Calculus
Good Books for reference:
Syllabus for Calculus
Real numbers
Functions of a real variable
Limits, continuity, differentiability, mean value theorem
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
Taylor’s theorem with remainders
Indeterminate forms
Maxima and minima
Asymptotes
Curve tracing
Functions of two or three variables
Limits
Continuity
Partial derivatives
Maxima and minima
Lagrange’s method of multipliers
Jacobian
Riemann’s definition of definite integrals
Indefinite integrals
Infinite and improper integrals
Double and triple integrals (evaluation techniques only)
Lecture 1: Introduction to multiple integrals
Lecture 2: Double integrals over the Bounded non rectangular regions
Lecture 3: Reversing the order of integration
Areas, surface and volumes