Conquer Calculus from First Principles — Differential & Integral, Both in One!

Built for BSc First Semester Mathematics students, Ready to Read — Differential Calculus & Integral Calculus is a student-first textbook that transforms one of the most challenging subjects into a clear, step-by-step learning journey. Whether you're building on Class 12 calculus or encountering degree-level rigor for the first time, this book makes every theorem, technique, and application fully accessible.

📐 Topics Covered

Part I — Differential Calculus

• Limits & continuity — definitions, theorems & standard limits
• Differentiability — first principles, rules of differentiation
• Successive differentiation — nth derivatives, Leibnitz theorem
• Partial differentiation — Euler's theorem, homogeneous functions
• Tangents & normals, curvature & asymptotes
• Rolle's theorem, Mean Value theorems — Lagrange & Cauchy
• Taylor's & Maclaurin's series expansions
• Maxima & minima — single & two variable functions

Part II — Integral Calculus

• Indefinite integration — standard forms, substitution & integration by parts
• Integration of rational & irrational functions
• Definite integrals — properties & evaluation techniques
• Reduction formulae — Wallis's formula & applications
• Beta & Gamma functions — definitions, properties & interrelation
• Applications of integration — area, arc length, volume & surface of revolution
• Double & triple integrals — introduction & evaluation

✅ Key Features

• Lucid, step-by-step explanations from basic to advanced level
• Abundant solved examples after every concept for exam clarity
• Chapter-end exercises: MCQs, short answers & university-style long questions
• Important theorems stated clearly with proofs & geometric interpretations
• Aligned with major Indian university syllabi (NEP 2020 compatible)
• Ideal for self-study, classroom use & last-minute semester revision

From limits and derivatives to definite integrals and their applications, Ready to Read: Differential Calculus & Integral Calculus gives BSc Mathematics first-year students the conceptual depth and problem-solving confidence to score high in their semester examinations.