**MA201
Mathematics – III**

**Course
Content/ Syllabus**

__Complex Analysis:__

Complex numbers and elementary properties. Complex functions - limits, continuity and differentiation.
Cauchy-Riemann equations. Analytic
and harmonic functions. Elementary functions. Anti-derivatives and path
(contour) integrals. Cauchy-Goursat
Theorem. Cauchy's integral formula, Morera's Theorem. Liouville's
Theorem, Fundamental Theorem of Algebra and Maximum Modulus Principle. Taylor series. Power series. Singularities and Laurent series. Cauchy's
Residue Theorem and applications. Mobius transformations.

__Partial Differential Equations (PDEs):__

First
order partial differential equations; solutions of linear and nonlinear first
order PDEs; classification of second-order PDEs; method of characteristics;
boundary and initial value problems (Dirichlet and
Neumann type) involving wave equation, heat conduction equation, Laplace equations
and solutions by method of separation of variables (Cartesian coordinates); initial
boundary value problems in non-rectangular coordinates.

__Fourier Series, Fourier & Lalplace Transforms:__

Laplace
and inverse Laplace transforms; properties, convolutions; solution of ODE and
PDE by Laplace transform; Fourier series, Fourier integrals; Fourier
transforms, sine and cosine transforms; solution of PDE by Fourier transform.

Texts:

- J. W. Brown
and R. V. Churchill, Complex Variables and Applications, 7
^{th}Edition Mc-Graw Hill, 2004. (Note: Any Edition is fine) - I.
N. Sneddon, Elements of Partial Differential Equations,
McGraw Hill, 1957.
- K. Sankara Rao, Introduction to Partial Differential Equations,
3
^{rd}Edition*, PHI, 2010.

*For Sankara
Rao book: Buy latest 3^{rd} Edition. Previous editions do not contain first order
PDEs.

References:

- J. H. Mathews and R. W. Howell, Complex Analysis for
Mathematics and Engineering, 3
^{rd}Edition, Narosa,1998. - S. J. Farlow, Partial
Differential Equations for Scientists and Engineers, Dover Publications,
1993.
- R. Haberman, Elementary
Applied Partial Differential equations with Fourier Series and Boundary
Value Problem, 4
^{th}Edition, Prentice Hall, 1998. - S. Ross, Differential Equations, 3
^{rd}Edition, Wiley India, 1984.