University - Modelling with first order differential equations

About this free course

This free course provides a sample of level 2 study in Mathematics: www.open.ac.uk/courses/find/mathematics.

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You can experience this free course as it was originally designed on OpenLearn, the home of free learning from The Open University: www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics-education/modelling-first-order-differential-equations/content-section-0.

There youll also be able to track your progress via your activity record, which you can use to demonstrate your learning.

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978-1-4730-1564-7 (.kdl)
978-1-4730-0796-3 (.epub)

Introduction

This course lays the foundations of Newtonian mechanics and in particular the procedure for solving dynamics problems. The prerequisite skills needed for this course are the ability to solve first- and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a force.

This OpenLearn course provides a sample of level 2 study in Mathematics.

Learning outcomes

After studying this course, you should be able to:

• understand and use the basic terms for the description of the motion of particles: position, velocity and acceleration

• understand, use and differentiate vector functions

• understand the fundamental laws of Newtonian mechanics

• solve mechanics problems in one dimension by drawing a sketch, choosing a suitable x-axis and origin, drawing a force diagram, applying Newtons second law, taking the x-component, and making suitable substitutions

• solve mechanics problems in one dimension that involve one or more of the forces of gravity, friction, air resistance and water resistance.

1 Modelling with first order differential equations

The main teaching text of this course is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. When prompted after exercise 2.2 to watch the video for this course, return to this page and watch the four clips below. After you've watched the clips, return to the workbook.

Click the link below to open the workbook (PDF, 1.0 MB).

Workbook

Click the link below to open the answerbook (PDF, 0.4 MB).

Answer book

Workbook contents

• Introduction

• 1 Describing motion

  • 1.1 The motion of a particle

  • 1.2 One-dimensional motion

• 2 A theory of motion

• 3 Predicting motion

• 4 Some more force models

  • 4.1 Friction

  • 4.2 Air resistance

  • 4.3 Water resistance

Click play on the blank screen below to watch the low resolution version of 'A question of Newton', or 'Launch in a separate player' for the high resolution version.

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A question of Newton - Part 1

Click play or 'Launch in a separate window' to continue watching 'A question of Newton'.

Video content is not available in this format.

A question of Newton - Part 2

Click play or 'Launch in a separate window' to see the third part of the video.

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A question of Newton - Part 3

Click play or 'Launch in a separate window' to watch the final part of the video.

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A question of Newton - Part 4

Conclusion

This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.

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