This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II.
The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Elementary Calculus for free.
- Title
- Elementary Calculus
- Author(s)
- Michael Corral
- Published
- 2021-01-02
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 346
- Language
- English
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Preface Contents 1 The Derivative 1.1 Introduction 1.2 The Derivative: Limit Approach 1.3 The Derivative: Infinitesimal Approach 1.4 Derivatives of Sums, Products and Quotients 1.5 The Chain Rule 1.6 Higher Order Derivatives 2 Derivatives of Common Functions 2.1 Inverse Functions 2.2 Trigonometric Functions and Their Inverses 2.3 The Exponential and Natural Logarithm Functions 2.4 General Exponential and Logarithmic Functions 3 Topics in Differential Calculus 3.1 Tangent Lines 3.2 Limits: Formal Definition 3.3 Continuity 3.4 Implicit Differentiation 3.5 Related Rates 3.6 Differentials 4 Applications of Derivatives 4.1 Optimization 4.2 Curve Sketching 4.3 Numerical Approximation of Roots of Functions 4.4 The Mean Value Theorem 5 The Integral 5.1 The Indefinite Integral 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Integration by Substitution 5.5 Improper Integrals 6 Methods of Integration 6.1 Integration by Parts 6.2 Trigonometric Integrals 6.3 Trigonometric Substitutions 6.4 Partial Fractions 6.5 Miscellaneous Integration Methods 6.6 Numerical Integration Methods 7 Analytic Geometry and Plane Curves 7.1 Ellipses 7.2 Parabolas 7.3 Hyperbolas 7.4 Translations and Rotations 7.5 Hyperbolic Functions 7.6 Parametric Equations 7.7 Polar Coordinates 8 Applications of Integrals 8.1 Area Between Curves 8.2 Average Value of a Function 8.3 Arc Length and Curvature 8.4 Surfaces and Solids of Revolution 8.5 Applications in Physics and Statistics 9 Infinite Sequences and Series 9.1 Sequences and Series 9.2 Tests for Convergence 9.3 Alternating Series 9.4 Power Series 9.5 Taylor's Series Appendix A Answers and Hints to Selected Exercises GNU Free Documentation License History Index
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