MATH115 Geometry and Calculus

Lecturer: Dr. Bernd Schulze $$ Office: Fylde B11

Chapters

1.	Vectors
2.	Curves
3.	Functions of two or more variables
4.	Double integrals: general regions and change of variable
5.	Volumes and surface areas of solids

The printed notes have gaps which will be completed in lectures. The same notes with gaps, as well as the exercises, are also on Moodle.

Recommended text books

J. Gilbert and C. Jordan, Guide to Mathematical Methods, 2nd ed., Palgrave (2002)

Marsden, J.E. and Tromba, A.J., Vector Analysis - useful for vectors

Anton, H. Calculus - also useful for vectors

First, we study vectors in two- and three-dimensional space and see some applications to finding equations of lines and planes. We then consider some different ways of describing curves and surfaces via equations or parameters, and we use partial differentiation to determine tangent lines and planes, as well as using integration to calculate the length of a curve.

In the second half of the course, we study functions of several variables. When attempting to calculate an integral over one variable, we often substitute one variable for another more convenienent one; here we will see the equivalent technique for a double integral, where we have to substitute two variables simultaneously. We also investigate some methods for finding maxima and minima of a function subject to certain conditions.

Finally, we use (double) integrals to calculate volumes and surface areas of various solids.