Jharkhand University of Technology, Jharkhand, Computer Engineering Semester 1, Mathematics – I Syllabus

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Unit - 1 Functions of one variable

Unit – 1

Function of one variable

1.1 Function of one variable Successive Differentiation

1.2 Leibnitz Theorem

1.3 Expansion of a function into Taylors and Maclaurin’sSeries

1.4 Function of two or more variables Partial derivatives

1.5 Euler’s Theorem

1.6 Taylor’s Expansion

1.7 Maxima Minima of a function of two variables

1.8 Lagrange’s method of undetermined multipliers

Unit - 2 Reduction formula for integrals

Unit 2

Reduction formula for integrals

2.1 Reduction formula for integrals

2.2 Improper integrals and its convergence

2.3 Beta and Gamma Functions and Their Properties

2.4 Differentiation under integral sign

2.5 Applicationsof integrals as length area volume and surface area of revolution

Unit - 3 Vector Space

Unit 3

Vector Space

3.1 Vector addition and scalar multiplication

3.2 Linear dependence of vectors

3.3 Linear independence of vectors

3.4 Basis and dimension

3.5 Linear transformations range and kernel of a linear map

3.6 Rank and nullitytheorem and inverse of a linear transformation

3.7 Composition of linear maps

3.8 Matrix associated with a linear mapping

Unit - 4 Matrices

Unit – 4

Matrices

4.1 Rank of a matrix Echelon form and Normal form

4.2 System of linear Equationsconsistency and inconsistency

4.3Eigenvalues and Eigenvectors

4.4 Diagonalization ofsquare matrices

4.5CayleyHamilton Theorem

4.6 Inner product spaces

4.7 GramSchmidt orthogonalizationprocess

Unit - 5 First order ordinary Differential Equations

Unit – 5

First Order Ordinary Differential Equations

5.1 Exact differential Equations

5.2 Linear and Bernoulli’s Equations

5.3 Euler’s Equations

5.4 Equations Not of First Degree Equations Solvable For P

5.5 Equations Solvable For Y

5.6 Equations Solvable for X and Clairaut’s Type

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Other Subjects of Semester-1
Physics-i
Basic electrical engineering
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