#### MATH123

# Concepts of Calculus

These notes are designed for students who have not done any calculus at school. They are designed particularly for Economics students.

These notes are very similar to those called “Elementary Calculus” which are designed for students with a similar background who will be studying Science or Engineering. The differences are mainly as follows.

- These notes do not cover the calculus of the trigonometric functions, something of little relevance to Economics students.
- These notes include a chapter on Lagrange Multipliers. While this is can be useful in a science context it is normally left to an advanced course. However they get used in Economics courses at an earlier stage. Of course the treatment here is much more superficial than in an advanced calculus course where it is “done properly”.

There are many textbooks that cover the material here. Where these notes differ from the standard treatment of introductory 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
- CHAP07 Integration
- CHAP08 Lagrange Multipliers
- CHAP09 Newton’s Method
- CHAP10 Logs and Exponentials
- CHAP11 Numerical Integration
- CHAP12 Differential Equations
- CHAP13 Areas Between Curves
- APPENDIX