# Calculus

Calculus is the mathematical science dealing with changing quantities. One use of calculus is determining air travel times which are affected by changing conditions.

### Overview

In calculus we study how the change in one variable affects the change in another variable.

Calculus has developed into one of the most important branches, or strands of mathematics. The word calculus is the Latin word for “pebble”. People once used pebbles to solve problems in calculus. This reveals its original simplicity. Rather than memorizing the rules and processes to merely get the right answer, we will once again use the “pebbles” found in the Mortensen Math kit to help visualize the concepts and reveal the simplicity of calculus.

The founder of calculus was the Christian theologian, scientist, and mathematician, Sir Isaac Newton. He discovered the basic theorem of calculus. He also discovered the secrets of light and color and showed how the universe is held together by the law of gravity. These three major contributions to science were all “discovered” during an 18 month period in his life. He is sometime described as “one of the greatest names in the history of human thought” because of these fundamental contributions to mathematics, physics, and astronomy. One item to note, however, is that he actually wrote more books on theology and man’s relationship to God than all of his scientific writings combined. Now we all know his source of inspiration.

In these calculus workbooks, we will be taking you on a journey that will allow you to trace Newton’s steps in discovering this theorem and also allow you to discover the theorem of calculus on your own.

There are two main branches of calculus – integral calculus and differential calculus. Both branches deal with changing quantities. Integral calculus is finding the quantity of something and knowing the rate at which it is changing. In differential calculus we will be finding the rate at which a certain quantity changes. This rate of change will be called the derivative.

In the first level of calculus we will be laying the visual foundation upon which these theorems are based. Do not be deceived by the simplicity of the workbooks. It is necessary that much time be spent in building a solid visual understanding of this foundation. While doing this the student will also be developing his skills in arithmetic, problem solving, and measurement. Remember mathematics is the study of numbers. In all branches of mathematics we simply count numbers. We visualize the concept and then count the numbers. It is that simple.

In the second level of calculus (the second ten books), the workbooks progress more quickly and the beauty of calculus begins to unfold. A solid visual foundation must be established by this time.

There are 5 levels of Calculus available – 10 books a level.
Each book has about 20 pages ≈ 1000 pages in total.

The calculus sequence includes many arithmetic, algebraic, and problem solving concepts and is a good place to use story problems to link the manipulative model to real objects.