If the currently listed section times do not suit you, please contact me to arrange a more suitable time, pending availability. 


PREREQUISITES:
   
Your learner will need to have prior knowledge of the following:
- Algebra I / Elementary Algebra
- Algebra II / Intermediate Algebra
- Basic Geometry - we cover some Geometry in the Precalculus part of this course
- Basic Trigonometry - we cover some Trigonometry in the Precalculus part of this course
- Know How to Use a Scientific Calculator

If you are unsure as to whether your learner has already covered these pre-requisites, please contact me for further details; I also offer another course which covers these topics, therefore your learner may need to take that course first before enrolling in this course.

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Calculus is the study of how things change. 

It provides a framework for modelling systems in which there is change, and a way to deduce the predictions of such models. 

The fundamental idea of calculus is to study change by studying "instantaneous " change, by which we mean changes over tiny intervals of time.

With this, you get the ability to find the effects of changing conditions on the system being investigated. 

By studying these, you can learn how to control the system to do make it do what you want it to do. 

Calculus, by giving engineers and you the ability to model and control systems gives them (and potentially you) extraordinary power over the material world.

The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes. 

This was responsible for the industrial revolution and everything that has followed from it, including almost all of the major advances of the last few centuries.

It turns out that such changes tend to be lots simpler than changes over finite intervals of time. 

This means they are lots easier to model. 

In fact calculus was invented by Newton, who discovered that acceleration, which means change of speed of objects could be modelled by his relatively simple laws of motion.

This leaves us with the problem of deducing information about the motion of objects from information about their speed or acceleration. 

The details of calculus involve the interrelations between the concepts exemplified by speed and acceleration and that represented by position.

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Precalculus:

Day 1: Functions

Day 2: Linear Functions

Day 3: Polynomial and Rational Functions

Day 4: Exponential and Logarithmic Functions

Day 5: Trigonometric Functions

Day 6: Periodic Functions

Day 7: Trigonometric Identities and Equations

Day 8: Further Applications of Trigonometry

Day 9: Systems of Equations and Inequalities

Day 10: Analytic Geometry

Day 11: Sequences, Probability, and Counting Theory

Day 12: Introduction to Calculus

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Calculus:

Day 13: Functions and Graphs

Day 14: Limits

Day 15: Derivatives

Day 16: Applications of Derivatives

Day 17: Integration - Part 1

Day 18: Applications of Integration - Part 1

Day 19: Integration - Part 2

Day 20: Applications of Integration - Part 2

Day 21: Techniques of Integration

Day 22: Introduction to Differential Equations

Day 23: Sequences and Series

Day 24: Power Series

Day 25: Parametric Equations and Polar Coordinates - Part 1

Day 26: Parametric Equations and Polar Coordinates - Part 2

Day 27: Vectors in Space

Day 28: Vector-Valued Functions

Day 29: Differentiation of Functions of Several Variables

Day 30: Multiple Integration

Day 31: Vector Calculus 

Day 32: Second-Order Differential Equations