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Introduction to Differential Equations

所在平台: EdxArchive

课程类别: 其他类别

大学或机构: MITx

授课老师： Arthur Mattuck David Jerison Haynes Miller

课程主页: https://www.edx.org/archive/introduction-differential-equations-mitx-18-031x

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课程简介

Scientists and engineers understand the world through differential equations. You can too.

课程大纲

  • Use linear differential equations to model physical systems using the input / system response paradigm.
  • Solve linear differential equations with constant coefficients.
  • Gain intuition for the behavior of a damped harmonic oscillator.
  • Understand solutions to nonlinear differential equations using qualitative methods.

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课程详情

How do you design:

  • A boat that doesn’t tip over as it bobs in the water?
  • The suspension system of a car for a smooth ride?
  • Circuits that tune to the correct frequencies in a cell phone?

How do you model:

  • The growth of antibiotic resistant bacteria?
  • Gene expression?
  • Online purchasing trends?

The answer: Differential Equations.

Differential equations are the language of the models we use to describe the world around us. In this mathematics course, we will explore temperature, spring systems, circuits, population growth, and biological cell motion to illustrate how differential equations can be used to model nearly everything in the world around us.

We will develop the mathematical tools needed to solve linear differential equations. In the case of nonlinear differential equations, we will employ graphical methods and approximation to understand solutions.

Image by bizoo_n

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