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