# Applied Mathematics 1 Semester 1 (FE First Year) BE Biotechnology University of Mumbai Topics and Syllabus

University of Mumbai Syllabus For Semester 1 (FE First Year) Applied Mathematics 1: Knowing the Syllabus is very important for the students of Semester 1 (FE First Year). Shaalaa has also provided a list of topics that every student needs to understand.

The University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Semester 1 (FE First Year) Applied Mathematics 1 Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Semester 1 (FE First Year) Applied Mathematics 1 in addition to this.

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 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 Matrices and Numerical Methods Old

201 Solution of System Of Linear Algebraic Equations

Solution of system of linear algebraic equations, by

• Gauss Elimination Method (Review)
• Guass Jordan Method
• Crouts Method (LU)
• Gauss Seidal Method    and
• Jacobi iteration (Scilab programming for above methods is to be taught  during lecture hours)
202 Types of Matrices and Rank of a Matrix
• 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 forms, system of homogeneous and non –homogeneous equations, their consistency and solutions. Linear dependent and independent vectors.

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

301 Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof)
• Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof).
• Deductions from Euler’S Theorem
302 Partial Differentiation
• Partial derivatives of first and higher order, total differentials, differentiation of composite and implicit functions.
303 Successive Differentiation
• nth derivative of standard functions.
• Leibnitz’s Thoerem (without proof) and problems.

### University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for 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
• Regression Analysis (to be introduced for estimation only) (Scilab programming related to fitting of curves is to be taught during lecture hours)
402 Maxima and Minima of a Function of Two Independent Variables
• Lagrange’s method of undetermined multipliers with one constraint.
• Jacobian, Jacobian of implicit function.
• Partial derivative of implicit function using jacobian.
403 Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series
• Taylor’s Theorem (Statement only) and Taylor’s series, Maclaurin’s series (Statement only).
• Expansion of ex , sinx, cosx, tanx, sinhx, coshx, tanhx, log(1+x), sin‐1 x, cos1 x, Binomial series.
• Indeterminate forms, L‐ Hospital Rule, problems involving series also.

### University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 Syllabus for 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 sin nθ, cos nθ 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 a complex number and Hyperbolic functions. Inverse Circular and
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 Logarithm of Complex Numbers , Successive Differentiation

601 Successive Differentiation
602 Logarithm of Complex Numbers