ALL DETAIL RELATED MATHEMATICS I

NOTES AVAILABLE BELOW THE CONTENT

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Unit-1: Matrices

  1. Elementary transformations, Inverse of a matrix, Rank of matrix, Solution of system of linear equations, Characteristic equation
  2. Cayley-Hamilton Theorem and its application
  3. Linear Dependence and Independence of vectors, Eigen values and Eigen vectors, Complex Matrices
  4. Hermitian, Skew-Hermitian and Unitary Matrices, Applications to Engineering problems.

Unit-2: Differential Calculus- I

  1. Successive Differentiation (nth order derivatives), Leibnitz theorem
  2. Curve tracing, Partial derivatives,
  3. Euler’s Theorem for homogeneous functions, Total derivative, Change of variables.

Unit-3: Differential Calculus-II

  1. Expansion of functions by Taylor’s and Maclaurin’s theorems for functions of one and two variables,
  2. Maxima and Minima of functions of several variables, Lagrange’s method of multipliers, Jacobians, Approximation of errors.

Unit-4: Multiple integration

  1. Double integral, Triple integral, Change of order of integration
  2. Change of variables, Beta and Gama function and their properties
  3. Dirichlet’s integral and its applications to area and volume, Liouville’s extensions of Dirichlet’s integral.

Unit-5: Vector Calculus

  1. Vector differentiation: Gradient, Curl and Divergence and their Physical interpretation, Directional derivatives.
  2. Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s Divergence theorem, Green’s theorem and Stoke’s theorem (without proof) and their applications.

QUESTION PAPER CHAPTER WISE

Matrices DOWNLOAD

Differential Calculus- I DOWNLOAD

Differential Calculus-II DOWNLOAD

Multiple integration DOWNLOAD

Vector Calculus DOWNLOAD

ALL DETAIL RELATED MATHEMATICS II

NOTES AVAILABLE BELOW THE CONTENT

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Unit -1: Ordinary Differential Equation of Higher Order

  1. Linear differential equation of nth order with constant coefficients, Simultaneous linear differential equations, Second order linear differential equations with variable coefficients
  2. Solution by changing independent variable, Method of variation of parameters

Unit-2: Laplace Transform

  1. Laplace transform, Existence theorem, Properties of Laplace Transform, Laplace transform of derivates and integrals
  2. Unit step function, Laplace transform of periodic function, Inverse Laplace transform
  3. Convolution theorem. Application of Laplace Transform to solve ordinary differential equations and simultaneous differential equations.

Unit-3: Sequence and Series

  1. Definition of Sequence and series with examples,
  2. Convergence of series, Tests for convergence of series, Ratio test, D’ Alembert’s test, Raabe’s test, Comparison test. Fourier series, Half range Fourier sine and cosine series.

Unit-4: Complex Variable–Differentiation

  1. Functions of complex variable, Limit, Continuity and differentiability
  2. Analytic functions, Cauchy- Riemann equations (Cartesian and Polar form),
  4. Harmonic function, Method to find Analytic functions, Milne’s Thompson Method, Conformal mapping, Mobius transformation and their properties.

Unit-5: Complex Variable Integration

  1. Complex integration, Cauchy- Integral theorem, Cauchy integral formula, Taylor’s and Laurent’s series,
  3. singularities and its classification, zeros of analytic functions, Residues, Cauchy’s Residue theorem and its application.

QUESTION PAPER CHAPTER WISE

Ordinary Differential Equation of Higher Order DOWNLOAD

Laplace Transform DOWNLOAD

Sequence and Series DOWNLOAD

Complex Variable–Differentiation DOWNLOAD

Complex Variable Integration DOWNLOAD