I am pleased to announce the official release of the Math By Rishabh Series – Calculus, a complete, concept-driven collection designed to build true mathematical understanding from first principles to advanced applications.

This series is not a collection of shortcut notes or formula handbooks. It is a systematic learning journey through calculus—structured to develop intuition, logical clarity, and long-term mastery.

Calculus is often taught as a toolbox of techniques. In this series, calculus is treated as a language of change, accumulation, and structure, connecting geometry, analysis, and physical reasoning into one coherent framework.

Why This Series Was Written

Over years of teaching high-school advanced mathematics, Olympiad preparation, and competitive examinations, I observed a recurring issue:

Students could compute, but they did not truly understand.

Formulas were memorized. Procedures were followed. But intuition, structure, and reasoning were missing.

The Math By Rishabh Series – Calculus was written to address this gap.

Each book in the series:

• Builds concepts from first principles
• Explains why formulas work, not just how to use them
• Emphasizes geometry, logic, and structure
• Trains students to think like mathematicians

What the Calculus Series Includes

The series is divided into six focused volumes, each dedicated to one core pillar of calculus.

1. Limits and Continuity

Foundations of Mathematical Change

This volume lays the philosophical and logical groundwork of calculus.

• Meaning of limits as approximation and convergence
• Left-hand, right-hand, and infinite limits
• Algebraic, graphical, and conceptual interpretations
• Continuity as a structural property, not a definition to memorize
• Discontinuities explained geometrically and intuitively

This book ensures that students understand calculus before computing calculus.

2. Differentiation

Rates of Change and Local Behavior

Differentiation is developed as a study of local change, not a mechanical process.

• Derivative as a limit and as a rate
• Tangents, velocity, and physical interpretation
• Standard derivatives derived logically
• Chain rule, implicit differentiation, and parametric forms
• Structure-driven problem solving

Students learn to see derivatives, not just calculate them.

3. Applications of Differentiation

Geometry, Optimization, and Strategy

This volume transforms differentiation into a powerful problem-solving tool.

• Increasing/decreasing behavior and curve sketching
• Maxima–minima from geometric reasoning
• Mean Value Theorems and their significance
• Optimization without blind computation
• Examiner-focused strategies and common traps

The emphasis is on thinking, not memorization.

4. Integration

Accumulation, Area, and Structure

Integration is introduced as the inverse language of change.

• Integral as a limit of sums
• Area, signed area, and accumulation
• Fundamental Theorem of Calculus—conceptually developed
• Definite and indefinite integrals unified
• Technique selection guided by structure

This book establishes integration as a logical extension of differentiation, not a separate topic.

5. Applications of Integration

Geometry, Physics, and Real Quantities

One of the most comprehensive and concept-rich volumes of the series.

• Area under and between curves
• Volumes of solids (disk, washer, shells)
• Centroids and Pappus’s theorems
• Arc length, surface area, curvature
• Work, energy, fluid pressure
• Olympiad- and ISI-level applications

Every formula is motivated, never assumed.

6. Differential Equations

Dynamics, Change, and Mathematical Models

The final volume presents calculus in its most powerful form: modeling change.

• First-order differential equations
• Geometric interpretation via slope fields
• Exact, linear, Bernoulli, and higher-order equations
• Systems of differential equations
• Numerical methods (Euler, Runge–Kutta)
• Real-world modeling: growth, decay, mechanics, circuits

This book connects calculus directly to real phenomena and professional mathematics.

Pedagogical Features Across the Series

Each book includes:

• Worked Examples at every level
• Four-tier graded exercises
• Common errors and examiner traps
• Self-assessment tests
• Strategy-focused problem-solving sections

The series is designed to be both:

• A learning guide
• A long-term reference

Who This Series Is For

• High-achieving students of IB (AA HL / SL) and Cambridge IGCSE, AS & A-Level Mathematics seeking depth beyond syllabus coverage
• Students who want to strengthen mathematical concepts beyond the school curriculum
• Learners who enjoy solving challenging mathematical problems and value reasoning over rote methods
• Aspirants preparing for IIT-JEE, ISI, CMI, STEP, and Olympiads
• Undergraduate students aiming for conceptual clarity and long-term mastery
• Teachers looking for a deep, structured, and rigorous reference

This series is written for serious learners—those who do not just want to pass exams, but want to understand mathematics as a coherent discipline.

Explore More

🔹 Mathematics Elevate Academy – Advanced mathematics learning with depth and structure
🔹 Math By Rishabh – Concept-first books designed for clarity, rigor, and mastery

Visit: Mathematics Elevate Academy and Math By Rishabh

A Philosophy, Not Just Books

The Math By Rishabh Series reflects a simple belief:

Mathematics should be understood from first principles, taught with rigor, and learned with depth.

Calculus is not a hurdle—it is a gateway.
This series is written to help you walk through it with confidence.

– Rishabh Kumar
Founder, Mathematics Elevate Academy
Math By Rishabh Series