# Elementary Calculus

These notes are designed for students who have done very little mathematics in high school and, in particular, have never done any calculus. They are designed particularly for students who will be studying Science or Engineering.

These notes are very similar to those called “Concepts of Calculus” which are designed for the same category of student but who will be studying Economics. The differences are mainly as follows.

- The calculus of the trigonometric functions are discussed here as they are highly important in Science and Engineering.
- These notes do not include chapters on Lagrange Multipliers and Differential Equations. Although these topics are very useful in Science and Engineering too, they are normally left to an advanced course when they can be treated more fully.

There are many textbooks that cover the material here. Where these notes differ from the standard treatment of algebra and calculus are:

- There is a long introduction to calculus that explores, qualitatively, the three "faces" of a graph – height, slope and area. The point is made that a graph tells a story and aspects of that story are revealed by all three. In the opening chapter on calculus there is a graph displayed that tells several different stories under several different interpretations.
- The chapter on numerical integration highlights the cubic fit method that in many ways is superior to Simpson's Rule. It appears here for the first time.

[Please note that all links are to Adobe .pdf documents. They will open in a separate browser window.]

- Introduction and Contents
- CHAP01 Graphs and Their Stories
- CHAP02 The x-y Plane
- CHAP03 Differentiation
- CHAP04 Tangents and Normals
- CHAP05 Maxima and Minima
- CHAP06 Optimization Problems
- CHAP07 Newton's Method
- CHAP08 Integration
- CHAP09 Areas Between Curves
- CHAP10 Logs and Exponentials
- CHAP11 Trigonometric Functions
- CHAP12 Numerical Integration
- APPENDIX