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.