미적분학

미적분학 입문

• 미적분학 입문

재미있는 문제들

• 미분가능하고, 도함수가 연속이 아닌 함수
• 단진자의 주기와 타원적분
• n차원 구면의 부피(면적)
• n차원 공의 부피
• 3차원 kissing number 와 solid angle
• 포락선(envelope)과 curve stitching
• 삼각치환
• 바이어슈트라스 치환
• 곡선의 매개화
  • 원의 매개화와 삼각함수의 탄생
  • 피타고라스 쌍(Pythagorean triple)
  • \(x^3+y^3=z^3\) 의 매개화
  • \(x^4+y^4=z^4\) 의 매개화

역사

• 수학사 연표

메모

• Cowell, Simon, and Philippe Poulin. “Early Transcendental Analysis.” arXiv:1506.03697 [math], June 10, 2015. http://arxiv.org/abs/1506.03697.
• Karjanto, N. ‘Calculus Teaching and Learning in South Korea’. arXiv:1504.07803 [math], 29 April 2015. http://arxiv.org/abs/1504.07803.
• http://clem.mscd.edu/~talmanl/

라이프니츠의 정리 (Leibniz integral rule), 미분 기호 아래에서의 적분 (integral under differential the sign) [1]

• Bascelli, Tiziana, Emanuele Bottazzi, Frederik Herzberg, Vladimir Kanovei, Karin Katz, Mikhail Katz, Tahl Nowik, David Sherry, and Steven Shnider. 2014. “Fermat, Leibniz, Euler, and the Gang: The True History of the Concepts of Limit and Shadow.” arXiv:1407.0233 [math], July. http://arxiv.org/abs/1407.0233.

관련된 항목들

• q-초기하급수(q-hypergeometric series)와 양자미적분학(q-calculus)

노트

말뭉치

1. And you have a qualitative notion of calculus.
2. So what does calculus add for me?
3. The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes.
4. Are you trying to claim that I will know enough about calculus to model systems and deduce enough to control them?
5. Before calculus was invented, all math was static: It could only help calculate objects that were perfectly still.
6. You'll understand why calculus is useful in so many areas if you know a bit about its history as well as what it is designed to do and measure.
7. Gottfried Leibniz and Isaac Newton, 17th-century mathematicians, both invented calculus independently.
8. There are two types of calculus: Differential calculus determines the rate of change of a quantity, while integral calculus finds the quantity where the rate of change is known.
9. Calculating curves and areas under curves The roots of calculus lie in some of the oldest geometry problems on record.
10. It was the calculus that established this deep connection between geometry and physics—in the process transforming physics and giving a new impetus to the study of geometry.
11. Finding the formula of the derivative function is called differentiation, and the rules for doing so form the basis of differential calculus.
12. Depending on the context, derivatives may be interpreted as slopes of tangent lines, velocities of moving particles, or other quantities, and therein lies the great power of the differential calculus.
13. “It’s not the subject of calculus as formally taught in college,” Droujkova notes.
14. Many people live to a ripe and happy old age without knowing calculus, for example.
15. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine – see Calculus (medicine)).
16. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.
17. The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way.
18. Madhava of Sangamagrama and the Kerala School of Astronomy and Mathematics thereby stated components of calculus.
19. The first subfield is called differential calculus.
20. The second subfield is called integral calculus.
21. Even though these 2 subfields are generally different form each other, these 2 concepts are linked by the fundamental theorem of calculus.
22. Though it is complicated to use well, calculus does have a lot of practical uses - uses that you probably won't comprehend at first.
23. Enroll Info: This is the first semester of the calculus honors sequence.
24. For more than 30 years, calculus has been seen as the pinnacle of high school math—essential for careers in the hard sciences, and an explicit or unspoken prerequisite for top-tier colleges.
25. But now, math and science professionals are beginning to question how helpful current high school calculus courses really are for advanced science fields.
26. He’s been working with K-12 and university systems to develop a statistics pathway as an alternative to classical calculus.
27. Today, some 800,000 students nationwide take calculus in high school, about 15 percent of all high schoolers, and nearly 150,000 take the course before 11th grade.
28. Here are sample exams problems from first year calculus, in tex format, sorted by problem area.
29. of animated and graphical demonstrations of calculus and related topics, from the University of Vienna.
30. Tutorials for the Calculus Phobe : A collection of animated calculus tutorials in Flash format.
31. : A collection of animated calculus tutorials in Flash format.
32. Fundamental Theorems of Calculus The fundamental theorems of calculus are deep results in analysis that express definite integrals of continuous functions in terms of antiderivatives.
33. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus.
34. The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus.
35. There are also several free online calculators that you may find VERY useful in solving those tricky calculus problems, or for checking your answers.
36. During my venture into AI/ML space, I realized how difficult, mathematical ideas (such as calculus and vector algebra) were made in school and college than they really were!
37. This article is an attempt to explain calculus and its applications, in a fundamental way without using the infamous jargons and big dreaded calculus equations.
38. I anticipate that this reading will unfold the beauty, simplicity, and magic of calculus and mathematics, in general.
39. What is calculus and why is it needed?
40. While many people believe that calculus is supposed to be a hard math course, most don't have any idea of what it is about.
41. The good news is that if you remember your algebra and are reasonably good at it then calculus is not nearly as difficult as its reputation supposes.
42. This article attempts to explain just what calculus is about--where it came from and why it is important.
43. First, a little history leading up to the discovery of calculus, or its creation, depending on your philosophy.
44. We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab.
45. We propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows.
46. Calculi of more than 15 mm are termed giant salivary gland calculi and are infrequently reported in the literature.
47. Here, we report a case of unusually large submandibular gland calculus of 5 cm in greatest dimension which caused erosion of the oral cavity.
48. Prerequisite: No formal pre-requisites; an understanding of pre-calculus will be assumed.
49. You get explanations that make differentiation and integration -- the main concepts of calculus -- understandable and interesting.
50. Learn business calculus for the real world This self-teaching course conquers confusion with clarity and ease.
51. Who says business calculus has to be boring?
52. The main ideas which underpin the calculus developed over a very long period of time indeed.
53. In fact, because of this work, Lagrange stated clearly that he considers Fermat to be the inventor of the calculus.
54. Huygens was a major influence on Leibniz and so played a considerable part in producing a more satisfactory approach to the calculus.
55. MATH 1106 is an option for students whose major requires only one semester of calculus.
56. It introduces some fundamental concepts of calculus and provides a brief introduction to differential equations.
57. MATH 1110 is the best choice for students who plan to take more calculus and is recommended for students who aren't sure about their plans but want to keep their options open.
58. It goes in depth on the fundamental concepts of calculus, such as limits, derivatives, and integrals.
59. This book is based on an honors course in advanced calculus that we gave in the 1960's.
60. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.
61. These prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra.
62. Vector space calculus is treated in two chapters, the differential calculus in Chapter 3, and the basic theory of ordinary differential equations in Chapter 6.
63. Calculus is the combined mathematics of differential calculus and integral calculus.
64. As early as 6th grade, kids may take a placement exam that sets them on an academic pathway that’s designed to lead to high school calculus, or exclude them from it.
65. The Math 1530 student is assumed to be versed in the standard pre-calculus topics of functions, graphing, solving equations and the exponential, logarithmic and trigonometric functions.
66. No prior exposure to differential calculus is assumed by the instructors of this class (though many students have had calculus before).
67. This is a pre-calculus review chapter and may be briefly discussed or assigned at the discretion of the instructor.
68. While incoming students should be familiar with the topics in this chapter, some may be ill-prepared for calculus.
69. Beginning in 2009, the MAA, with support from the National Science Foundation, has undertaken a series of studies of college calculus.

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• [{'LEMMA': 'calculus'}]