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20th January 2020, 03:43 PM
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| Re: FE sem 2 Syllabus Mumbai University
The syllabus for First Year Engineering (Semester I & II) of Bachelor of Engineering Program offered by University of Mumbai is as follows: FEC101 Applied Mathematics‐I Module‐1: Complex Numbers Pre‐requisite: Review of Complex Numbers‐Algebra of Complex Number, Different representations of a Complex number and other definitions, D’Moivre’s Theorem. 1.1.Powers and Roots of Exponential and Trigonometric Functions. 1.2. Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ 1.3.Circular functions of complex number and Hyperbolic functions. Inverse Circular and Inverse Hyperbolic functions. Separation of real and imaginary parts of all types of Functions. Module‐2:Logarithm of Complex Numbers , Successive Differentiation 2.1. Logarithmic functions, Separation of real and Imaginary parts of Logarithmic Functions. 2.2. Successive differentiation: nth derivative of standard functions. Leibnitz’s Theorem (without proof) and problems Module‐3:Matrices Pre‐requisite: Inverse of a matrix, addition, multiplication and transpose of a matrix 3.1. 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 in normal form, system of homogeneous and non –homogeneous equations, their consistency and solutions. Linear dependent and independent vectors. Application of inverse of a matrix to coding theory. Module‐4: Partial Differentiation 4.1. Partial Differentiation: Partial derivatives of first and higher order. Total differentials, differentiation of composite and implicit functions. 4.2. Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof).Deductions from Euler’s Theorem Syllabus First Year Engineering of Bachelor of Engineering Program University of Mumbai     |