MATH123 Concepts of Calculus
This is an introductory course on
calculus for those who haven’t studied it before. It emphasises
the concepts rather more than the technicalities and contains many examples and
illustrations.
It’s particularly suitable
for economics students and hence includes an elementary chapter on Lagrange
Multipliers, something not normally done at this introductory level. It also
contains a numerical technique for finding areas under curves that’s
superior to Simpson’s Rule. This is the Cubic Fit Method and it’s
not found elsewhere.
[Please note that
all links are to Adobe .pdf documents. They will open
in a separate browser window.]
- Introduction
and Table of Contents
- Chapter
1: Graphs and the Stories They Tell
Chapter
2: The x-y Plane - Chapter
3: Differentiation
- Chapter
4: Tangents and Normals
- Chapter
5: Maxima and Minima
- Chapter
6: Optimisation Problems
- Chapter
7: Integration
- Chapter
8: Lagrange Multipliers
- Chapter
9: Newton’s Method
- Chapter
10: Simpson’s Rule
- Chapter
11: Log and Exponential Functions
- Chapter
12: Differential Equations
- Chapter
13: Areas Between Curves
- Appendix