# Mathematics – I Notes VSSUT | M-I Notes VSSUT

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## Mathematics – I Notes VSSUT – M-I Notes VSSUT of Total Complete Notes

Please find the download links of Mathematics – I Notes VSSUT | M-I Notes VSSUT are listed below:

#### Module – 1

Limit of function,Left hand and right hand limits,

Limit of a function by sequential approach,Continuity,Types of discontinuities,

Differentiability of functions,Left and right derivative,Mean Value Theorems,

On the basis of a certin amount of knowledge about the derivative of a function, mean value
theorems enable us to get some information about the function itself.

#### Module – 2

Linear Algebra, Matrix,Symmetric and Skew symmetric, Equal matrix,

Scalar Multiplication,Matrix multiplication,Some Properties of matrix multiplication,

Special Matrices,Trangular Matrices,Upper and Lower triangular matrices ,

Diagonal matrices,diagonal matrices,Transpose of a product,

Inner product of vectors,Linear system of equations, Gauss Elimination,

Matrix form of linear equation,Gauss Elimination Method,

Rank of a matrix, Linear Independence,Linear Independence and Dependence ,

Rank of a Matrix,Vector spaces and subspaces,

Inverse of a matrix, Gauss Jordan Elimination.

#### Module – 3

First order differential equation,Solution of a differential equation,

Verification of solution,Separable differential equation,

Exact differential equations and Integrating Factor,Integrating Factors,

Linear Differential equation, Bernoulli Equation,Linear Differential Equations of second and
higher order,

A differential equation is an equation involving derivatives of one
or more dependent variable with respect to one or more independent variable,

Second order Homogeneous Equations with constant coefficients,Euler-Cauchy Equation,

Solution by undetermined coefficients,Rules for the method od undetermined coefficients,

Modification Rule,Solution by variation of parameters.

#### Module – 4

Series solution of Differential Equations,Home Work,Theory of Power-series Method;

Radius of Convergence,Radius of Convergence or Circle of Convergence,

Legendre’s Equation, Legendre Polynomials, Frobenious Method, Bessel’s Equation, Bessel’s functions,Gamma Function.

#### References Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, Inc, New York, 2006. J. Sinha Roy and S.Padhy, A course on Ordinary and partial differential equations, Kalyani Publishers, 2010.

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