Calculus
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This wikibook aims to be a high quality calculus textbook through which users can master the discipline. Standard topics such as limits, differentiation and integration are covered, as well as several others. Please contribute wherever you feel the need. You can simply help by rating individual sections of the book that you feel were inappropriately rated!
1.8 Hyperbolic logarithm and angles
2.5 Formal Definition of the Limit
2.6 Proofs of Some Basic Limit Rules
Basics of Differentiation
[edit | edit source]3.2 Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.5 Higher Order Derivatives: an introduction to second order derivatives
3.7 Derivatives of Exponential and Logarithm Functions
3.8 Derivatives of Hyperbolic Functions
Applications of Derivatives
[edit | edit source]3.12 Extrema and Points of Inflection
3.17 Approximating Values of Functions
Basics of Integration
[edit | edit source]4.2 Fundamental Theorem of Calculus
Integration Techniques
[edit | edit source]4.6 Derivative Rules and the Substitution Rule
4.8 Trigonometric Substitutions
4.10 Rational Functions by Partial Fraction Decomposition
4.11 Tangent Half Angle Substitution
Applications of Integration
[edit | edit source]4.18 Volume of Solids of Revolution
Parametric Equations
[edit | edit source]5.1 Introduction to Parametric Equations
5.2 Differentiation and Parametric Equations
5.3 Integration and Parametric Equations
Polar Equations
[edit | edit source]5.5 Introduction to Polar Equations
5.6 Differentiation and Polar Equations
5.7 Integration and Polar Equations
Sequences
[edit | edit source]Series and Tests
[edit | edit source]Convergence
[edit | edit source]6.10 Absolute and Conditional Convergence
Series and Calculus
[edit | edit source]Exercises
[edit | edit source]
Introduction to Multivariable Calculus
[edit | edit source]7.2 Curves and Surfaces in Space
7.4 Introduction to multivariable calculus
Differentiation
[edit | edit source]7.7 The chain rule and Clairaut's theorem
7.9 Directional derivatives and the gradient vector
7.10 Derivatives of Multivariate Functions
7.11 Inverse Function Theorem, Implicit Function Theorem (optional)
Integration
[edit | edit source]- Old: Double Integrals
Vector calculus
[edit | edit source]7.15 Vector Calculus Identities
7.16 Inverting Vector Calculus Operators
7.17 Points, Paths, Surfaces, and Volumes
7.18 Helmholtz Decomposition Theorem
7.19 Discrete Analog to Vector Calculus
8.1 Ordinary Differential Equations
8.2 Partial Differential Equations
Advanced Integration Techniques
[edit | edit source]Further Analysis
[edit | edit source]9.2 Systems of Ordinary Differential Equations
Formal Theory of Calculus
[edit | edit source]References
[edit | edit source]- Lester R. Ford, Sr. & Jr. (1963) Calculus, McGraw-Hill via HathiTrust
- w:Mellen W. Haskell (1895) On the introduction of the notion of hyperbolic functions Bulletin of the American Mathematical Society 1(6):155–9.