Jharkhand University of Technology, Jharkhand, Mechanical Engineering Semester 1, Mathematics-I Syllabus

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Unit - 1 Function 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 Matrices

Unit – 3

Matrices

3.1 Rank of a matrix Echelon form and Normal form

3.2 System of linear Equationsconsistency and inconsistency

3.3 Eigen values and Eigen vectors

3.4 Diagonalization of square matrices

3.5 CayleyHamilton Theorem

Unit - 4 First order ordinary Differential Equations

Unit – 4

First Order Ordinary Differential Equations

4.1 Exact differential Equations

4.2 Linear and Bernoulli’s Equations

4.3 Euler’s Equations

4.4 Equations Not of First Degree Equations Solvable For P

4.5 Equations Solvable For Y

4.6 Equations Solvable for X and Clairaut’s Type

Unit - 5 Infinite Series

Unit 5

Infinite Series

5.1 Infinite Series Convergence of series

5.2 Comparison test

5.3 pTest

5.4 Cauchy’s nth Root test

5.5 D Alembert’s Ratio Test

5.6 Rabies Test

5.7 Logarithmic test

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