Building Fluid Solvers For Computer Graphics Part 1

Learn how fluid solvers are built from scratch without prior knowledge. This first course covers all the math needed.

What you'll learn

Learn all the mathematical background behind fluid simulations and fluid solvers.

Understand the basics of differential and integral calculus.

Proceed with your knowledge to learn about multivariable calculus which is the core of fluid simulations.

Learn some topics in linear algebra that are important in graphics in fluid simulations

Requirements

If you know some simple prep school math, you are ready

Description

Do you wanna build your fluid simulating program like Houdini and Realflow someday (also called fluid solver)? Now, you can learn how to do that as simple as eating cakes, here is your start point in this long roadVolume 1 will be about the math behind the stuff. starting with Calculus 1 (Differential Calculus) basics and explaining the stuff we will need later on. Then , Calculus 2 (Integral Calculus) ,then , Calculus 3 (which is the most important and called Multi-variable Calculus). I will also tend to explain some Linear Algebra concepts we will use. You don't need any prior knowledge (just some simple preparatory school math will do it) . It's completely for beginners as I will do my best to make the concepts simple for everyone. We are going to start with what it's a function and continue leveling up till multivariable calculus.What you will be learning in each chapter :Chapter 1 : Differential CalculusIn this chapter , we will begin our journey in the math starting with calculus 1 and explaining the concepts we will need in our process . We will learn what’s a function and what’s a derivative. After that, we will differentiate our functions with different techniques.Chapter 2 : Integral CalculusIntegration is the opposite of differentiation so we will talk about how to integrate our functions with different techniques.Chapter 3 : Extra math in the core , Multivariable Calculus.In this chapter we will finish the concepts of Calculus we need. Calculus 3 is the most important in our work . We will start to differentiate the multi-variable functions and integrate them. I will explain the most important derivative operators we need like gradient, divergence , curl, laplacian and many more ! Be ready for partial derivatives !CAUTION: Building fluid solvers is a huge field, no one can teach you how to build a full cool solver like Houdini which is built by hundreds of developers and takes years of development. This series is giving you the key to enter this field as an aspiring developer or even learning how solvers work to help you in your work as an FX TD. You will end the series by having the main points and the main body of the codes that you need to continue the journey.

Overview

Section 1: Chapter 1 - Starting with math , Differential Calculus

Lecture 1 What's a function

Lecture 2 Graphing A function

Lecture 3 What's A limit

Lecture 4 Derivatives Part 1

Lecture 5 Derivatives Part 2

Lecture 6 Derivatives Part 3

Lecture 7 Derivatives Part 4

Lecture 8 Derivatives Part 5

Lecture 9 Derivatives Part 6

Lecture 10 Derivatives Part 7

Lecture 11 Derivative Part 8

Lecture 12 Derivatives Part 9

Lecture 13 Derivatives Part 10

Section 2: Chapter 2 - More In Math , Integral Calculus

Lecture 14 Starting with integral sums

Lecture 15 What is antiderivative

Lecture 16 Reverse Power Rule

Lecture 17 Some Integration Rules

Lecture 18 Integration by Parts

Lecture 19 U-Subsitution

Lecture 20 Definite Integral

Lecture 21 Fundamental Theoream Of Calculus

Section 3: Chapter 3 - Math from hell , Multivariable Calcululus

Lecture 22 What's Multivariable Calculus

Lecture 23 Scalar Valued Functions

Lecture 24 Graphing more than two demensions

Lecture 25 Vectors

Lecture 26 Vector Valued Functions Part1

Lecture 27 Vector Valued Functions Part2

Lecture 28 Partial Derivatives Part1

Lecture 29 Partial Derivatives Part2

Lecture 30 Partial Derivatives Part3

Lecture 31 Partial Derivatives Part4

Lecture 32 Gradient Introduction

Lecture 33 Gradient Example

Lecture 34 Directional Derivatives

Lecture 35 Multivariable Chain Rule

Lecture 36 Divergence Part1

Lecture 37 Divergence Part2

Lecture 38 Rotation in 2D (Curl Part1)

Lecture 39 Rotation in 3D (Curl Part2)

Lecture 40 Curl Formula (Curl Part3)

Lecture 41 Curl Example (Curl Part4)

Lecture 42 Laplacian

Lecture 43 Line Integration Part 1

Lecture 44 Line Integration Part 2

Lecture 45 Double Integration Part1

Lecture 46 Double Integration Part 2

Lecture 47 Triple Integrals

Lecture 48 Divergance Theorem Part 1

Lecture 49 Divergence Theoren Part 2

Lecture 50 Surface Integrals

Lecture 51 3D Flux

Simplest availlable, for people with basic prep scool math knowledge.,People curious about how fluid solvers are created and don't know how to start.,People who want to learn about how fluid solvers are created and how they work without spending a lot of time and money to collect all of the knowledge they want from different sources and different fields, here, everything is in one series,People who want things simplified; here are examples and illustrations in many different ways to make complicated stuff easy.