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A Basic Course in Mathematics for Polytechnic Vol.1 by NABAJYOTI DUTTA & PRANJAL TALUKDAR

**Contents
GROUP – A: ALGEBRA
Chapter-1 1 – **
Complex Numbers **

Definition

Geometric representation

Modulus, amplitude

Polar form of a complex number

Rationalisation, addition, multiplication, conjugate

Square root of a complex number

Cube root of unity

De Moivre’s Theorem (statement only)

Simple problems

**Chapter-2 **-**
Partial Fractions **

Definition

Proper and improper fractions

To resolve proper fraction into partial fraction with non- repeated linear factors

Repeated linear factors and irreducible non-repeated quadratic factors

Simple problems

**Chapter-3 **-**
Permutation and Combination **

Factorial notation and basic principle of counting

Deduction of formulae for permutation and combination

**Chapter-4 **-**
Binomial Theorem **

Binomial Theorem for positive integral index (statement only)

General term, middle term, specific terms

Co-efficient of , Terms independent of

Problems with engineering applications

**Chapter-5 **-**
Logarithm **

Introduction

Definition

Laws of logarithm

Problems related to Laws of Logarithm and application

**Chapter-6 **-**
Series **

Arithmetic Progression Series, arithmetic mean, sum to n-terms

Geometric Progression Series, geometric mean, sum to n-terms

Sum to infinity of a G.P.Series

Exponential Series

Logarithmic Series

**Chapter-7 **-**
Matrix **

Definition

Types of matrix – row matrix, column matrix, square matrix, diagonal matrix, unit matrix, symmetric matrix, skew-symmetric matrix

Algebra of matrices: equality, addition, subtraction, scalar multiplication, multiplication

Simple application problems

**Chapter-8 **-**
Determinants **

Definition and expansion of determinants of third order, minors , co-factors

Properties of determinants and problems using properties

Solution of simultaneous equations using Crammer’s rule

**GROUP – B: TRIGONOMETRY**

Chapter-9 **-**

Trigonometric Ratios

Introduction

Compound Angles and Associated Angles

Transformation of sum or differences into products and products into sum or differences

Multiple and sub-multiple Angles

Solution of Trigonometric Equations (angle between 0 and 2π)

Trigonometric Identities

**Chapter-10 **-**
Inverse Trigonometric Functions **

Introduction

Definition and basic concepts

Properties of Inverse Trigonometric Functions.

**Chapter-11 **-**
Properties of Triangles**

Introduction

Relation between the sides and angles of a triangle

Sine – Cosine formulae

**GROUP – C: MENSURATION**

Chapter-12 **-**

Area of Curvilinear Figures

Area of Curvilinear Figures using Simpson’ rule

**Chapter-13 **-**
Volume and Surface Area**

Volume and Surface area of prism

Pyramid, Zone and sector of a sphere, Frustum of pyramid and cone.

**GROUP – D
CO-ORDINATE GEOMETRY OF TWO-DIMENSIONS**

Chapter-14 **-**

Cartesian and Polar Coordinate System

Introduction

Cartesian coordinate system

Polar coordinate system

Relation between Cartesian and Polar coordinate system

Distance between two points in Cartesian coordinate system

Distance between Two points in Polar coordinate system

**Chapter-15 **-**
Straight Line**

Introduction

Slope or gradient

Different forms of straight lines, Point-slope from, Point-point form, Intercept form, Perpendicular form

Angle between two straight lines

Equation of parallel and perpendicular straight lines

Distance of a point from a straight line, Distance between two straight lines

Weight | 0.45 kg |
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