A Basic Course in Mathematics for Polytechnic (Vol–I) is a foundation-level mathematics textbook meticulously prepared for First Semester Polytechnic students following the latest syllabus prescribed by technical education boards. Authored by Nabajyoti Dutta, Bulendra Limboo, Bismeeta Buragohain, and Pranjal Talukdar, and published by Mahaveer Publications, this book builds the essential mathematical skills required for all diploma engineering branches.

The book covers the crucial mathematical topics that form the backbone of technical and engineering studies. Concepts are presented in a clear, step-by-step, and student-friendly manner, making it easy for learners with varying levels of mathematical background to understand and apply core principles.

Each chapter includes solved examples, formula summaries, practice exercises, and application-based questions, enabling students to develop accuracy, speed, and confidence required for both academic and competitive examinations.

GROUP–A: ALGEBRA

Chapter 1: Complex Numbers

• Definition & representation

• Geometric interpretation

• Modulus & amplitude

• Polar form & Euler form

• Square root of complex numbers

• Cube root of unity

• De Moivre’s Theorem (statement)

• Simple problems

Chapter 2: Partial Fractions

• Proper & improper fractions

• Linear factors & repeated factors

• Irreducible quadratic factors

• Decomposition techniques

• Simple problems

Chapter 3: Permutation & Combination

• Basic counting principles

• Permutation & combination formulas

• Engineering application-based problems

Chapter 4: Binomial Theorem

• Binomial theorem for positive integer index

• General term, middle term & specific terms

• Coefficient of $x^r$

• Terms independent of $x$

• Application-based problems

Chapter 5: Logarithm

• Definition

• Laws of logarithms

• Problems based on logarithm laws

Chapter 6: Series

• Arithmetic progression (A.P.), arithmetic mean & n-terms

• Geometric progression (G.P.), geometric mean & n-terms

• Sum to infinity (G.P.)

• Exponential series

• Logarithmic series

Chapter 7: Matrix

• Definition and classification of matrices

• Row matrix, column matrix, square matrix

• Symmetric & skew-symmetric matrices

• Algebra of matrices: addition, subtraction, scalar multiplication

• Simple applications

Chapter 8: Determinants

• Determinants of third order

• Properties of determinants

• Solution of simultaneous linear equations (Crammer’s rule)

 GROUP–B: TRIGONOMETRY

Chapter 9: Trigonometric Ratios

• Introduction

• Compound angles

• Transformation of sum/difference into products

• Multiple and sub-multiple angles

• Trigonometric equations (0 to 2π)

• Trigonometric identities

Chapter 10: Inverse Trigonometric Functions

• Definition and concepts

• Properties & related problems

Chapter 11: Properties of Triangles

• Relations among side lengths & angles

• Sine and cosine formulae

• Applications in engineering geometry

 GROUP–C: MENSURATION

Chapter 12: Area of Curvilinear Figures

• Simpson’s 1/3rd rule

• Engineering application problems

Chapter 13: Volume & Surface Area

• Volume & surface area of prisms

• Pyramids, frustums, zones & sectors

• Surface area & volume of spheres and cones

 GROUP–D: COORDINATE GEOMETRY OF TWO DIMENSIONS

Chapter 14: Cartesian & Polar Coordinate System

• Introduction

• Cartesian coordinates

• Polar coordinates

• Conversions between systems

• Distance between two points (Cartesian & Polar)

Chapter 15: Straight Line

• Slope or gradient

• Point-slope, point-point & intercept forms

• Perpendicular form

• Angle between two lines

• Equations of parallel & perpendicular lines

• Distance of a point from a line

• Distance between two parallel lines