University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus - Free PDF Download
University of Mumbai Syllabus 2025-26 Semester 1 (FE First Year): The University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for the examination year 2025-26 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 2025-26 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 2025-26 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 Course Structure 2025-26 With Marking Scheme
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Syllabus
1: Complex Numbers Old [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
1.01 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 [Revision]
1.02 Separation of Real and Imaginary Parts of All Types of Functions [Revision]
1.03 Circular Functions of Complex Number and Hyperbolic Functions.Inverse Circular and Inverse Hyperbolic Functions. Logarithmic Functions. [Revision]
1.04 Powers and Roots of Exponential and Trigonometric Functions [Revision]
2: Matrices and Numerical Methods Old [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
2.01 Solution of System Of Linear Algebraic Equations [Revision]
2.02 Types of Matrices and Rank of a Matrix [Revision]
3: Differential Calculus Old [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
3.01 Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof) [Revision]
3.02 Partial Differentiation [Revision]
3.03 Successive Differentiation [Revision]
4: Application of Partial Differentiation, Expansion of Functions , Indeterminate Forms and Curve Fitting Old [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
4.01 Fitting of Curves by Least Square Method for Linear, Parabolic, And Exponential [Revision]
4.02 Maxima and Minima of a Function of Two Independent Variables [Revision]
4.03 Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series [Revision]
5: Complex Numbers [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
- 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
6: Logarithm of Complex Numbers , Successive Differentiation [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
6.01 Successive Differentiation [Revision]
- Successive Differentiation
- nth Derivative of Standard Functions
- Leibnitz’S Theorem (Without Proof) and Problems
6.02 Logarithm of Complex Numbers [Revision]
- Logarithmic Functions
- Separation of Real and Imaginary Parts of Logarithmic Functions
7: Matrices [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
- 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
8: Partial Differentiation [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
- 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
9: Applications of Partial Differentiation , Expansion of Functions [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
- 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
10: Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations [Revision]
University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus
- 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)
