| Line 9: | Line 9: | ||
=== <big> 1.1 Concept </big> === | === <big> 1.1 Concept </big> === | ||
| − | <font size="3px"> Previously, we learnt to solve equations with numbers as solutions. For example, for linear equations <math>ax+b=0</math> with respect to <math>x</math> and <math>a≠0</math>, the solution is going to be <math>x=-\frac{b}{a}</math>. For quadratic equations <math>ax<sup>2</sup>+bx+c=0</math> with respect to <math>x</math> and <math>a≠0</math>, the solution is going to be <math>x={\frac{-b±\sqrt[2]{b | + | <font size="3px"> Previously, we learnt to solve equations with numbers as solutions. For example, for linear equations <math>ax+b=0</math> with respect to <math>x</math> and <math>a≠0</math>, the solution is going to be <math>x=-\frac{b}{a}</math>. For quadratic equations <math>ax<sup>2</sup>+bx+c=0</math> with respect to <math>x</math> and <math>a≠0</math>, the solution is going to be <math>x={\frac{-b±\sqrt[2]{b^2-4ac}}{2a}}</math>. <font size="3px"> |
Revision as of 15:45, 11 October 2017
Introduction to Differential Equations
A slecture by Yijia Wen
1.0 Abstract
When I was first learning differential equations myself, I felt hard to understand the textbook and my lecture notes. After winning the battle, now I am trying to build up those concepts again and explain them in an easier and more concise way. It is not that academic, aiming for intuitive understanding.
1.1 Concept
Previously, we learnt to solve equations with numbers as solutions. For example, for linear equations $ ax+b=0 $ with respect to $ x $ and $ a≠0 $, the solution is going to be $ x=-\frac{b}{a} $. For quadratic equations $ ax<sup>2</sup>+bx+c=0 $ with respect to $ x $ and $ a≠0 $, the solution is going to be $ x={\frac{-b±\sqrt[2]{b^2-4ac}}{2a}} $.
