrals
Green’s theorem
Stokes’ theorem
Gauss divergence theorem
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