Digital Textbook

Fundamentals of Mathematics

Name: Fundamentals of Mathematics
Author: Prof. Mithun Mondal

From sets to differential equations — a complete, chapter-by-chapter course in mathematics for higher secondary and IIT-JEE

Prof. Mithun Mondal Class 11–12 & IIT-JEE Free & Open Access

6Parts

34Chapters

∞Worked Problems

Welcome

One book, built one chapter at a time

This is a living, web-native edition of a complete higher-secondary and competitive-exam mathematics course. Each of the 34 chapters lives on its own page — readable on any device, searchable, and free to share. The journey starts with the language of sets and functions and ends with vectors, three-dimensional geometry, linear programming, and probability.

Every chapter is mapped to the Class 11–12 syllabus and the JEE Main & Advanced curriculum, so the same pages serve board preparation and competitive practice. Pick any chapter below to begin, or follow the six parts in order for a full first course in mathematics.

How to use this book. Each part groups chapters by theme. Click a chapter card to open its dedicated page with concepts, formulae, worked reasoning, and solved problems pitched at JEE level.

Part 1

Algebra & Number Systems

Sets · Functions · Complex Numbers · Series · Counting · Binomial

01Sets, Relations and Functions 02Complex Numbers 03Quadratic Equations and Theory of Equations 04Sequences and Series 05Permutations and Combinations 06Binomial Theorem 07Principle of Mathematical Induction 08Logarithms and Inequalities

Part 2

Matrices & Determinants

Matrix Algebra · Determinants · Systems of Linear Equations

09Matrices 10Determinants

Part 3

Trigonometry

Identities · Equations · Triangles · Inverse Functions · Applications

11Trigonometric Ratios and Identities 12Trigonometric Equations 13Properties and Solutions of Triangles 14Inverse Trigonometric Functions 15Heights and Distances

Part 4

Coordinate Geometry

Straight Lines · Circles · Parabola · Ellipse · Hyperbola

16Straight Lines 17Pair of Straight Lines 18Circles 19Parabola 20Ellipse 21Hyperbola

Part 5

Calculus

Limits · Derivatives · Applications · Integration · Differential Equations

22Functions, Limits and Continuity 23Differentiability and Differentiation 24Applications of Derivatives 25Indefinite Integration 26Definite Integration 27Area Under Curves 28Differential Equations

Part 6

Vectors, 3D Geometry & Probability

Vectors · 3D Geometry · Probability · Statistics · Linear Programming · Reasoning

29Vector Algebra 30Three-Dimensional Geometry 31Probability 32Statistics 33Linear Programming 34Mathematical Reasoning

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Start Here

Begin with Chapter 1 — Sets, Relations and Functions

Every idea in higher mathematics is phrased in the language of sets and functions. The first chapter builds that vocabulary so the rest of the course reads cleanly. Open Chapter 1 →