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:

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

 

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

 

References:

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