About Us

Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc

More about us

Keep Connect with Us

  • =

Login to Your Account


JOIN OUR 150,890 + FANS
JOIN OUR 763 + FANS

Calculus Free Books


Calculus is a branch of mathematics that studies motion and change. Originally called "infinitesimal calculus" or "the calculus of infinitesimals", it has two main branches: "differential calculus" and "integral calculus". Differential calculus deals with instantaneous rates of change and the slopes of curves, while integral calculus focuses on areas under or between curves. British mathematician "Isaac Newton" and German mathematician "Gottfried Wilhelm Leibniz" independently developed the foundations of calculus in the late 17th century. Calculus is an essential part of many other fields, including physics, chemistry, biology, economics, finance, and actuarial science. Before the development of calculus, mathematics was largely "motionless", it could only describe static objects. But the universe is constantly changing. From the stars in space to the cells in our bodies, nothing is ever truly at rest. Calculus is the branch of mathematics that allows us to study how things move, grow, expand, shrink, and travel.


Did you know that "calculus" originally meant “stone”? The word comes from Latin, because in ancient times, people used stones to perform calculations. Calculus is a major branch of mathematics that studies rates of change and areas under curves. Although Isaac Newton and Gottfried Wilhelm Leibniz are credited with developing modern calculus in the 17th century, its roots go much further back. Early forms of calculus appeared across different civilizations: - "Egypt (c. 1820 BC):" Papyrus records show calculations of volumes and areas. - "Greece:" "Archimedes" used the method of exhaustion to find areas under curves. - "China:" "Liu Hui" and "Zu Chongzhi" explored areas and volumes of circles and spheres. - "Middle East:" "Alhazen (965–1040 CE)" studied volumes of curved surfaces. - "India:" The "Kerala school (14th century)" developed infinite series and early forms of the Taylor series. Later, European mathematicians like "Barrow, Fermat, Pascal, and Descartes" expanded Newton’s and Leibniz’s ideas, while "Bolzano, Cauchy, Riemann," and "Dedekind" brought greater precision to limits, integrals, and real numbers. If you want to explore calculus further, there are many excellent free books available online. Here’s a list of some great "free calculus books" to help you start learning!

'
Free Calculus Books
A First Course in Infinitesimal Calculus- Daniel Murray
This textbook introduces beginners to "calculus", covering "derivatives", "integrals", and their applications in geometry and problem-solving. The book explains fundamental concepts clearly, with step-by-step examples, helping students build a strong foundation in mathematics while understanding practical uses of calculus.
Active Calculus Multivariable - Steve Schlicker
This is a student-focused "multivariable calculus" textbook that uses "active learning" to teach vectors, partial derivatives, and multiple integrals. Through guided activities and real examples, it builds strong "conceptual understanding" and helps students confidently apply calculus to real-world problems.
Advanced Calculus - Edwin Bidwell Wilson
This text explains the deeper and more rigorous side of calculus. It covers topics like "vector analysis", limits, differentiation, and integration, helping students connect theory with real applications in mathematics, "physics", and "engineering".
Advanced Calculus - Lynn Loomis, Shlomo Sternberg
This text is a clear, rigorous guide to "multivariable calculus", "analysis", and "proofs". It teaches higher-level mathematical concepts like vector calculus and differentiable manifolds, helping students build strong problem-solving skills and transition from standard calculus to advanced, abstract mathematics.
An Elementary Course of Infinitesimal Calculus - PDF
This text is a clear and easy guide to "calculus". It explains "differentiation" and "integration" with simple examples, helping students understand how these methods are applied in geometry, physics, and real-world problem solving, making complex concepts more approachable.
An Elementary Treatise on the Calculus Alexander Gibson
This book is a classic introduction to "calculus", aimed at beginners. It covers key topics like "differentiation", "integration", and their applications in a clear, structured way. Though dated, it offers valuable insights into early mathematical teaching and helps build a strong foundation in calculus.
An Elementary Treatise On the Calculus for Engineering
This text is a clear guide to "calculus". It explains "differentiation" and "integration" with simple examples, showing how these tools are used to solve real engineering and physics problems, helping students understand and apply mathematics practically.
An Introduction to Calculus Based on Graphical - Gibson
This textbook is a clear guide to learning "calculus". It explains "differentiation" and "integration" using graphs and visual examples, helping beginners understand slopes, rates of change, and areas under curves in an intuitive and easy-to-follow way.
APEX Calculus - Gregory Hartman
This "Free Textbook" is a clear and student-friendly textbook covering limits, derivatives, and integrals. It explains concepts step by step with examples and exercises. It is ideal for beginners, offering strong understanding of "Calculus Concepts" and practical "Problem Solving" skills.
Applications of the Calculus to Mechanics - E. Hedrick
This book teaches how "calculus" is used in "mechanics" to solve real-world problems. The book provides clear methods, step-by-step examples, and practical "applications", helping students, engineers, and anyone interested in applying mathematical principles to physical systems understand and analyze motion and forces effectively.
Applied Calculus: Introductory Textbook - Bisacre PDF
This text teaches "calculus" in a practical way for "physics" and "engineering" students. It explains limits, derivatives, and integrals using real-world examples from thermodynamics, electricity, and chemistry. The book is accessible, student-friendly, and connects math directly to applied science problems.
Business Calculus with Excel - Mike May
This is a practical textbook for "business students". It teaches "calculus" using "Excel", helping learners understand functions, derivatives, and optimization through real-world examples like cost, revenue, and profit. The book focuses on applied learning and practical spreadsheet skills.
Calculus - Gilbert Strang | FreeMathematicsBooks
This text is a clear guide to "derivatives", "integration", and "functions". It covers single- and multivariable calculus with examples and exercises, helping students understand core concepts, solve real-world problems, and build a strong foundation in mathematics for further study in science, engineering, and applied fields.
Calculus by Herman March, Henry Wolff - PDF
This textbook explores "calculus" using "algebra"-based methods. This book presents a clear "theory" of differentiation, integration, and series, focusing on understanding concepts rather than just computations. Ideal for students and mathematicians seeking a deeper grasp of mathematical foundations.
Calculus I, II, III - Marsden & Weinstein
This is a complete textbook series covering **Single-Variable Calculus", "Multivariable Calculus", and "Vector Calculus". With clear explanations, examples, and exercises, it helps students build strong understanding and practical problem-solving skills in calculus.
Calculus by WikiBooks - PDF link
This textbook offers a beginner-friendly guide to "calculus", covering key topics like "differentiation", integration, and limits. With clear examples and step-by-step explanations, it helps readers build a strong foundation in "mathematical concepts", making it ideal for those new to calculus and its practical applications.
Calculus-Based Physics I - Jeffrey Schnick
This is an easy-to-understand textbook for learning "mechanics", "energy", and "momentum" using calculus. It explains motion, forces, waves, and thermodynamics with clear examples and exercises, helping students apply mathematical concepts to solve real-world physics problems in science and engineering courses.
Calculus-Based Physics II - Jeffrey Schnick
This is an easy-to-understand textbook for learning "electricity", "magnetism", and "optics" using calculus. It explains electric fields, circuits, magnetic forces, and light with clear examples and exercises, helping students apply math to real-world physics problems in science and engineering courses.
Calculus in Context - James Callahan, David Cox
This is a practical textbook teaching "Calculus Concepts", "Applied Calculus", and "Problem Solving". It uses real-world examples, clear explanations, and exercises to help students understand derivatives, integrals, and differential equations in meaningful, everyday contexts.
Calculus: Early Transcendentals - David Guichard
This text teaches "calculus" concepts clearly, covering "derivatives", "integrals", and early transcendental functions like exponential and trigonometric functions. With step-by-step examples, exercises, and practical applications, it helps students build strong problem-solving skills and understand how to apply mathematics in real-world situations.
Calculus Of Finite Differences - George Boole
This textbook explains "calculus" for discrete systems, focusing on "finite differences" in sequences and series. The book provides clear methods, examples, and practical "applications", helping students and mathematicians understand and solve problems in discrete mathematics and analyze numerical patterns effectively.
The Calculus for Engineers and Physicists -Robert Smith
This text introduces key "calculus" concepts, including "differentiation", integration, and multivariable calculus. The book emphasizes practical examples and real-world applications, providing students with essential mathematical tools for solving problems in "engineering" and "physics".
Calculus and Graphs by Leonard Passano - PDF
This is an introductory "calculus" book that teaches "derivatives", "integration", and "limits" using clear explanations and visual "graphs". Designed for science and engineering students, it emphasizes practical understanding, helping beginners connect algebraic and geometric concepts while solving real-world problems effectively.
Calculus for the Life Sciences 1 - Cornette & Ackerman
This text teaches "calculus" using real biological examples. It covers "derivatives", limits, and basic differential equations, helping students understand patterns in populations, enzyme reactions, and ecosystems through "mathematical modeling". Ideal for life science learners building strong foundational skills.
Calculus for the Life Sciences 2 - Cornette & Ackerman
This book teaches "calculus" through real biological examples. It focuses on "mathematical modeling" of populations, ecology, and genetics, helping students build strong "life sciences" problem-solving skills while understanding how derivatives, integrals, and equations describe changes in living systems.
Calculus and Linear Algebra Vol. 1 - Wilfred Kaplan
This is a beginner-friendly textbook covering "Single-Variable Calculus", "Linear Algebra", and "Vector Spaces". Step-by-step explanations, examples, and exercises make it ideal for students building strong foundational math skills.
Calculus and Linear Algebra Vol. 2 - Wilfred Kaplan
This is a clear, advanced textbook covering "Multivariable Calculus", "Linear Algebra", and "Matrix Theory". With step-by-step explanations, examples, and exercises, it helps students connect concepts and build strong problem-solving skills in higher-level mathematics.
Calculus Made Easy - Silvanus P Thompson
This textbook simplifies key "calculus" concepts such as "differentiation", "integration", and "limits". Through clear explanations and practical examples, it makes these complex topics approachable for beginners. The book aims to provide an intuitive understanding of calculus, free from overwhelming technical details.
Calculus For The Practical Man by J. E. Thompson -PDF
This book teaches "calculus" in a clear, easy-to-understand way. Focusing on "practical" methods, it shows how derivatives, differentials, and rates of change work. With real-world "applications", the book helps students, engineers, and self-learners apply calculus to solve everyday problems confidently.
Calculus & Probability - Bruno Belevan
This is an easy-to-use textbook for "commerce" and "social science" students. It teaches "calculus" and probability with real-world examples, covering optimization, integration, and decision-making tools, helping students understand and apply math concepts to practical business and social problems.
Calculus & Probability for Actuarial Students - A Henry
This textbook is a concise guide combining "calculus", "finite differences", and "probability" tailored for actuarial learners. It introduces derivatives, integrals, discrete approximations, and basic probability with practical examples. Ideal for building a strong mathematical foundation before advanced actuarial studies.
Calculus: Theory and Applications - Kenneth Kuttler
This book teaches "calculus" with clear explanations and practical examples. It covers limits, "derivatives", "integrals", and multivariable topics, combining rigorous theory with real-world applications. This book helps students understand concepts, solve problems, and connect mathematical ideas to practical situations.
Community Calculus - David Guichard, Neal Koblitz
This is an open-access textbook covering "Single-Variable Calculus", "Multivariable Calculus", and "Problem Solving". It uses clear explanations, examples, and exercises to help students understand calculus concepts and apply them to real-world situations.
Difference Equations Differential Equations Slaughter
This textbook introduces "calculus" by connecting "difference equations" with "differential equations". It provides a clear transition from discrete to continuous mathematics, focusing on problem-solving techniques and practical applications. The book helps students understand key concepts through hands-on learning and real-world examples.
Differential and Integral Calculus - De Morgan Augustus
This text is a clear guide to "differential calculus" and "integral calculus". With step-by-step examples, it helps students understand derivatives, integrals, and limits while building strong skills in "mathematical analysis" and applying calculus concepts to real-world problems in science and engineering.
Elementary Calculus by Frederick Woods - PDF
This text teaches "calculus" in a clear, easy-to-understand way. It covers the "fundamentals" like derivatives, differentials, and integrals, with plenty of exercises. Real-world "applications" in physics, mechanics, and geometry help learners see how calculus solves practical problems.
Elementary Calculus by Michael Corral - Free PDF
This textbook introduces foundational "calculus" concepts such as "derivatives", integration, and limits. The book focuses on building a strong "conceptual understanding", with clear explanations and practical applications. It's perfect for beginners seeking to grasp key ideas and solve real-world problems in calculus.
Elementary Calculus by Percey Smith - PDF
This is a clear and beginner-friendly "calculus" textbook focusing on "differentiation", "integration", and "limits". Designed for science and engineering students, it uses practical examples and step-by-step explanations to make core concepts easy to understand, helping learners build a strong foundation in applied mathematics.
Elementary Textbook on the Calculus - Virgil Snyder
This text book offers a clear introduction to "calculus", covering key concepts like "limits", derivatives, and integrals. The book focuses on building a solid foundation for "mathematical understanding", making it ideal for students to grasp both the theory and practical applications of calculus.
Elements of Infinitesimal Calculus - George Chandler
This book introduces "calculus" using intuitive infinitesimals, making complex concepts like "differentiation", "integration", and "limits" easier for beginners. Filled with examples and practical applications, it focuses on understanding rather than formal rigor, ideal for students seeking a clear, hands-on approach to foundational calculus principles.
Essentials of Calculus by Edgar Townsend - PDF
This textbook introduces "calculus" in a clear, practical way, focusing on "differentiation", "integration", and "limits". Filled with examples and real-world applications, it helps beginners and applied-science students understand fundamental concepts without heavy theory, making calculus accessible, intuitive, and useful for solving everyday mathematical problems.
Exercises and Problems in Calculus - John Erdman
This is a practice-based book that helps students learn calculus through problem solving. It covers limits, functions, and derivatives with guided exercises. The book builds strong "understanding", "problem-solving", and "learning" skills through practice.
Formal Logic or, The Calculus of Inference by De Morgan
This text introduces "logic" in a clear, structured way. It teaches the principles of "inference", showing how to distinguish necessary from probable conclusions. The book explains the "calculus" of reasoning, providing beginners and scholars with tools to analyze arguments and apply logical thinking effectively.
Foundations of Infinitesimal Calculus - Keisler Jerome
This text explains "infinitesimals", "derivatives", and "integrals" using hyperreal numbers. It provides a clear, rigorous alternative to traditional calculus, making advanced concepts intuitive while grounding them in modern mathematics, helping students and instructors understand and apply nonstandard analysis effectively.
Foundations of Infinitesimal Calculus by K.D. Stroyan
This text explains calculus using "infinitesimals" instead of traditional limits. It builds ideas like derivatives, integrals, and continuity through "nonstandard analysis", offering a rigorous yet intuitive view of "calculus foundations" for advanced students and curious learners.
Fractional Calculus (Theory & App.) - Keith Oldham
This text covers the "theory" and "applications" of fractional derivatives and integrals. It extends traditional calculus to arbitrary orders, offering a detailed exploration of "fractional calculus". The book combines theoretical depth with practical insights, making it valuable for various scientific fields.
Higher Math for Students of Chemistry & Physics- Mellor
This text teaches essential "mathematics" for science students, covering "differential calculus", "integral calculus", analytical geometry, series, and applied methods. The book emphasizes practical problem-solving, linking mathematical theory directly to real-world applications in chemistry and physics.
Treatise on Infinitesimal Calculus by Price Bartholome
This text is a clear guide to "differential calculus" and "integral calculus". With worked examples and explanations, it helps students understand derivatives, integrals, and limits while building strong skills in "mathematical analysis" and applying calculus concepts to real-world problems.
Informal Calculus: Bio & Eco Sciences - Tyler Seacrest
This is an easy-to-understand textbook for "biology" and "environmental science" students. It teaches "calculus" using real-world examples like population models, streamflow, and ecological data, helping learners apply math concepts to understand change, growth, and patterns in natural systems.
Notes on Calculus II Integral Calculus - Miguel A Lerma
This is a clear guide to "integral calculus". It explains "integration techniques", the Fundamental Theorem, and real applications like area and volume. The notes also introduce "series and sequences", helping students build strong problem-solving skills in a simple, step-by-step way.
Introduction to Calculus I Heinbockel - Download Link
This text is a clear, beginner-friendly "calculus textbook". It covers limits, derivatives, and basic integration with step-by-step explanations. The book helps students build a strong foundation in "calculus basics" and is often used as an "open-access resource".
Introduction to Calculus II - J. H. Heinbockel
This text builds on basic calculus and focuses on integration, series, and applications. The book explains ideas step by step with clear examples. It helps students improve "understanding", "problem-solving", and "mathematical skills" in higher-level calculus.
Intuitive Infinitesimal Calculus - Viktor Blasjo
This is a clear and student-friendly textbook that explains "Calculus Concepts" using "Infinitesimals" instead of complex formal proofs. It covers derivatives, integrals, and series with simple explanations, helping learners build strong understanding and improve "Problem Solving" skills.
Mathematics for Engineering Students by Keller & Knox
This text is a practical guide that teaches essential "mathematical concepts" like algebra, calculus, and differential equations, tailored for engineering applications. The book emphasizes "problem-solving" and real-world "engineering challenges", helping students build strong mathematical foundations for technical success.
Mechanics of Engineering by Julius Weisbach - PDF
This is a classic engineering book that explains "mechanics", "statics", and "hydraulics" in a practical way. It introduces calculus for solving engineering problems and combines theory with real-world applications, making it a foundational guide for students and engineers learning classical mechanical principles.
Multivariable Calculus by Don Shimamoto
This is an easy-to-follow textbook for learning "multivariable calculus". It covers "partial derivatives", multiple integrals, and "vector calculus" with clear explanations and practical exercises. Students can understand and apply key theorems like Green’s, Stokes’, and the divergence theorem in real-world math and science problems.
CPL-3 Multivariable Calculus - Joel Feldman
This is a clear and student-friendly textbook covering "multivariable calculus", "vector calculus", and "partial derivatives". It explains concepts step-by-step, includes practical examples, and emphasizes problem-solving, helping students understand advanced calculus and apply it confidently in mathematics, physics, and engineering.
A Problem Text in Advanced Calculus by John Erdman PDF
This textbook offers a series of challenging "advanced calculus" problems, focusing on "real analysis", sequences, and multivariable calculus. The book is designed to enhance problem-solving abilities and deepen theoretical understanding, making it a valuable resource for students looking to master advanced calculus concepts.
Problems in the Calculus, with Formulas and Suggestions
This book helps learners master "calculus" through clear examples, practical "formulas", and guided "problem-solving". This classic book builds understanding step by step, making complex mathematical ideas easier for students, teachers, and self-learners to apply with confidence.
Teaching and Learning of Calculus - David Bressoud
This text examines effective "teaching" strategies and student learning in "calculus", addressing challenges in concept comprehension while offering insights to improve instruction and "student engagement". It bridges theory with practice, aiming to enhance overall understanding and the quality of "calculus education".
The Calculus by Ellery Williams Davis - PDF
This textbook is a clear guide to learning "calculus". It explains "differentiation" and "integration" with simple examples and exercises, helping students understand how these tools are used in physics, engineering, and other fields. The book builds a strong foundation in "mathematics".
The calculus for beginners by John William Mercer - PDF
This text introduces "calculus" in a clear, easy-to-follow way for "beginners". It explains differentiation, integration, and essential principles with practical "applications", helping learners understand concepts and build a strong foundation for further study in mathematics, science, and engineering.
The Calculus Of Observations by E.T Whittaker - PDF
This text focuses on precise "observations" and reliable data analysis. It uses "calculus" to address "error" in measurements, offering practical strategies for scientists, mathematicians, and students to enhance the accuracy and understanding of experimental results.
Understanding Basic Calculus - S. K. Chung
This text explains basic calculus concepts in a clear and simple way. The book focuses on limits, differentiation, and integration with easy examples. It helps beginners develop strong "conceptual understanding", effective "learning", and confident "problem-solving" skills.
Vector Analysis - Josiah Gibbs, Edwin Wilson
This is a classic math book that explains "vector analysis" in a clear and practical way. It introduces key ideas of "vector calculus" and shows their use in physics and "engineering mathematics", shaping modern scientific learning.
Vector Calculus by Michael Corral
This is an "open-access textbook" for advanced calculus students. It explains "vector algebra", partial derivatives, multiple integrals, and line and surface integrals in a clear, step-by-step way. The book is designed for science and engineering students learning multivariable calculus.

.