- published: 22 Aug 2012
- views: 839024
Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot.
Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and process calculus.
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Advanced Placement Calculus (also known as AP Calculus, AP Calc AB / AP Calc BC, or AP Calc) is used to indicate one of two distinct Advanced Placement courses and examinations offered by College Board in calculus: AP Calculus AB and AP Calculus BC.
AP Calculus AB is an Advanced Placement calculus course taken by high school students. The course is traditionally taken after precalculus and is the first calculus course offered at most schools except for the regular calculus class. The Pre-Advanced Placement pathway for math will help prepare students for further Advanced Placement classes and exams.
According to the College Board:
The AP Program includes specifications for two calculus courses and the exam for each course. The two courses and the two corresponding exams are designated as Calculus AB and Calculus BC. Calculus AB can be offered as an AP course by any school that can organize a curriculum for students with advanced mathematical ability.
Calculus 1 Lecture 1.1: An Introduction to Limits
I want you to feel that you could have invented calculus for yourself, and in this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus. Full playlist: http://3b1b.co/calculus Support for these videos comes primarily from Patreon: https://patreon.com/3blue1brown Special thanks to the following supporters: http://3b1b.co/eoc1-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this p...
What is calculus? In this video, we give you a quick overview of calculus and introduce the limit, derivative and integral. We begin with the question “Who invented Calculus?” Next, we talk about the two main tools you’ll study: derivatives and integrals. To understand both of these you’ll first learn about limits. After you learn how to compute the derivative and integral for basic functions and apply them to real-world problems, you’ll move up to higher dimensions and study things like “partial derivatives” and “multiple integrals.” ************** If you would like to help us make new videos, you can support us through Patreon at https://www.patreon.com/socratica We also welcome Bitcoin donations! Our Bitcoin address is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you!! ******* W...
This video will give you a brief introduction to calculus. It does this by explaining that calculus is the mathematics of change. A couple of examples are presented, and then limits, derivatives, and integrals are introduced. For more videos please visit http://www.mysecretmathtutor.com
This video shows how calculus is both interesting and useful. Its history, practical uses, place in mathematics and wide use are all covered. If you are wondering why you might want to learn calculus, start here!
why study differentiation and integration
http://bit.ly/qYnN40 Want to see the ENTIRE Calculus in 20 Minutes for FREE? Click on this link to see all 20 minutes in the full multimedia environment.
Easy to understand explanation of integrals and derivatives using 3D animations.
This calculus review video tutorial provides an introduction / basic overview of the fundamental principles taught in an IB or AP calculus AB course. This video is also useful for students taking their first semester of college level calculus. It cover topics such as graphing parent functions with transformations, limits, continuity, derivatives, and integration. This video contains plenty of examples and practice problems. Calculus Video Playlist: https://www.youtube.com/watch?v=rCxi-O79sVo&t=25s&index=1&list=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV Access to Premium Videos: https://www.patreon.com/MathScienceTutor Here is a list of topics: 1. Graphing Parent Functions With Transformations 2. Linear Functions, Quadratic & Cubic Functions 3. Rational Functions, Fractions, Square Roots, ...
If you are wondering what Calculus is, or what you're teacher was ranting on about, this is a quick look at the basic idea behind it all. The next part is here: http://youtu.be/wD4FLB0Sp54 Don't worry, I'm still going to make Quantum mechanics videos too :)
Check out the new merch! http://casuallyexplained.com/ Although often attributed to Isaac Newton in the mid 17th century, it was in fact Gottfried Leibniz who first invented MyMathLab. #WolframAlphaLife
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Put my anger on the shelf
Awaking from this dreadful tragedy
I return to myself
Beginning to dwell in this elegy