(0:00) Summer school course on Financial Math. (1:21) Plan for the lecture. (2:42) Scalar line integrals (application: mass of a thin wire). (10:23) Example to find the mass of a thin wire (first approximate it, then find the exact mass). (16:06) Vector line integrals (application: work done by a force).
Based on "Fundamentals of Complex Analysis, with Applications to Engineering and Science", by E.B. Saff and A.D. Snider (3rd Edition). "Visual Complex Analysis", by Tristan Needham, is also referred to a lot. Mathematica is often used, especially to visualize complex analytic (conformal) mappings.