5.1 & 5.3 Introduction to Calculus

  2. Calculus
  3. 5.1 & 5.3 Introduction to Calculus
    4. 40'

Differentiating

This is the first of three sections on differential calculus. This is significant branch of mathematics with lots of applications. It builds very nicely on other concepts in the course and those you are likely to have covered previously. The whole principle is based around examining 'Rates of change'.

Key Concepts

In this unit you should learn to

  • Understand the basic principles of differential calculus as rate of change
  • Differentiate polynomial functions and use this work out gradients
  • Differentiate functions involving negative indices
  • Use basic differentiation to solve problems about gradients
 

Essentials

Slides Gallery

Use these slides to review the material and key points covered in the videos.

 

1. Introduction - what is calculus about

This video puts the whole idea in to some context and shows how calculus builds carefully on work already done.

 

2. The Gradient function

Here we introduce the idea of deriving a function which tells about the gradient of the function we started with.

 

3. Differentiating polynomials

At this point we move on to the general pattern for deriving the gradient function.

 

4. Negative indices and differentiating

This is a focus on dealing with negative indices. They are a potential pitfall, but if you are careful there should be no problem.

 

5. Finding gradients

Here we apply the techniques to find the gradient of a given function at any point.

 
 

Summary

Review these condensed 'key point' flashcards to help you check and keep ideas fresh in your mind.

 

Test yourself

Self Checking Quiz

Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.

 

Exam Style Questions

The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.

Question 1

Video Solution

 

Question 2

Video Solution

 

Question 3

Video Solution

 
 

MY PROGRESS

How much of 5.1 & 5.3 Introduction to Calculus have you understood?