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!
Precalculus
1.1 Algebra 1.2 Trigonometric functions 1.3 Functions 1.4 Graphing linear functions 1.5 Exercises
Limits
2.1 An Introduction to Limits 2.2 Finite Limits 2.3 Infinite Limits 2.4 Continuity 2.5 Formal Definition of the Limit 2.6 Proofs of Some Basic Limit Rules 2.7 Exercises
Differentiation
Basics of Differentiation
3.1 Differentiation Defined 3.2 Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule 3.5 Higher Order Derivatives: an introduction to second order derivatives 3.6 Implicit Differentiation 3.7 Derivatives of Exponential and Logarithm Functions 3.8 Some Important Theorems 3.9 Exercises
Applications of Derivatives
3.10 L'Hôpital's Rule 3.11 Extrema and Points of Inflection 3.12 Newton's Method 3.13 Related Rates 3.14 Optimization 3.15 Euler's Method 3.16 Exercises
Integration
Basics of Integration
4.1 Definite integral 4.2 Fundamental Theorem of Calculus 4.3 Indefinite integral 4.4 Improper Integrals
Integration Techniques
4.5 Infinite Sums 4.6 Derivative Rules and the Substitution Rule 4.7 Integration by Parts 4.8 Trigonometric Substitutions 4.9 Trigonometric Integrals 4.10 Rational Functions by Partial Fraction Decomposition 4.11 Tangent Half Angle Substitution 4.12 Reduction Formula 4.13 Irrational Functions 4.14 Numerical Approximations 4.15 Exercises
Applications of Integration
4.16 Area 4.17 Volume 4.18 Volume of solids of revolution 4.19 Arc length
Parametric and Polar Equations
Parametric Equations
- Introduction to Parametric Equations
- Differentiation and Parametric Equations
- Integration and Parametric Equations
- Exercises
Polar Equations
Sequences and Series
Sequences
Series
- Definition of a Series
- Series
- Limit Test for Convergence
- Comparison Test for Convergence
- Integral Test for Convergence
Series and calculus
Exercises
Multivariable and Differential Calculus
- Vectors
- Lines and Planes in Space
- Multivariable Calculus
- Derivatives of multivariate functions
- The chain rule and Clairaut's theorem
- Inverse function theorem, implicit function theorem
- Vector calculus
- Vector calculus identities
- Inverting vector calculus operators
- Points, paths, surfaces, and volumes
- Helmholtz Decomposition Theorem
- Discrete analog to Vector calculus
- Exercises
Differential Equations
Extensions
Advanced Integration Techniques
Further Analysis
Formal Theory of Calculus
References
- 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.