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Elementary Calculus 2e

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Elementary Calculus 2e

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.

CalculusMathematics
Author
Michael Corral
Publisher
Schoolcraft College
Source
LibreTexts
License
GNU FDL
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 57 sections
  1. 01: The Derivative
  2. 1.01: Introduction to Derivatives
  3. 1.02: The Derivative- Limit Approach
  4. 1.03: The Derivative- Infinitesimal Approach
  5. 1.04: Derivatives of Sums Products and Quotients
  6. 1.05: The Chain Rule
  7. 1.06: Higher Order Derivatives
  8. 02: Derivatives of Common Functions
  9. 2.01: Inverse Functions
  10. 2.02: Trigonometric Functions and Their Inverses
  11. 2.03: The Exponential and Natural Logarithm Functions
  12. 2.04: General Exponential and Logarithmic Functions
  13. 03: Topics in Differential Calculus
  14. 3.01: Tangent Lines
  15. 3.02: Limits- Formal Definition
  16. 3.03: Continuity
  17. 3.04: Implicit Differentiation
  18. 3.05: Related Rates
  19. 3.06: Differentials
  20. 04: Applications of Derivatives
  21. 4.01: Optimization
  22. 4.02: Curve Sketching
  23. 4.03: Numerical Approximation of Roots of Functions
  24. 4.04: The Mean Value Theorem
  25. 05: The Integral
  26. 5.01: The Indefinite Integral
  27. 5.02: The Definite Integral
  28. 5.03: The Fundamental Theorem of Calculus
  29. 5.04: Integration by Substitution
  30. 5.05: Improper Integrals
  31. 06: Methods of Integration
  32. 6.01: Integration by Parts
  33. 6.02: Trigonometric Integrals
  34. 6.03: Trigonometric Substitutions
  35. 6.04: Partial Fractions
  36. 6.05: Miscellaneous Integration Methods
  37. 6.06: Numerical Integration Methods
  38. 07: Analytic Geometry and Plane Curves
  39. 7.01: Ellipses
  40. 7.02: Parabolas
  41. 7.03: Hyperbolas
  42. 7.04: Translations and Rotations
  43. 7.05: Hyperbolic Functions
  44. 7.06: Parametric Equations
  45. 7.07: Polar Coordinates
  46. 08: Applications of Integrals
  47. 8.01: Area Between Curves
  48. 8.02: Average Value of a Function
  49. 8.03: Arc Length and Curvature
  50. 8.04: Surfaces and Solids of Revolution
  51. 8.05: Applications in Physics and Statistics
  52. 09: Infinite Sequences and Series
  53. 9.01: Sequences and Series
  54. 9.02: Tests for Convergence
  55. 9.03: Alternating Series
  56. 9.04: Power Series
  57. 9.05: Taylor's Series