MATH 141 Chapter Notes -Simply Connected Space, Antiderivative, Glossary Of Topology
Document Summary
The basic theme here is that complex line integrals will mirror much of what we"ve seen for multi- variable calculus line integrals. But, just like working with is easier than working with sine and cosine, complex line integrals are easier to work with than their multivariable analogs. At the same time they will give deep insight into the workings of these integrals. Line integrals are also called path or contour integrals. Given the ingredients we de ne the complex line integral () by (1a) You should note that this notation looks just like integrals of a real variable. We don"t need the vectors and dot products of line integrals in 2. Also, make sure you understand that the product (()) () is just a product of complex numbers. An alternative notation uses = + to write (1b) Let"s check that equations 1a and 1b are the same.
