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Here I am also provide you the Calicut University B.Tech MathematicsThird Semester ME syllabus. this is as follows:
Module I: Functions of a Complex Variable (13 hours)
Functions of a Complex Variable – Limit – Continuity – Derivative of a Complex function –
Analytic functions – Cauchy-Riemann Equations – Laplace equation – Harmonic Functions
– Conformal Mapping – Examples: Zn, sinz, cosz, sinhz, coshz, (z1/Z ) – Mobius
Transformation.
Module II: Functions of a Complex Variable (13 hours)
Definition of Line integral in the complex plane – Cauchy’s integral theorem (Proof of
existence of indefinite integral to be omitted) – Independence of path – Cauchy’s integral
formula – Derivatives of analytic functions (Proof not required) – Taylor series – Laurent
series – Singularities and Zeros – Residues
– Residue Integration method – Residues and Residue theorem – Evaluation of real
integrals.
Module III: Linear Algebra (13 hours) - Proofs not required Vector spaces – Definition,
Examples – Subspaces – Linear Span – Linear Independence – Linear Dependence – Basis –
Dimension – Ordered Basis – Coordinate Vectors – Transition Matrix – Orthogonal and
Orthonormal Sets – Orthogonal and Orthonormal Basis – Gram-Schmidt orthogonolisation
process – Inner product spaces –Examples.
Module IV: Fourier Transforms (13 hours)
Fourier Integral theorem (Proof not required) – Fourier Sine and Cosine integral
representations – Fourier Transforms – Fourier Sine and Cosine Transforms – Properties of
Fourier Transforms
