The content of the modules:
- Functions I
- Limits and continuity
- Introduction to differential calculus
- The calculus of trigonometric functions
- Exponential and logarithmic functions.
Calculus is used in pure and applied mathematics, the physical sciences, the biological and medical sciences, computer science, statistics, engineering, economics, and in many other areas.
Some simple examples of applications in biology and physics are given in the History and applications section of this module. Further applications to other fields are discussed in the modules The calculus of trigonometric functions, Exponential and logarithmic functions, Growth and decay and Motion in a straight line.
In this module, we consider three topics:
- graph sketching
- maxima and minima problems
- related rates.
We will mainly focus on nicely behaved functions which are differentiable at each point of their domains. Some of the examples are very straightforward, while others are more difficult and require technical skills to arrive at a solution.