Calculus
- Page ID
- 3227
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Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
- Supplemental Modules (Calculus)
- Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus has two primary branches: differential calculus and integral calculus. Multivariable calculus is the extension of calculus in one variable to functions of several variables. Vector calculus is a branch of mathematics concerned with differentiation and integration of vector fields.
- Calculus (OpenStax)
- The text guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.
- Front Matter
- 1: Functions and Graphs
- 2: Limits
- 3: Derivatives
- 4: Applications of Derivatives
- 5: Integration
- 6: Applications of Integration
- 7: Techniques of Integration
- 8: Introduction to Differential Equations
- 9: Sequences and Series
- 10: Power Series
- 11: Parametric Equations and Polar Coordinates
- 12: Vectors in Space
- 13: Vector-Valued Functions
- 14: Differentiation of Functions of Several Variables
- 15: Multiple Integration
- 16: Vector Calculus
- 17: Second-Order Differential Equations
- 18: Appendices
- Back Matter
- Calculus (Guichard)
- This general calculus book covers a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus.
- Front Matter
- 1: Analytic Geometry
- 2: Instantaneous Rate of Change- The Derivative
- 3: Rules for Finding Derivatives
- 4: Transcendental Functions
- 5: Curve Sketching
- 6: Applications of the Derivative
- 7: Integration
- 8: Techniques of Integration
- 9: Applications of Integration
- 10: Polar Coordinates and Parametric Equations
- 11: Sequences and Series
- 12: Three Dimensions
- 13: Vector Functions
- 14: Partial Differentiation
- 15: Multiple Integration
- 16: Vector Calculus
- 17: Differential Equations
- Back Matter
- Calculus 3e (Apex)
- Front Matter
- 1: Limits
- 2: Derivatives
- 3: The Graphical Behavior of Functions
- 4: Applications of the Derivative
- 5: Integration
- 6: Techniques of Integration
- 7: Applications of Integration
- 8: Sequences and Series
- 9: Curves in the Plane
- 10: Vectors
- 11: Vector-Valued Functions
- 12: Functions of Several Variables
- 13: Multiple Integration
- 14: Appendix
- Back Matter
- Map: Calculus - Early Transcendentals (Stewart)
- Front Matter
- 1: Functions and Models
- 2: Limits and Derivatives
- 3: Differentiation Rules
- 4: Applications of Differentiation
- 5: Integrals
- 6: Applications of Integration
- 7: Techniques of Integration
- 8: Further Applications of Integration
- 9: Differential Equations
- 10: Parametric Equations And Polar Coordinates
- 11: Infinite Sequences And Series
- 12: Vectors and The Geometry of Space
- 13: Vector Functions
- 14: Partial Derivatives
- 15: Multiple Integrals
- 16: Vector Calculus
- 17: Second-Order Differential Equations
- Back Matter
- Map: University Calculus (Hass et al.)
- 1: Functions
- 2: Limits and Continuity
- 3: Differentiation
- 4: Applications of Definite Integrals
- 5: Integration
- 6: Applications of Definite Integrals
- 7: Integrals and Transcendental Functions
- 8: Techniques of Integration
- 9: Infinite Sequence and Series
- 10: Parametric Equations and Polar Coordinates
- 11: Vectors and the Geometry of Space
- 12: Vector-Valued Functions and Motion in Space
- 13: Partial Derivatives
- 14: Multiple Integrals
- 15: Integration in Vector Fields
- 16: First-Order Differential Equations
- 17: Second-Order Differential Equations
- Yet Another Calculus Text - A Short Introduction with Infinitesimals (Sloughter)
- This text is an introduction to calculus based on the hyperreal number system and uses infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, none are provided for the hyperreals. The text is aimed primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most o
- Applied Calculus (Calaway, Hoffman, and Lippman)
- Page notifications On picture_as_pdf Readability Cite this page An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus.
- Informal Calculus with Applications to Biological and Environmental Sciences (Seacrest)
- This book is an approachable introduction to calculus with applications to biology and environmental science. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.
- Book: Active Calculus (Boelkins et al.)
- The style of the Active Calculus text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number.
- Front Matter
- 1: Understanding the Derivative
- 2: Computing Derivatives
- 3: Using Derivatives
- 4: The Definite Integral
- 5: Finding Antiderivatives and Evaluating Integrals
- 6: Using Definite Integrals
- 7: Differential Equations
- 8: Sequences and Series
- 9: Multivariable and Vector Functions
- 10: Derivatives of Multivariable Functions
- 11: Multiple Integrals
- 12: Appendices
- Back Matter
- CLP-1 Differential Calculus (Feldman, Rechnitzer, and Yeager)
- This textbook covers single variable Differential Calculus.
- CLP-2 Integral Calculus (Feldman, Rechnitzer, and Yeager)
- This textbook covers single variable Integral Calculus.
- CLP-3 Multivariable Calculus (Feldman, Rechnitzer, and Yeager)
- This textbook covers multivariable Calculus. There are chapters on vectors and geometry in 2 and 3 dimensions, partial derivatives, and multivariable integrals.
- CLP-4 Vector Calculus (Feldman, Rechnitzer, and Yeager)
- This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem).
- Vector Calculus (Corral)
- The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. The content in this Textmap is complemented by Vector Calculus Modules in the Core and the Vector Calculus (UCD Mat 21D) Libretext.
- The Calculus of Functions of Several Variables (Sloughter)
- This textbook corresponds with a 300-level mathematics course taught at Furman University. Students should have completed four semesters of college level calculus prior to attempting this course.
- Differential Calculus for the Life Sciences (Edelstein-Keshet)
- Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this course, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates.
- Front Matter
- 1: Power functions as building blocks
- 2: Average rates of change, average velocity and the secant line
- 3: Three Faces of the Derivative - Geometric, Analytic, and Computational
- 4: Differentiation rules, simple antiderivatives and applications
- 5: Tangent lines, Linear Approximation, and Newton’s Method
- 6: Sketching the Graph of a Function using Calculus Tools
- 7: Optimization
- 8: Introducing the Chain Rule
- 9: Chain Rule Applied to Related Rates and Implicit Differentiation
- 10: Exponential Functions
- 11: Differential equations for exponential growth and decay
- 12: Solving Differential Equations
- 13: Qualitative Methods for Differential Equations
- 14: Periodic and Trigonometric Functions
- 15: Cycles, Periods, and Rates of Change
- 16: Additional Exercises
- 17: Appendices
- Back Matter
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