Description: This Introduction to Calculus course 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).
Enrolling in the course (cost $45) you have:
- a trainer to answer questions,
- regular tests,
- discussion forums,
- a certificate for those who pass.
Course start: 14th September 2020 - 4 weeks
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.
Cost: $45. Part 1 of this course is free
Course created and delivered by Kenneth Williams.
Any queries can be sent to firstname.lastname@example.org
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