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

## 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

## 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
• 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)