Punyashlok Ahilyadevi Holkar Solapur University, Maharashtra, Computer Engineering Semester 1, Engineering Mathematics I Syllabus

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Unit - 1 Successive Differentiation and Mean Value Theorem

Unit 1

Successive Differentiation and Mean Value Theorem

1.1 Definition and Symbol

1.4 Statements of Leibnitz’s Theorem without proof

1.6 Rolle’s Mean Value Theorem

1.7 Lagrange’sMean Value Theorem

1.8 Cauchy’s Mean Value Theorem

Unit - 2 Expansion of Functions and Indeterminate forms

Unit2

Expansion of Functions and Indeterminate forms

2.1 Statement of Maclaurin’s series without proof

2.2 Expansion of Standard functions and examples using Maclaurin’s series

2.3 Expansion of functions by standard series method

2.4 Differentiation and Integration method of substitution

Unit - 3 Matrices

Unit 3

Matrices

3.1 Definition of Symmetric SkewSymmetric and orthogonal

3.2 Matrices

3.3 Rank of Matrix

3.4 Canonical form or normal form of matrix

3.5 System of Simultaneous Linear Equations

3.6 Homogeneous and nonhomogeneous

3.7 Linear dependence and independence of vectors

3.8 Cayley – Hamilton Theorem without proof

3.9 Inverse by Cayley Hamilton Theorem

3.10 Eigen values Eigen vectors and their properties

Unit - 4 Multivariable Differential Calculus

Unit4

Multivariable Differential Calculus

4.1 Partial Multivariable derivatives of first and higher order variable to be treated as constant

4.2 Total derivative

4.3 Partial Multivariable Differentiation of composite function

4.4 Homogeneous functions and Euler’s Theorem without proof

Unit - 5 Applications of Multi variable Differential Calculus

Unit 5

Applications of Multivariable Differential Calculus

5.1 Jacobians Properties of Jacobians Jacobians of composite functions

5.2 Errors and approximations

5.3 Maxima and minima of functions of two variables

5.4 Lagrange’s method of Undetermined multipliers one condition

Unit - 6 Vector Differential Calculus

Unit 6

Vector Differential Calculus

6.1 Velocity vector acceleration vector

6.2 6.2. Tangential and normal component of acceleration

6.3 Vector differential operator gradient Divergence and curl

6.4 Directional Derivatives Angle between surfaces

6.5 Solenoidal and irrotational field

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Other Subjects of Semester-1
Engineering physics
Communication skills
Engineering chemistry
Engineering mechanics
Basic mechanical engineering
Basic electrical & electronics engineering
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