MA2103 : Mathematical Methods II (Autumn 2021) | Academic Portal of IISER Kolkata

Details of MA2103 (Autumn 2021)

Level: 2

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
MA2103	Mathematical Methods II	Amit Ghosal

Syllabus
Part I: Partial Differential Equations: Separation of Variables - Classification, solution of partial differential equations by method of separation of variables with special emphasis on the Laplace/Poisson equations. Part II: Fourier Series: Elementary Introduction to Fourier Series - Fourier coefficients, Fourier series of a function, summation of series using Fourier series. Part III: Probability and Statistics: Probability - Events, notion of probability, conditional probability, independence, Bayes' theorem, law of large numbers and the central limit theorem (statement only). Statistics - Mean, median, mode; variance; correlation and regression. Numerical Methods: Root finding by the bisection, regula falsi and Newton-Raphson method; solving ordinary differential equations by the Euler and Runge-Kutta methods; interpolation and extrapolation from data sets.

Syllabus

Part I: Partial Differential Equations: Separation of Variables - Classification, solution of partial differential equations by method of separation of variables with special emphasis on the Laplace/Poisson equations.
Part II: Fourier Series: Elementary Introduction to Fourier Series - Fourier coefficients, Fourier series of a function, summation of series using Fourier series.
Part III: Probability and Statistics: Probability - Events, notion of probability, conditional probability, independence, Bayes' theorem, law of large numbers and the central limit theorem (statement only).
Statistics - Mean, median, mode; variance; correlation and regression.
Numerical Methods: Root finding by the bisection, regula falsi and Newton-Raphson method; solving ordinary differential equations by the Euler and Runge-Kutta methods; interpolation and extrapolation from data sets.

Prerequisite
Mathematical Methods I (MA1202)

References
Apostol, T.M., Calculus I (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2011. Apostol, T.M., Calculus II (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2017. Arfken, G. B., Weber, H. and Harris, F., Essential Mathematical Methods for Physicists and Engineers, Academic Press, 2003. Boas, M. L., Mathematical Methods In the Physical Sciences (3rd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2006. Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010.

References

Apostol, T.M., Calculus I (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2011.

Apostol, T.M., Calculus II (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2017.

Arfken, G. B., Weber, H. and Harris, F., Essential Mathematical Methods for Physicists and Engineers, Academic Press, 2003.

Boas, M. L., Mathematical Methods In the Physical Sciences (3rd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2006.

Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010.

Sl. No.	Programme	Semester No	Course Choice
1	IP	1	Not Allowed
2	IP	3	Not Allowed
3	IP	5	Not Allowed
4	MR	1	Not Allowed
5	MR	3	Not Allowed
6	MS	3	Elective
7	MS	5	Not Allowed
8	MS	7	Not Allowed
9	MS	9	Not Allowed
10	RS	1	Not Allowed
11	RS	2	Not Allowed