1683172195

## Harmonic Numbers | Extending the Harmonic Numbers to the Reals

The harmonic numbers are the partial sums of the harmonic series - sums of whole number reciprocals. This video explores how we can extend their domain to the entire real line.

The animations for this video were made with the community edition of Manim (https://www.manim.community). Huge thanks to everyone who worked on the library, as well as the members of the Discord server who answered my many questions.

00:00 - Intro
1:45 - Graphing the Harmonic Numbers
2:47 - A Recursive Formula
4:23 - Using the Recursive Formula
7:33 - The Super Recursive Formula
8:52 - Finding the Interval
11:27 - Example: H(0.5)
11:59 - Deriving the Solution
13:10 - Graphing the Solution

1666005484

## CBSE Syllabus for Class 9 Maths Term 1 & Term 2 2022-2023

The following is the CBSE Syllabus for the Class 9 Maths Term 1 & Term 2 exam. Understanding the CBSE Class 9  Math syllabus will help students to develop an effective learning program. In addition, students will know the important topics that are expected to be asked in the test.

1665657720

## BitCircuits

Boolean circuit tree implementation that uses bit strings to cache evaluation results and bitwise operations to evaluate new circuits based on existing trees.

## API

The API is very simple. Trees consist of Operations (interior nodes), Variables, and Constants (both of which are leaf nodes). Right now all operations are functions of two parameters.

### Variable

The constructor takes a single parameter, an integer in [0,5] (there are six possible variables.

### Constant

The constructor takes a single boolean.

### Operation

The constructor takes a function to apply, this must be a bitwise function that can operate on integers, and two sub-trees, to which the function will be applied.

### evaluate

Evaluates a tree for a given set of variable values. The variable values are specified as a bit string, where variable 5 is the high order bit and variable 0 is the low order bit.

### equal

Determine whether two trees describe the same function.

## Examples

using BitCircuits

and(left, right) = left & right
or(left, right) = left | right

a = Variable(0)
b = Variable(1)

p = Operation(or, a, b) # p = a + b
q = Operation(and, a, b) # q = ab
r = Operation(and, a, p) # r = a(a + b)

evaluate(p, 0b000010) # true
evaluate(p, 0b000000) # false

equal(p, q) # false

Author: um-tech-evolution
Source Code: https://github.com/um-tech-evolution/BitCircuits.jl

1662369116

## Introduction Into Basic Electronics for Beginners

This video provides an introduction into basic electronics for beginners.  It covers topics such as series and parallel circuits, ohm's law, light emitting diodes, resistors, potentiometers, voltage divider circuits and more.

Electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification and rectification, which distinguishes it from classical electrical engineering, which only uses passive effects such as resistance, capacitance and inductance to control electric current flow. - wikipedia

1659341142

## Analytic Continuation and the Zeta Function | Clearly Explained

In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for complex inputs and make sense of what it is the Riemann Hypothesis is claiming.

Chapters:
00:00 zetamath does puzzles
00:23 Recap
02:40 Bombelli and the cubic formula
08:45 Evaluating real functions at complex numbers
12:33 Maclaurin series
21:22 Taylor series
27:19 Analytic continuation
35:57 What goes wrong
48:19 Next time

If you would like to support the production :  https://patreon.com/zetamath

1657080480

## Cách soạn công thức toán học trong Markdown trên Github

### Hỗ trợ toán học hiện có sẵn trong Markdown trên GitHub. Bạn có thể sử dụng các dấu phân cách $và $$nguyên bản trong Markdown trên GitHub để chèn các biểu thức toán học trong cú pháp kiểu TeX và LaTeX. Biểu thức toán học là chìa khóa để chia sẻ thông tin giữa các kỹ sư, nhà khoa học, nhà khoa học dữ liệu và nhà toán học. Chúng tôi vui mừng thông báo rằng các biểu thức toán học hiện có thể được hiển thị nguyên bản trong Markdown trên GitHub. Hỗ trợ hiển thị các biểu thức toán học đã là một tính năng được yêu cầu cao trong hơn 8 năm . Từ hôm nay, bạn có thể sử dụng dấu$$$phân cách nguyên bản trong Markdown trên GitHub để chèn các biểu thức toán học theo cú pháp kiểu TeX và LaTeX. Nội dung này sau đó được hiển thị bằng thư viện MathJax rất phổ biến .

Ví dụ: Markdown sau đây,

When $a \ne 0$, there are two solutions to $(ax^2 + bx + c = 0)$ and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

sẽ hiển thị dưới dạng:

Nguồn bài viết gốc tại https://github.blog

#markdown #github #maths #mathematic

1657008915

## How to Multiply and Divide Integers

In this video, I'll show you how to add and subtract integers.

The multiplication and division of integers are two of the basic operations performed on integers. Multiplication of integers is the same as the repetitive addition which means adding an integer a specific number of times. For example, 4 × 3 means adding 4 three times, i.e 4 + 4 + 4 = 12. Division of integers means equal grouping or dividing an integer into a specific number of groups. For example, -6 ÷ 2 means dividing -6 into 2 equal parts, which results in -3. Let us learn more about the multiplication and division of integers in this video.

1654652664

## Essence of linear algebra | Dot products and duality

Dot products are a nice geometric tool for understanding projection.  But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation.

1650687473

## Matrix exponentials, determinants, and Lie algebras | Simple Explanation

In today's video we will learn about Exponential Matrix, determinant and Lie algebra

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations.

1650444129

## How to Solve Exponential Equation Quickly | Mathematical Olympiad

Can you solve the given exponential equation for x? Today we will teach you tips and tricks to solve the given olympiad math question in a simple and easy way.  Learn how to prepare for Math Olympiad fast! Step-by-step tutorial by PreMath.com

Exponential equations, as their name suggest, involve exponents. We know that the exponent of a number (base) indicates the number of times the number (base) is multiplied. But, what happens if the power of a number is a variable? When the power is a variable and if it is a part of an equation, then it is called an exponential equation. We may need to use the connection between the exponents and logarithms to solve the exponential equations.

1650382450

## How to Find the Area of ​​a Triangle | Step-by-Step Tutorial

Learn how to find the area of triangle ABC by using the exterior angle theorem and the pythagorean theorem. Fast and easy explanation by PreMath.com

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle. To apply the theorem, we first need to identify the exterior angle and then the associated two remote interior angles of the triangle.

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle. To apply the theorem, we first need to identify the exterior angle and then the associated two remote interior angles of the triangle.

1650095075

## Divergence Operator | The Divergence of a Vector Field

This video introduces the divergence operator from vector calculus, which takes a vector field (like the fluid flow of air in a room) and returns a scalar field quantifying how much the vector field is locally expanding or contracting at every point.  The divergence is a fundamental building block in vector calculus.

%%% CHAPTERS %%%
0:00 Introduction & Overview
3:30 The Divergence is a Linear Operator
4:41 Example of Positive Divergence
8:05 Example of Negative Divergence
10:25 Example of Zero Divergence
13:58 Vector Field is a Differential Equation
16:17 Recap
17:20 Divergence of a Gradient is the Laplacian

1649991505

## Quantum Mechanics Course | Quantum Physics Full Course For Beginners

Quantum physics also known as Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

In this course you will learn about Quantum #mechanics from the beginning to the end. The following topics of Quantum mechanics have been discussed in this course:

⌨️  (0:00:00) Introduction to quantum mechanics
⌨️  (0:16:23) The domain of quantum mechanics
⌨️  (0:24:18) Key concepts of quantum mechanics
⌨️  (0:34:04) A review of complex numbers for QM
⌨️  (0:48:12) Examples of complex numbers
⌨️  (1:01:47) Probability in quantum mechanics
⌨️  (1:12:17) Variance of probability distribution
⌨️  (1:26:16) Normalization of wave function
⌨️  (1:51:47) Position, velocity and momentum from the wave function
⌨️  (2:10:59) Introduction to the uncertainty principle
⌨️  (2:24:32) Key concepts of QM - revisited
⌨️  (2:37:45) Separation of variables and Schrodinger equation
⌨️  (3:09:55) Stationary solutions to the Schrodinger equation
⌨️  (3:15:47) Superposition of stationary states
⌨️  (3:25:37) Potential function in the Schrodinger equation
⌨️  (3:48:10) Infinite square well (particle in a box)
⌨️  (4:00:58) Infinite square well states, orthogonality - Fourier series
⌨️  (4:08:07) Infinite square well example - computation and simulation
⌨️  (4:39:27) Quantum harmonic oscillators via ladder operators
⌨️  (5:16:48) Quantum harmonic oscillators via power series
⌨️  (5:28:32) Free particles and Schrodinger equation
⌨️  (5:34:37) Free particles wave packets and stationary states
⌨️  (6:10:33) Free particle wave packet example
⌨️  (6:13:43) The Dirac delta function
⌨️  (6:20:49) Boundary conditions in the time independent Schrodinger equation
⌨️  (6:24:39) The bound state solution to the delta function potential TISE
⌨️  (6:43:29) Scattering delta function potential
⌨️  (6:55:49) Finite square well scattering states
⌨️  (7:07:39) Linear algebra introduction for quantum mechanics
⌨️  (7:10:34) Linear transformation
⌨️  (7:13:04) Mathematical formalism is Quantum mechanics
⌨️  (7:37:52) Hermitian operator  eigen-stuff
⌨️  (8:01:23) Statistics in formalized quantum mechanics
⌨️  (8:24:26) Generalized uncertainty principle
⌨️  (8:54:36) Energy time uncertainty
⌨️  (9:16:33) Schrodinger equation in 3d
⌨️  (9:19:56) Hydrogen spectrum
⌨️  (9:31:14) Angular momentum operator algebra
⌨️  (9:57:17) Angular momentum eigen function
⌨️  (10:18:08) Spin in quantum mechanics
⌨️  (10:22:23) Two particles system
⌨️  (10:58:03) Free electrons in conductors
⌨️  (11:09:23) Band structure of energy levels in solids

⭐️ Credit ⭐️
Course Author:  Brant Carlson

1649904721

This book introduces the mathematics behind computer programming.

Publication date: 02 Jul 2021
Document Type: Textbook

Excerpts from the Preface:

Liu Xinyu wrote:

This interesting story reflects an important mathematical idea, isomorphism. A difficult problem can be transformed to an isomorphic one, which is mathematical equivalent and easy to solve. A line of 9 numbers corresponds to a 3 x 3 grids; the sum target of fifteen corresponds to one of the rows, columns, and diagonals; Lo Shu pattern corresponds to magic square of order 3. This is what this book intents to tell: programming is isomorphic to mathematics. Just like in art and music, there are interesting stories and mathematicians behind the great minds.

There is another further idea in this story: under the surface of the problem hides the theoretical essence, which is abstract and need to understand. With the rapid development of artificial intelligence and machine learning, can we keep moving forward with a little cleverness and engineering practice? Are we going to open the mysterious black box to find the map to the future?

#programming #math #computerprogramming #mathematic #ebook #book #textbook

1646107911

## Calculus for Machine Learning - Full Course

Calculus is an important field in mathematics and it plays an integral role in many machine learning algorithms. This course is for those who want to learn calculus in depth as well as for machine learning enthusiasts. You will be learning most of the crucial concepts of calculus with comprehensive explanation.

### Calculus 2 For Beginners - Full Course ☞ https://morioh.com/p/36b4c0c1ac6e

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. This course is for those who want to learn calculus in depth as well as for machine learning enthusiasts. You will be learning most of the crucial concepts of calculus with comprehensive explanation.

⌨️ (0:05)         A Preview of Calculus
⌨️ (37:25)       The Limit of a Function.
⌨️ (1:14:30)    The Limit Laws
⌨️ (1:51:00)    Continuity
⌨️ (2:16:52)    The Precise Definition of a Limit
⌨️ (2:45:52)    Defining the Derivative
⌨️ (3:10:16)    The Derivative as a Function
⌨️ (3:34:28)    Differentiation Rules
⌨️ (4:04:05)    Derivatives as Rates of Change
⌨️ (4:39:40)    Derivatives of Trigonometric Functions
⌨️ (4:55:30)    The Chain Rule
⌨️ (5:15:08)    Derivatives of Inverse Functions
⌨️ (5:40:18)    Implicit Differentiation
⌨️ (6:06:28)    Derivatives of Exponential and Logarithmic Functions
⌨️ (6:31:32)    Partial Derivatives
⌨️ (6:53:10)    Related Rates
⌨️ (7:19:48)    Linear Approximations and Differentials
⌨️ (7:42:56)    Maxima and Minima
⌨️ (8:01:59)    The Mean Value Theorem
⌨️ (8:21:21)    Derivatives and the Shape of a Graph
⌨️ (8:45:59)    Limits at Infinity and Asymptotes
⌨️ (9:11:35)    Applied Optimization Problems
⌨️ (9:42:36)    L'Hopital's Rule
⌨️ (10:14:01)  Newton's Method
⌨️ (10:35:24)   Antiderivatives

#calculus #machinelearning #datascience #maths #mathematic