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Mathematical Methods-I

  •  Units 4
  •  Lessons 37
  •  No. of Downloads 357
  •  Course Type Post Graduate
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Syllabus

Real Analysis: Convergence and divergence of infinite series, use of comparison tests -D’Alembert’s Ratio - test, Cauchy’s nth root test, Raabe’s test, Kummer’s test, Gauss test. Absolute and conditional convergence. Riemann integration, concept of Lebesgue integration, power series, Fourier, Laplace and Laplace -Steiltjes’ transformation, multiple integrals

Convergence and divergence of infinite series

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Use of comparison test, D’Alembert’s Ratio- test, Cauchy’s nth root test

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Raabe’s test, Kummer’s test

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Gauss test. Absolute and conditional convergence

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Riemann integration

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Concept of Lebesgue integration

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Power series

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Fourier transformation

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Laplace and Laplace -Steiltjes’ transformation

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Multiple integrals

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Syllabus

Calculus: Limit and continuity, differentiation of functions, successive differentiation, partial differentiation, mean value theorems, Taylor and Maclaurin’s series. Application of derivatives, L’hospital’s rule. Integration of rational, irrational and trigonometric functions. Application of integration

Limit of a function

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Continuity of a function

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Differentiation of functions

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Methods of differentiation

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Successive differentiation

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Partial differentiation

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Mean value theorems, Taylor and Maclaurin’s series

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Application of derivatives, L’hospital’s rule

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Integration of rational, irrational and trigonometric functions

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Application of integration

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Syllabus

Differential equation: Differential equations of first order, linear differential equations of higher order with constant coefficient

Introduction to Differential equations

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Formation of Differential equations & Solution by Variable Separable method

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Homogeneous Differential equation & Linear Differential equation

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Bernoulli’s equation & Exact Differential equation

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Linear differential equations of second and higher order with constant coefficient

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Linear differential equations of second and higher order with constant coefficients with Particular integral of the type e^ax ,cosax or sinax and x^n

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Linear differential equations of second and higher order with constant coefficients with Particular integral of the type e^ax g(x) & xcosax or xsinax

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Simultaneous first order Linear Differential equations with constant coefficients

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Syllabus

Numerical Analysis: Simple interpolation, Divided differences, Numerical differentiation and integration.

Simple Interpolation

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Simple Interpolation: Bessel’s and Everett’s Formulae, Vandermonde Matrix

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Interpolation with unevenly spaced points

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Divided Differences

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Numerical Differentiation

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Numerical Differentiation

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Numerical Integration

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Numerical Integration

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Numerical Integration

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