Discrete mathematics | Calculus | Finite differences | Numerical differential equations | Linear operators in calculus | Non-Newtonian calculus | Numerical analysis | Mathematical analysis | Applied mathematics | Algebraic topology
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change. Discrete calculus has two entry points, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of piece-wise linear curves. Integral calculus concerns accumulation of quantities and the areas under piece-wise constant curves. These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with their discrete form. The development is dependent on a parameter, the increment of the independent variable. If we so choose, we can make the increment smaller and smaller and find the continuous counterparts of these concepts as limits. Informally, the limit of discrete calculus as is infinitesimal calculus. Even though it serves as a discrete underpinning of calculus, the main value of discrete calculus is in applications. (Wikipedia).
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Introduction to Discrete and Continuous Functions
This video defines and provides examples of discrete and continuous functions.
From playlist Introduction to Functions: Function Basics
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Maths for Programmers: Introduction (What Is Discrete Mathematics?)
Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s
From playlist Maths for Programmers
Intro to Discrete Math - Welcome to the Course!
Welcome to Discrete Math. This is the start of a playlist which covers a typical one semester class on discrete math. I chat a little about why I love discrete math, what you should expect, and how an online discrete math course is structured. FULL PLAYLIST: https://www.youtube.com/watch
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
11_3_5 When is a multivariable function continuous
Determining where is multivariable function is continuous.
From playlist Advanced Calculus / Multivariable Calculus
Calculus - Continuous functions
This video will describe how calculus defines a continuous function using limits. Some examples are used to find where a function is continuous, and where it is not continuous. Remember to check that the value at c and the limit as x approaches c exist, and agree. For more videos please
From playlist Calculus
[Discrete Mathematics] Surjective Functions Examples
In these video we look at onto functions and do a counting problem. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIz
From playlist Discrete Math 1
The formal definition of a sequence.
We have an intuitive picture of sequences (infinite ordered lists). But there is a formal definition of sequences based out of the idea of a specific function between sets, specifically from the positive integers to the real numbers. ►Full DISCRETE MATH Course Playlist: https://www.youtu
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
New Algorithm for Data Fitting
For the latest information, please visit: http://www.wolfram.com Speakers: Mustafa Atici & Ferhan Atici Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and more.
From playlist Wolfram Technology Conference 2016
Counting with Triple Intersections // Example & Formula
Suppose three sets overlap such that they have a triple intersection of all three sets. How many elements are there total? In this video we will explore a counting argument when we have a Venn Diagram which is a union of three sets, and will see how to use the data about how many there are
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t
From playlist Book Reviews
Math for Game Developers: Fundamentals of Calculus
This video is a gentle introduction to the fundamentals of Calculus for Physics and Game Programmers. We'll start by looking at the basic concepts of physics simulation, deltatime, and proceed to discuss continuous functions and discrete functions. You'll learn about differentiation and
From playlist Summer of Math Exposition Youtube Videos
In this video I will show you a very good book on discrete math. This book has lots of the math that you need for computer science. It also has full solutions to every single problem. The book is titled Concrete Mathematics and it was written by Graham, Knuth, Patashnik. Here is the book:
From playlist Book Reviews
Q&A with Calculus Developers: Live with the R&D team
Presentation starts at 1:00 In this stream, Devendra and Daniel answer Calculus & Algebra give a glimpse of recent and upcoming features in symbolic calculus, many of which have been motivated by frequent requests from users and then answer related questions from the community." Follow us
From playlist Live with the R&D Team
Discrete Math Book for Beginners
This is a really good discrete math book for beginners. I think this is easier to read than some of the other discrete math books out there. If you are taking discrete math I highly recommend this one. The book is called Discrete Mathematical Structures and it was written by Kolman, Busby
From playlist Book Reviews
You Might Be Making This Mistake
Often times we can solve really amazing problems by switching the integral symbol and the discrete sum symbol - but are we even allowed to do this? Let's find out when we can switch the integral and sum! (switch integral and series) Some of the links below are affiliate links. As an Amaz
From playlist Series, Series, Series
Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Discrete Mathematics for Computer Science
In this video I will show you an older book on Discrete Mathematics. This is a course that Computer Science majors take in college in the United States. Discrete Math is considered a very tough course as many people struggle with it because it is very different from Calculus. I hope this h
From playlist Book Reviews
The End of Discrete Math - Congrats! Some final thoughts...
You've made it to the end of Discrete Math! Congratulations! Mastering math is no easy task, and I'm proud of the work you've done so far. If you missed anything, the full playlist for Discrete math is here: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS You can
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)