University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus - Free PDF Download
University of Mumbai Syllabus 2024-25 Semester 1 (FE First Year): The University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for the examination year 2024-25 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 2024-25 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 2024-25 is below.
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 2024-25 With Marking Scheme
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Syllabus
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
- Successive Differentiation
- nth Derivative of Standard Functions
- Leibnitz’S Theorem (Without Proof) and Problems
- 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)
