Applied mathematics btech cse 3rd semester

 Unit I: 8 lecture hours

Fourier series and its applications: Euler’s formulae, Dirichlet’s conditions, Change of

interval, Fourier expansion of even and odd functions, Fourier expansion of square wave,

Rectangular wave; Saw-toothed wave; half & full rectified wave functions, Harmonic

analysis.

Unit II: 12 lecture hours

Fourier integrals and Transforms: Fourier integral theorem, Fourier sine integral, Fourier

cosine integral, Fourier sine Transform, Fourier cosine transform, Fourier transform and its

properties, Finite Fourier sine transform, Finite Fourier cosine transform, Fourier transforms

of derivatives.

Unit III: 12 lecture hours

Complex Numbers and Functions of Complex Variables: De Moivre's theorem, Roots of

complex numbers, Euler's theorem, Logarithmic Functions, Circular and Hyperbolic

Functions, Limit, Continuity and Derivatives of complex functions, Cauchy-Riemann

equations, necessary and sufficient conditions for a function to be analytic, polar form of

the Cauchy-Riemann equations. Harmonic functions, application to flow problems

Unit IV: 8 lecture hours

Complex Integration and Conformal mapping: Standard mappings (linear, square, inverse

and bilinear), Complex line integral, Cauchy's integral theorem, Cauchy's integral

formula, Zeroes and Singularities, Taylor series, Laurent’s series, Calculation of residues,

Residue theorem, Application of residue theorem to solve real integrals.

Photo