A Basic Course in Mathematics for Polytechnic Vol.1

Description

“Master the foundational mathematics needed for polytechnic studies with ‘A Basic Course in Mathematics for Polytechnic Vol.1’ by Nabajyoti Dutta and Pranjal Talukdar, an essential publication from Mahaveer Publications, Dibrugarh. This comprehensive volume provides a strong foundation of mathematical knowledge, making it an invaluable resource for students preparing for successful careers in engineering and technology.”

Contents
GROUP – A: ALGEBRA
Chapter-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