University of Mumbai, Maharashtra (Mumbai University), Computer Engineering Semester 1, Engineering Mathematics-1 Syllabus

Unit - 1 Complex Numbers

Unit 1

Complex Numbers

1.2 Algebra of Complex numbers

1.3 Different forms of a complex numbers

1.4 DE MOIVRE’S Theorem

1.7 Roots of complex numbers

Unit - 2 Hyperbolic function and Logarithm of Complex Numbers

Unit 2

Hyperbolic function and Logarithm of complex numbers

2.1 Exponential Function The exponential function for the real variable x

2.3Hyperbolic Function if z is any real and complex numbers

2.4Inverse Circular functions

2.5Inverse Hyperbolic functions

2.6 Separation of Real and Imaginary Parts of Complex numbers

2.7 Logarithmic Function of a Complex Variable

2.8 Separation of real and imaginary parts of a logarithmic function

Unit - 3 Partial Differentiation

Unit 3

Partial Differentiation

3.1 Function of Several Variables

3.2 Limit Continuity and their Properties

3.3 Partial Derivative First order and Higher order

3.4 Composite function

3.5 Euler’s theorem

3.6 Deduction From Euler’s theorem

Unit - 4 Applications of Partial Differentiation and Successive differentiation

Unit – 4

Application of Partial Differentiation and Successive Differentiation

4.1 Maxima and Minima of a function of two independent variables

4.2Lagrange’s method of Undetermined Multipliers

4.4 Leibnitz’s rule

Unit - 5 Matrices

Unit5

Matrices

5.1 Matrices

5.2 Types of Matrices and their properties

5.3 Rank of Matrix using Echelon form

5.4 Normal form of a matrix

5.5 PAQ form of a matrix A

5.6 System of homogenous equation their consistency and solution

5.7 System of non homogenous equation their consistency and solution

Unit - 6 Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function

Unit6

Numerical solution of Transcendental Equations System of Linear equations and Expansion of Functions.

6.1 Solution of Transcendental equations

6.2 Solution of System of Linear Algebraic Equations

6.3.Expansion of functions