Description: This Introduction to Calculus course in 18 video lessons offers a very easy and natural way to understand and apply the techniques of a subject that is usually considered difficult. Only a knowledge of simple graphs, gradients and basic algebra is required (so children can, and have, taken this course).
Note: the last four lessons are there to prepare the student for parts of later courses (the Advanced Diploma and Applied Maths courses).
You can join this course any time.
Enrolling in the course you have:
- 18 video lessons
- a trainer to answer questions,
- regular tests,
- discussion forums,
- a certificate for those who pass.
Course start: You can join this course any time.
Mode: 100 % Online.
18 Video Lessons with online Tests and Forum discussions.
Self paced: watch 4 or 5 videos each week at any time that suits you. Lessons are 20 minutes long on average. Each lesson/video has a test at the end.
Enrol and study from any part of the globe.
No prerequisites - anyone can join.
Course created and delivered by Kenneth Williams.
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1 Growth and Limits
* Different types of growth.
* How limits can be used in mathematics.
* What is meant by the gradient of a curve
2 Gradient of a Secant
* What is meant by gradient of a secant
* How to work it out
* And a simple way to get the answers more easily
3 Gradient of a Tangent
* How to use previous result to get a simple formula for the gradient at any point on any parabola
* How to find maximum and minimum values using calculus
* How to use calculus to help sketch curves
* Practical examples
* How to form your own equation and optimise
5 Cubics and Beyond
* We extend the method to cubic and higher order equations.
* The second derivative
6 Negative Powers
* How to find gradients when the power is negative
7 Fractional Powers
* How to find gradients when the power is a fraction.
8 Ratio of Gradients
* We see that for the curves y = ax^n there is a ratio of gradients that is equal to the power, n.
* And how we can use that ratio to get gradients.
9 Area Under a Parabola
* How we can easily get areas under a parabola
* How to use symmetry to extend the method
10 Ratio of Areas
* How to get the area under a straight line, sloping or horizontal
* How to get the area under a cubic curve
* How the various results are unified
* How to get the area under a curve which is defined by several terms
* What integration is
* What the 'constant of integration' is and how to find it
* The quick way to integrate
* The symbol for integration
* How to integrate a series of terms
12 Integration and Area
* How integration and areas are connected
* How we can use the integration notation to describe areas
* How a formula can give positions, speeds and accelerations
* How these formulae are related through differentiation and integration
14 Differential Equations
* What a differential equation is
* How to construct a differential equation
* How to use a simple pattern to construct the equation
* How to reverse that pattern to get a solution to differential equations
* What functions and their notation
16 Function of a Function
* The meaning and how to differentiate it
17 Products and Quotients
* How to differentiate products and quotients
18 The Exponential Function
* What it is and how to differentiate such functions