Rashtrasant Tukadoji Maharaj Nagpur University, Maharashtra, Computer Engineering Semester 1, Applied Mathematics – I Syllabus

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Unit - 1 Differential Calculus

UNIT 1

Differential Calculus

1.1 Successive Differentiation

1.2 Taylor’s Maclaurin’s series for one variable

1.3 Indeterminate forms

1.4 Curvature and Radius of curvature

1.5 Circle of Curvature

Unit - 2 Partial Differentiation

UNIT 2

Partial Differentiation

2.1 Functions of several variables

2.2 First and Higher order derivatives

2.3 Euler’s theorem

2.4 Chain rule and total differential coefficient

2.5 Jaccobians

2.6 Taylor’s Maclaurin’s series for two variables

2.7 Maxima Minima of functions of two variables

2.8Langrage’s method of undetermined multipliers

Unit - 3 Matrices

UNIT 3

Matrices

3.1 Matrix

3.2 Inverse of Matrix by adjoint method

3.3 Inverse by partition method

3.4 Solution of system of linear equations

3.5 Rank of Matrix

3.6 Consistency of linear system of equations

Unit - 4 First Order Differential Equations

UNIT 4

First Order Differential Equations

4.1 First orderfirst degree differential equations Linear Reducible to linear Exact differential equations excluding the case of I. F.

4.2 First order higher degree differential equations

4.3 Application of First order first degree differential equations to simple electrical circuits

Unit - 5 Higher Order Differential Equations

UNIT 5

Higher Order Differential Equations

5.1 Higher order differential equations with constant coeficients

5.2 The method of variation of parameters

5.3 Cauchy’s and Legendre’s homogeneous differential equations

5.4 Simultaneous linear differential equations

5.5 Differential equations of the type

5.6 Applications of differential equations to oscillations of a spring oscillatory electrical circuits deflection of beams.

5.7 Applications of differential equation of deflection of beams.

Unit - 6 Complex Number

UNIT 6

Complex Numbers

6.1 Cartesian Polar forms of Complex Numbers

6.2 Geometrical representation of fundamental operations on complex numbers

6.3 De Moivre’s theorem

6.4 Hyperbolic functions and their inverse

6.5 Logarithm of complex number

6.6 Separation of real and imaginary parts

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Other Subjects of Semester-1
Engineering physics
Engineering chemistry
Engineering graphics - i
Basic electrical engineering
Basics of civil engineering
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