Jawaharlal Nehru Technological University, Telangana, Mechanical Engineering Semester 1, Mathematics - I Syllabus

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Unit - 1 Matrices

UNIT1

Matrices

1.1. Matrices Types of Matrices Symmetric

1.2. Hermitian skewHermitian skewsymmetric matrix

1.3. Orthogonal matrices Unitary matrices

1.4. Rank of a matrix by echelon form and normal form

1.5. Inverse of nonsingular matrices by gaussjordan method

1.6. System of linear equations

1.7. Solving system of homogeneous and nonhomogeneous equations

1.8. Gauss elimination method

1.9. Gauss seidel iteration method

Unit - 2 Eigen values and Eigen vectors

Unit2

Eigen values and Eigen vectors

2.1. Linear transformation and orthogonal transformation

2.2. Eigen values and Eigen vectors and their properties

2.3. Diagonalization of a matrix

2.4. CayleyHamilton theorem without proof

2.5. Finding inverse and power of a matrix by CayleyHamilton theorem

2.6. Quadratic forms Nature of the Quadratic forms

2.7. Reduction of quadratic form to canonical form by orthogonal transformation

Unit - 3 Sequences & Series

UNIT – 3

Sequences Series

3.1. Sequence Definition of a sequence limit

3.2. Convergent Divergent and Oscillatory sequences

3.3. Series Convergent Divergent and Oscillatory series

3.4. Comparison test

3.5. ptest

3.6. DAlembert’s ratio test

3.7. Raabe’s test

3.8. Cauchy’s integral test

3.9. Cauchy’s root test

3.10. Logarithmic test

3.11. Alternating series Leibnitz test

3.12. Alternating convergent series Absolute and conditionally convergent

Unit - 4 Calculus

UNIT4

Calculus

4.1. Mean value theorem Rolle’s theorem

4.2. Lagrange’s mean value theorem with their geometrical interpretation and applications

4.3. Cauchy’s mean value theorem

4.4. Taylor’s series

4.5. Applications of definite integrals to evaluate surface areas and volumes of revolutions of curves only in Cartesian coordinates

4.6. Definition of improper integral Beta Gamma functions and their properties.

Unit - 5 Multivariable calculus (Partial Differentiation and applications)

UNIT5

Multivariable calculus

5.1. Definition of limit and continuity

5.2. Partial differentiation

5.3. Euler’s theorem

5.4. Total derivative

5.5. Jacobian

5.6. Functional dependence independence

5.7. Maxima and minima of function of two variables and three variables using method of Lagranges’s multiplier

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Other Subjects of Semester-1
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Engineering graphics
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