1598584080

Modern calculus**, **which can be defined as **“**the mathematical study of continuous change,” was developed independently by two of the great thinkers of the 17th and 18th centuries, namely, Isaac Newton and Gottfried Wilhelm Leibniz.

In this article, my focus will be on the work of Leibniz, and I will show, based mainly on the analysis in Dunham and Mena, how he derived the well-known formula for the integration by parts.

Figure 1: A portrait and a statue (without the wig) of Leibniz.

For an article about Isaac Newton’s early mathematical achievements, see the link below.

A Beautiful Proof of a Well-Known Mathematical Result

Gottfried Wilhelm Leibniz was the quintessential polymath. He made fundamental contributions to a broad range of topics, including philosophy, mathematics, linguistics, theology, engineering, jurisprudence, law, computer science, and geology. Leibniz once remarked that he often needed to use a substantial part of his week to document the thoughts of just a single morning (for an outstanding biography of Leibniz, see Antognazza).

Below, on the left, is a picture of his working space in his last residence in Hannover. On the right, the folding chair that he took with him when he traveled.

Figure 2: On the left, a picture of Leibniz’s workroom at his last residence in Hanover (source). On the right, the folding chair that he took with him when he traveled (source).

The titles of the three most famous articles on the Calculus that Leibniz published in the first scientific journal of German-speaking Europe, the *Acta* *Eruditorum*were:

*Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus*(1684)*De geometria recondite et analysi indivisibilium atque infinitorum*(1686)*Supplementum geometriae dimensoriae, seu generalissima omnium Tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditions*(1693)

In English, the titles are, respectively:

- “A new method for maxima and minima, and for tangents, that is not hindered by fractional or irrational quantities, and a singular kind of calculus for the above mentioned”
- “On a hidden geometry and analysis of indivisibles and infinite”
- “A Supplement to the Geometry of Measurements, or the Most General of all Quadratures to be Effected by a Motion: and likewise the various constructions of a curve from a given condition of the tangent.”

The title pages are shown in Fig. 3 below.

Figure 3: The three most famous articles on the Calculus that Leibniz published in the scientific journal Acta Eruditorum (source)

#math #mathematics #science #data science

1640918523

This video is designed to introduce calculus concepts for all math students and make the topic easy to understand.

Calculus is a branch of Mathematics that deals with the study of

limits, functions, derivatives , integrals and infinite series. The subject comes under the most important branches of applied Mathematics, and it serves as the basis for all the advanced mathematics calculations and engineering applications.

Calculus is used in a multitude of fields that you wouldn't ordinarily think would make use of its concepts. Among them are physics, engineering, economics, statistics, and medicine. Calculus is also used in such disparate areas as space travel, as well as determining how medications interact with the body, and even how to build safer structures. 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.

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1633432020

Calculus II is the second course involving calculus, after Introduction to Calculus. Because of this, you are expected to know derivatives inside and out, and also know basic integrals. In this course, we will cover about following calculus_2 topics in a very comprehensive way.

⭐ Table of Contents ⭐

⌨️ (0:05) Integration by parts

⌨️ (23:17) Trigonometric Integrals

⌨️ (0:54:30) Trigonometric substitution

⌨️ (1:20:07) Partial fractions

⌨️ (1:50:56) Other strategies for integration

⌨️ (2:06:42) Improper integrals

⌨️ (2:28:16) Double integrals

⌨️ (2:45:47) Antiderivatives

⌨️ (3:02:54) Derivative review

⌨️ (3:17:52) Approximating Areas

⌨️ (3:48:31) The definite integral

⌨️ (4:12:43) The fundamental theorem of calculus

⌨️ (4:41:26) Integration formulas and the net change theorem

⌨️ (4:59:56) Substitution

⌨️ (5:26:15) Integrals involving exponential and logarithmic function

⌨️ (5:41:58) Integral involving inverse trigonometric function

⌨️ (5:53:10) Area between curve

⌨️ (6:25:15) Determining volumes by slicing

⌨️ (6:55:34) Volumes of revolution cylindrical shells

⌨️ (7:26:23) Arc length of curve and surface area

⌨️ (7:57:31) Physical application

⌨️ (8:19:52) Moments and center of mass

⌨️ (8:54:17) Integrals, exponential function and logarithms

⌨️ (9:17:16) Exponential growth and decay

1598584080

Modern calculus**, **which can be defined as **“**the mathematical study of continuous change,” was developed independently by two of the great thinkers of the 17th and 18th centuries, namely, Isaac Newton and Gottfried Wilhelm Leibniz.

In this article, my focus will be on the work of Leibniz, and I will show, based mainly on the analysis in Dunham and Mena, how he derived the well-known formula for the integration by parts.

Figure 1: A portrait and a statue (without the wig) of Leibniz.

For an article about Isaac Newton’s early mathematical achievements, see the link below.

A Beautiful Proof of a Well-Known Mathematical Result

Gottfried Wilhelm Leibniz was the quintessential polymath. He made fundamental contributions to a broad range of topics, including philosophy, mathematics, linguistics, theology, engineering, jurisprudence, law, computer science, and geology. Leibniz once remarked that he often needed to use a substantial part of his week to document the thoughts of just a single morning (for an outstanding biography of Leibniz, see Antognazza).

Below, on the left, is a picture of his working space in his last residence in Hannover. On the right, the folding chair that he took with him when he traveled.

Figure 2: On the left, a picture of Leibniz’s workroom at his last residence in Hanover (source). On the right, the folding chair that he took with him when he traveled (source).

The titles of the three most famous articles on the Calculus that Leibniz published in the first scientific journal of German-speaking Europe, the *Acta* *Eruditorum*were:

*Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus*(1684)*De geometria recondite et analysi indivisibilium atque infinitorum*(1686)*Supplementum geometriae dimensoriae, seu generalissima omnium Tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditions*(1693)

In English, the titles are, respectively:

- “A new method for maxima and minima, and for tangents, that is not hindered by fractional or irrational quantities, and a singular kind of calculus for the above mentioned”
- “On a hidden geometry and analysis of indivisibles and infinite”
- “A Supplement to the Geometry of Measurements, or the Most General of all Quadratures to be Effected by a Motion: and likewise the various constructions of a curve from a given condition of the tangent.”

The title pages are shown in Fig. 3 below.

Figure 3: The three most famous articles on the Calculus that Leibniz published in the scientific journal Acta Eruditorum (source)

#math #mathematics #science #data science

1586441700

In this second series of mathematics for machine learning, Calculus has been presented in a very comprehensive way. Calculus is very crucial to understand and learn about Machine Learning. In this course, you will find everything you need to about calculus for machine learning.

**Topics**

- The Limit of a Function (0:00)
- Basic Differentiation Rules (12:27)
- The Chain Rule (27:03)
- Implicit Differentiation and Logarithms (39:55)
- Related Rates ( 45:10)
- L’Hopital’s Rule (1:00:34)
- Concavity and Inflection Points (1:15:00)
- Antiderivatives and Indefinite Integrals (1:29:00)
- The Definite Integral and Riemann Sums (1:41:16)
- The Fundamental Theorem of Calculus (01:59:50)
- The Substitution Method (2:14:09)
- Calculating Areas (2:28:06)
- Integration By Parts (2:45:50)
- Improper Integrals Bounded Intervals (03:01:04)
- Trigonometric Substitutions (03:19:11)
- Integration by Partial Fractions (03:35:33)

#machine-learning #calculus #developer #data-science

1603040400

*A frightening course made easy, fun, and remembered throughout life.*

We all being scared of calculus courses at the university. The professor would teach the subject and we couldn’t understand what was really happening. Even more, we wouldn’t be really sure whether it’ll be useful in real life except to pass all the exams. Here, we’ll help you with how you can rock calculus easily.

** Calculus can simply be defined as the change of mathematics**. Or a generalized form of mathematics important for most mathematical topics known for today.

The reason why calculus is perceived as difficult is how professors, teachers, and instructors teaching methods. They generally treat calculus something like mysterious, not having daily life applications and making it as complex as they could. Moreover, they treat the course like there’s nothing important about except for passing their courses.

#calculus #mathematics #coding #mathematics-education #machine-learning