![]() Studies techniques of solving separable differential equations. Applies Euler’s technique to approximate the solution of initial value problems. Applies the direction field technique to find graphical solutions of differential equations. Applies the integral calculus to find arc lengths, areas of surfaces of revolution and to solve force and work problems. Applies Simpson’s rule and other elementary numerical quadrature methods to approximate integrals. ![]() It is like travel: different kinds of transport have solved how to get to certain places.Studies the techniques of substitution, integration by parts, trigonometric integrals, partial fractions and trigonometric substitution to evaluate integrals. So we need to know what type of Differential Equation it is first. Over the years wise people have worked out special methods to solve some types of Differential Equations. But we also need to solve it to discover how, for example, the spring bounces up and down over time. Note: we haven't included "damping" (the slowing down of the bounces due to friction), which is a little more complicated, but you can play with it here (press play):Ĭreating a differential equation is the first major step. It has a function x(t), and it's second derivative d 2x dt 2 The spring pulls it back up based on how stretched it is ( k is the spring's stiffness, and x is how stretched it is): F = -kx ![]() The weight is pulled down by gravity, and we know from Newton's Second Law that force equals mass times acceleration:Īnd acceleration is the second derivative of position with respect to time, so:
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