Applied Mathematics 1 BE Civil Engineering Semester 1 (FE First Year) University of Mumbai Syllabus 2023-24

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University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus - Free PDF Download

University of Mumbai Syllabus 2023-24 Semester 1 (FE First Year): The University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for the examination year 2023-24 has been released by the , University of Mumbai. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2023-24 University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new University of Mumbai syllabus to prepare for their annual exam properly.

The detailed University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for 2023-24 is below.

CBCGS [2016 - current]
CBGS [2012 - 2015]
Old [2000 - 2011]

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Revised Syllabus

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 and their Unit wise marks distribution

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Course Structure 2023-24 With Marking Scheme

#Unit/TopicWeightage
C  Complex Numbers Old 
101  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 
102  Separation of Real and Imaginary Parts of All Types of Functions 
103  Circular Functions of Complex Number and Hyperbolic Functions.Inverse Circular and Inverse Hyperbolic Functions. Logarithmic Functions. 
104  Powers and Roots of Exponential and Trigonometric Functions 
CC  Matrices and Numerical Methods Old 
201  Solution of System Of Linear Algebraic Equations 
202  Types of Matrices and Rank of a Matrix 
CCC  Differential Calculus Old 
301  Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof) 
302  Partial Differentiation 
303  Successive Differentiation 
CD  Application of Partial Differentiation, Expansion of Functions , Indeterminate Forms and Curve Fitting Old 
401  Fitting of Curves by Least Square Method for Linear, Parabolic, And Exponential 
402  Maxima and Minima of a Function of Two Independent Variables 
403  Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series 
D  Complex Numbers 
DC  Logarithm of Complex Numbers , Successive Differentiation 
601  Successive Differentiation 
602  Logarithm of Complex Numbers 
DCC  Matrices 
DCCC  Partial Differentiation 
CM  Applications of Partial Differentiation , Expansion of Functions 
M  Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations 
 Total -
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Syllabus

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 100: Complex Numbers Old

101 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
102 Separation of Real and Imaginary Parts of All Types of Functions
103 Circular Functions of Complex Number and Hyperbolic Functions.Inverse Circular and Inverse Hyperbolic Functions. Logarithmic Functions.
104 Powers and Roots of Exponential and Trigonometric Functions

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 200: Matrices and Numerical Methods Old

201 Solution of System Of Linear Algebraic Equations
202 Types of Matrices and Rank of a Matrix

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 300: Differential Calculus Old

301 Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof)
302 Partial Differentiation
303 Successive Differentiation

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 400: Application of Partial Differentiation, Expansion of Functions , Indeterminate Forms and Curve Fitting Old

401 Fitting of Curves by Least Square Method for Linear, Parabolic, And Exponential
402 Maxima and Minima of a Function of Two Independent Variables
403 Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 500: Complex Numbers

  • Review of Complex Numbers‐Algebra of Complex Number  
  • Different Representations of a Complex Number and Other Definitions  
  • D’Moivre’S Theorem  
  • Powers and Roots of Exponential Function  
  • Powers and Roots of Trigonometric Functions  
  • Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ  
  • Expansion of sinnθ, cosnθ in powers of sinθ, cosθ  
  • .Circular Functions of Complex Number  
  • Hyperbolic functions of complex number  
  • Inverse Circular Functions  
  • Inverse Hyperbolic Functions  
  • Separation of Real and Imaginary Parts of All Types of Functions  

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 600: Logarithm of Complex Numbers , Successive Differentiation

601 Successive Differentiation
  • Successive Differentiation  
  • nth Derivative of Standard Functions  
  • Leibnitz’S Theorem (Without Proof) and Problems  
602 Logarithm of Complex Numbers
  • Logarithmic Functions  
  • Separation of Real and Imaginary Parts of Logarithmic Functions  

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 700: Matrices

  • Inverse of a Matrix  
  • Addition of a Matrix  
  • Multiplication of a Matrix  
  • Transpose of a Matrix  
  • Types of Matrices  
    • Row Matrix
    • Column Matrix
    • Zero or Null matrix
    • Square Matrix
    • Diagonal Matrix
    • Scalar Matrix
    • Unit or Identity Matrix
    • Upper Triangular Matrix
    • Lower Triangular Matrix
    • Triangular Matrix
    • Symmetric Matrix
    • Skew-Symmetric Matrix
    • Determinant of a Matrix
    • Singular Matrix
    • Transpose of a Matrix
  • Rank of a Matrix Using Echelon Forms  
  • Reduction to Normal Form  
  • PAQ in normal form  
  • System of Homogeneous and Non – Homogeneous Equations  
  • consistency and solutions of homogeneous and non – homogeneous equations  
  • Linear Dependent and Independent Vectors  
  • Application of Inverse of a Matrix to Coding Theory  

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 800: Partial Differentiation

  • Partial Derivatives of First and Higher Order  
  • Total Differentials  
  • Differentiation of Composite Functions  
  • Differentiation of Implicit Functions  
  • Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof)  
  • Deductions from Euler’S Theorem  

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 900: Applications of Partial Differentiation , Expansion of Functions

  • Maxima and Minima of a Function of Two Independent Variables  
  • Jacobian  
  • Taylor’S Theorem (Statement Only)  
  • Taylor’S Series Method  
  • Maclaurin’s series (Statement only)  
  • Expansion of 𝑒^𝑥 , sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), 𝑠𝑖𝑛−1 (𝑥),𝑐𝑜𝑠−1 (𝑥),𝑡𝑎𝑛−1 (𝑥)  
  • Binomial Series  

University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for Chapter 1000: Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations

  • Indeterminate Forms  
  • L‐ Hospital Rule  
  • Problems Involving Series  
  • Solution of Transcendental Equations  
  • Solution by Newton Raphson Method  
  • Regula – Falsi Equation  
  • Solution of System of Linear Algebraic Equations by Gauss Elimination Method  
  • Gauss Jacobi Iteration Method  
  • Gauss Seidal Iteration Method  

    (Scilab programming for above methods is to be taught during lecture hours)

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