Lecture 1 | Contents

Calculus for Beginners: Differentiation

This course is designed for you to get a grasp of the concept of differentiation as a novice in the subject and then, gradually enhance your understanding in a methodical way while enjoying it.

You do not need any prior knowledge of differentiation or calculus for this course. All you need is a reasonable understanding in algebra, which I assume you already have.

The author, with well over 15 years of experience in teaching mathematics in England and a solid experience in web development, has combined the best of both worlds in producing this unique course.

No text book, old or new, can match this course for the following reasons:

  • It offers students to learn differentiation interactively with few programmes, known as applets, embedded in the lectures of the course; it’s a unique experience for them - a game changer.
  • There are question-generators in some of the lectures; you can generate random questions along with the answers – and then work them out until you reach the latter.
  • The lectures are full of worked examples that progress gradually while enhancing the knowledge in key areas
  • There are ample practice questions to make sure you fully grasp the whole concept properly

In this context, a mere video tutorial cannot match this coure either, as the latter very rarely offers the inteactivity.

Who will benefit from this course?

  • GCSE, IGCSE, O-Level and A-Level students in the UK and Commonwealth Countries
  • High School students who want to learn mathematics to an advanced level
  • Any professional who thinks that calculus will be helpful for his progress in a technical or engineering career
  • Any mathematical enthusiast who wants to learn calculus

The course progresses in the following order, with lectures.

1.    The concept of gradient of a straight line

2.    The need of tangents to find the gradient of a curve

3.    The challenge of drawing an accurate tangent to a curve

4.    The issue faced that arises when too many tangents are drawn to a curve

5.    How differentiation helps us find the gradient of a curve without tangents very accurately

6.    Giving credit to the two geniuses who came up with differentiation almost 300 years ago - almost simultaneously – as a token of gratitude

7.    How to find the differential coefficient from first principles

8.    Coming up with a formula to find the differential coefficient of a function

9.    Increasing and decreasing functions

10. Stationary points - local maximum, local minimum and point of inflexion

11. Modelling with differentiation

12. Using differentiation to solve real life problems

The author is fully confident that not only will you understand differentiation fully, but also find the course as a stable stepping stone to make the next logical move in calculus - learning integration witth the same entusiasm and drive.