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how to solve exact equationsExact Equations:Condition: M(x,y) dx + N(x,y) dy = 0; Or dM/dy = dN/dxGiven that dM/dy = dN/dx, we can know that d^2f/dxdy(y goes first)=d^2f/dydx (x goes first), they are exact differentials.There exists a function f(x,y) s

how to solve linear 1st-order ODE’s by use of an integrating factorLinear DE: the power the derivative is raised to is 1, not the orderSeparable DE: can be written so that all x (/y) parts are on the same side.Eg: dy/dx=g(x)h(y)1st order DE:Standard

introduce how to solve separable equationsSeparable Equations:1 order equations with separable variablewritten in the form: f(x)dx=g(y)dy (seperate the variables and intergration)eg： y=q(x)进行积分H(y) = G(x) + cBoth are antiderivatives of p(y) = 1/h(

draw graphs of solutions to first-order ODE’s by using slope (or direction) fields 用两种方法绘制斜率场1st order DE：函数在 I 区间可导，连续确认x，y，那么函数在该点的切线斜率就已知，斜率场就可以被绘制Get a sense of what type of function that is and can satisfy with the DESlope and Direction FieldsCo

introduce the terms “initial value problem” and “boundary value problem”ppt来源于youtube：Mathispower4u视频

introduce definitions and terminology associated with differential equations2020.1.4