Osmania University, Telangana, Mechanical Engineering Semester 1, Mathematics - I Syllabus

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Unit - 1 Sequences and Series

UNIT 1

SEQUENCES AND SERIES

1.1 Sequences

1.2 Series

1.3 General properties of series

1.4 Series of positive terms

1.5 Comparison tests

1.6 tests of Convergence

1.7 D’Alembert’s ratio test

1.8 Cauchy’s nth root test

1.9 Raabe’s test

1.10 Logarithmic test

1.11 Alternating series

1.12 Series of positive and negative terms

1.13 Absolute convergence and Conditional convergence

Unit - 2 Calculus of one Variable

UNIT 2

CALCULUS OF ONE VARIABLE

2.1 Rolle’s Theorem

2.2 Lagrange’s and Cauchy’s mean value theorem

2.3 Taylor Series

2.4 Curvature Radius of Curvature and Circle of Curvature

2.6 Evolutes and Involutes

Unit - 3 Multivariable Calculus (Differentiation

UNIT 3

MULTIVARIABLE CALCULUS DIFFERENTIATION

3.1 Functions of two variables

3.2 Limits and continuity

3.3 Partial derivatives

3.4 Total differential and differentiability

3.5 Derivatives of composite and implicit functions Chain rule

3.6 Change of variables

3.7 Jacobin’s

3.8 Higher order partial derivatives

3.9 Taylor’s series of functions of two variables

3.10 Maximum and minimum values of functions of two variables

3.11 Lagrange’s method of undetermined multipliers

Unit - 4 Multivariable Calculus (Integration)

UNIT 4

MULTIVARIABLE CALCULUS INTEGRATION

4.1 Double integrals

4.2 Change of order of integration

4.3 Change of Variables from Cartesian to plane polar coordinates

4.4 Triple integrals

Unit - 5 Vector Calculus

UNIT 5

VECTOR CALCULUS

5.1 Scalar and vector fields

5.2 Gradient of a scalar field

5.3 Directional derivative

5.4 Divergence and Curl of a vector field

5.5 Line Surface and Volume integrals

5.6 Green’s theorem in a plane

5.7 Gauss’s divergence theorem

5.8 Stoke’s theorem without proofs and their verification

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Other Subjects of Semester-1
Physics
Indian constitution
Basic electrical engineering
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