# Concepts of Calculus

These notes are designed for students who need to strengthen their school mathematics.

A novel feature is the Cubic Fit Method of Numerical Integration. It is my own invention and, as far as I know, does not appear elsewhere. It uses fitted cubics and is somewhat more accurate than Simpson's Rule for about the same amount of work. Amazingly it consists of the Trapezium Rule with a correction factor that depends only on the derivatives at the two end-points.

[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 Logs and Exponentials
- CHAP06 Trigonometric Functions
- CHAP07 Maxima and Minima
- CHAP08 Optimization Problems
- CHAP09 Newton's Method
- CHAP10 Integration
- CHAP11 Areas Between Curves
- CHAP12 Numerical Integration
- CHAP13 Differential Equations
- CHAP14 Lagrange Multipliers
- APPENDIX