Dr. Babasaheb Ambedkar Marathwada University, Maharashtra, Computer Engineering Semester 1, Engineering Mathematics-I Syllabus

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Unit - 1 Matrices -I

UNIT1

MATRICES 1

1.1. Rank of a matrix

1.2. Canonical and Normal form of a matrix

1.3. Consistency of the system of linear equations Homogeneous Nonhomogeneous equation

Unit - 2 Matrices - II

UNIT2

Matrices II

2.1. Characteristic equation of matrix

2.2. Eigen values and Eigen vectors

2.3. CayleyHamilton theorem

2.4. Linear dependence and independence of vectors

2.5. Linear and orthogonal Transformations

Unit - 3 Complex Numbers With Applications

UNIT3

Complex Numbers with Application

3.1 Geometrical representation of a complex number

3.2. Standard form of a complex number

3.3. De’Moivre’s Theorem

3.4. Roots of a complex number

3.5. Circular and hyperbolic function

3.6. Relation between circular and hyperbolic functions

3.7. Inverse hyperbolic functions

3.8. Separation into real and imaginary parts of complex functions

3.9. Logarithm of complex numbers

Unit - 4 Successive Differentiation

UNIT4

Successive Differentiation

4.1. nth derivative of standard functions

4.2. Taylor’s Maclaurin’s theorem

4.3. Expansion of functions using standard series and method of differentiation integration

4.4. Indeterminate forms

4.5 Convergence of power series Ratio test

4.6. Comparison test

Unit - 5 Partial Differentiation

UNIT5

Partial differentiation

5.1. Partial derivatives

5.2. Total differentiation

5.3. Euler’s theorem on homogeneous functions

5.4. Change of independent variables

Unit - 6 Applications of partial differentiation

UNIT 6

Jacobian

6.1. Jacobian

6.2. Chain rule

6.3. Maxima and minima of function of two variables

6.4. Lagrange’s method of undetermined multipliers

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Other Subjects of Semester-1
Engineering physics
Engineering graphics
Basic civil engineering
Computer fundamentals i
Basic electrical engineering
Engineering chemistry & environmental science
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