Teaching for this module will take place throughout the year, with eight evenings in each of the autumn and spring terms and two evenings of revision and consolidation in the summer term. It also covers exact and numerical solutions of ordinary differential equations, as well as modelling problems using differential equations. It is like travel: different kinds of transport have solved how to get to certain places.This module aims to develop the ideas and techniques of calculus introduced in Calculus 1 to functions of more than one variable. 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 If f(x) is a function, then f(x) dy/dx is the differential equation, where f(x) is the derivative of the function, y is dependent variable and x is an. 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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