Blueprint for FE Mumbai University

Can you provide me the syllabus of First Year Engineering (Semester I & II) of Bachelor of Engineering offered by University of Mumbai?

[shikha]

The syllabus of First Year Engineering (Semester I & II) of Bachelor of Engineering offered by University of Mumbai is as follows:

FEC101 Applied Mathematics‐I

Module‐1: Complex Numbers:‐
1.1: Powers and Roots of Exponential and Trigonometric Functions.
1.2: Circular functions of complex number and Hyperbolic functions. Inverse Circular and Inverse Hyperbolic functions. Logarithmic functions.
1.3: Separation of real and Imaginary parts of all types of Functions.
1.4: Expansion of sinnθ, cosnθ in terms of sins and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ

Module‐2: Matrices and Numerical Methods:‐
2.1: Types of Matrices(symmetric, skew‐ symmetric, Hermitian, Skew
Hermitian,Unitary, Orthogonal Matrices and properties of Matrices).Rank of a
Matrix using Echelon forms, reduction to normal form, PAQ forms, system of homogeneous and non –homogeneous equations, their consistency and solutions. Linear dependent and independent vectors.
2.2: Solution of system of linear algebraic equations, by (1) Gauss
Elimination Method (Review) (2) Guass Jordan Method (3) Crouts Method (LU)
(4) Gauss Seidal Method and (5) Jacobi iteration (Scilab programming for above methods is to be taught during lecture hours)

Module‐3ifferential Calculus:‐
3.1: Successive differentiation: nth derivative of standard functions.
Leibnitz’s Thoerem (without proof) and problems.
3.2: Partial Differentiation: Partial derivatives of first and higher order, total differentials, differentiation of composite and implicit functions.
3.3: Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof).Deductions from Euler’s Theorem