Calculus – Ankita Publication

Calculus by Ankita Publication is a mathematics textbook covering Differential Calculus and Integral Calculus. It is suitable for B.A. and B.Sc. Part-I students of D.D.U. Gorakhpur University and Siddharth University, and is also useful for students pursuing Engineering and Polytechnic courses that include calculus in their syllabus.

The book is authored by Prof. S.K. Srivastava, Prof. H.S. Shukla, Dr. M.P. Tripathi and Dr. Vineet Kumar Yadav. It covers important mathematical concepts, differentiation techniques, curve analysis, integration methods, definite integrals and applications of integral calculus.

Key Features

• Covers both Differential Calculus and Integral Calculus.
• Useful for B.A. and B.Sc. Part-I Mathematics students.
• Also suitable for Engineering and Polytechnic students studying calculus.
• Includes important concepts, formulas and mathematical methods.
• Covers differentiation, curve tracing, multiple integrals and applications of integration.
• Published by Ankita Publication.

Detailed Contents

Part 1: Differential Calculus

Chapter 1: Successive Differentiation

• Definition and notation of derivatives
• Higher-order derivatives
• Standard results and differentiation methods

Chapter 2: Expansion of Functions

• Expansion of functions
• Important mathematical expansion methods

Chapter 3: Tangents and Normals

• Tangents to curves
• Normals to curves
• Related differentiation applications

Chapter 4: Asymptotes

• Asymptotes of curves
• Methods for finding asymptotes

Chapter 5: Curvature

• Curvature of curves
• Related mathematical concepts and formulas

Chapter 6: Partial and Total Differentiation

• Partial differentiation
• Total differentiation
• Applications of differentiation

Chapter 7: Envelopes and Evolutes

• Envelopes of curves
• Evolutes and related concepts

Chapter 8: Singular Points

• Singular points of curves
• Related analytical concepts

Chapter 9: Curve Tracing

• Curve tracing methods
• Analysis and graphical behaviour of curves

Part 2: Integral Calculus

Chapter 1: Integration of Irrational Algebraic Functions

• Integration of irrational algebraic functions
• Methods and related formulas

Chapter 2: Reduction Formulae

• Important reduction formulas
• Applications in integration

Chapter 3: Definite Integrals

• Definite integration
• Properties and evaluation methods

Chapter 4: Beta and Gamma Functions

• Beta function
• Gamma function
• Related integration formulas

Chapter 5: Multiple Integrals

• Multiple integration
• Methods and applications

Chapter 6: Areas of Curves (Quadrature)

• Finding areas under and between curves
• Applications of definite integrals

Chapter 7: Lengths of Curves (Rectification)

• Length of curves
• Methods of rectification

Chapter 8: Volumes and Surface Areas of Solids of Revolution

• Volumes of solids of revolution
• Surface areas of solids of revolution
• Applications of integral calculus

Book Details

• Book Title: Calculus
• Publisher: Ankita Publication
• Language: English
• Subject: Mathematics
• Main Topics: Differential Calculus and Integral Calculus
• University Courses: B.A. / B.Sc. Part-I
• Additional Course Relevance: Engineering and Polytechnic
• Authors: Prof. S.K. Srivastava, Prof. H.S. Shukla, Dr. M.P. Tripathi and Dr. Vineet Kumar Yadav

Who Can Use This Book?

This book can be useful for B.A. and B.Sc. students of D.D.U. Gorakhpur University and Siddharth University, as well as Engineering and Polytechnic students whose courses cover differential and integral calculus. Students should check their current course syllabus to confirm that the topics match their academic requirements.