Engineering Mathematics:

• COMPLEX NUMBERS AND INFINITE SERIES:
  • De Moivre?s theorem and roots of complex numbers
  • Euler?s theorem
  • Logarithmic Functions
  • Circular, Hyperbolic Functions and their Inverses
  • Convergence and Divergence of Infinite series
  • Comparison test d?Alembert?s ratio test
  • Higher ratio test
  • Cauchy?s root test
  • Alternating series
  • Lebnitz test, Absolute and conditioinal convergence
• CALCULUS OF ONE VARIABLE:
  • Successive differentiation
  • Leibnitz theorem
  • McLaurin?s and Taylor?s expansion of functions
  • Errors and Approximation
  • Asymptotes of Cartesian curves
  • Curveture of curves in Cartesian
  • parametric and polar coordinates
  • Tracing of curves in Cartesian
  • Parametric and polar coordinates (like conics, astroid, hypocycloid, Folium of Descartes, Cycloid, Circle, Cardiode, Lemniscate of Bernoulli, equiangular spiral)
  • Finding area under the curves, Length of the curves, volume and surface of solids of revolution
• ORDINARY DIFFERENTIAL EQUATIONS:
  • First order differential equations ? exact and reducible to exact form
  • Linear differential equations of higher order with constant coefficients
  • Solution of simultaneous differential equations
  • Variation of parameters
  • Solution of homogeneous differential equations
  • Canchy and Legendre forms
  • Eigen values and eigen vectors
  • Caley ? Hamilton theorem
• CALCULUS OF SEVERAL VARIABLES:
  • Partial differentiation
  • ordinary derivatives of first and second order in terms of partial derivaties
  • change of variables
  • Taylor?s theorem of two variables and its application to approximate errors
  • Maxima and Minima of two variables
  • Langranges method of undermined multipliers and Jacobians
• FUNCTIONS OF COMPLEX VARIABLES:
  • Derivatives of complex functions
  • Analytic functions
  • Cauchy-Riemann equations
  • Harmonic Conjugates
  • Conformal mapping
  • Standard mappings ? linear, square, inverse and bilinear
  • Complex line integral
  • Cauchy?s integral theorem
  • Cauchy?s integral formula
  • Zeros and Singularities
  • Taylor series
  • Laurents series
  • Calculation of residues
  • Residue theorem, Evaluation and real integrals
• VECTOR CALCULUS:
  • Derivatives of complex functions
  • Analytic functions
  • Cauchy-Riemann equations
  • Harmonic Conjugates
  • Conformal mapping
  • Standard mappings ? linear, square, inverse and bilinear
  • Complex line integral
  • Cauchy?s integral theorem
  • Cauchy?s integral formula
  • Zeros and Singularities
  • Taylor series
  • Laurents series
  • Calculation of residues
  • Residue theorem, Evaluation and real integrals
• Laplace Transformation:
  • Laplace Transformation
  • Inverse Laplace transformation Convolution Theorem
  • application to linear differential equations with constant coefficients
  • impulse functions
  • periodic functions
• Fourier Series:
  • Fourier Series
  • Euler?s formulae
  • even and odd functions
  • having arbitrary periods
  • half range expansion
  • Harmonic Analysis
• Fourier Transforms:
  • Fourier transform
  • Sine and Cosine transforms
  • Application to differential equations
• Special Functions:
  • Beta and Gamma functions
  • Bessels functions of first kind
  • Recurrence relations
  • modified Bessel functions of first kind
  • Ber and Be functions
  • Legendre Polynomial
  • Rodrigue?s formula
  • orthogonal expansion of function
• Partial Differential Equation:
  • Formation of first and second order linear equations
  • Laplace, Wave and heat conduction equation
  • initial and boundary value problems