A Basic Course in Mathematics for Polytechnic Vol.1

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