(BQ) Part 2 book "Advanced engineering mathematics" has contents: Complex numbers and functions, complex integration; complex integration; laurent series, residue integration; laurent series. residue integration; complex analysis and potential theory; numerics in general; numeric linear algebra,.and other contents. | ' , PA R T D Complex Analysis C HAP T E R 13 Complex Numbers and Functions C HAP T E R 14 Complex Integration C HAP T E R 1 5 Power Series, Taylor Series C HAP T E R 1 6 Laurent Series. Residue Integration C HAP T E R 17 Conformal Mapping C HAP T E R 18 Complex Analysis and Potential Theory Many engineering problems can be modeled, investigated, and solved by functions of a complex variable. For simpler problems, some acquaintance with complex numbers will suffice. This is true for simpler electric circuits and mechanical vibrating systems. For more complicated problems in heat conduction, fluid flow, electrostatics, etc., one needs the theory of complex analytic functions, briefly called complex analysis. The importance of the latter in applied mathematics has three main reasons: 1. Most importantly, the real and imaginary parts of an analytic function satisfy Laplace's equation in two real variables. Hence two-dimensional potential problems can be solved by methods for analytic functions, and this is often simpler than working in real. 2. Many complicated real and complex integrals in applications can be evaluated by the elegant methods of complex integration. 3. Most functions in engineering mathematics are analytic functions, and their study as functions of a complex variable leads to a deeper understanding of their properties and to interrelations in complex that have no analog in real calculus. 601 CHAPTER 13 Complex Numbers and Functions Complex numbers and their geometric representation in the complex plane are discussed in Secs. and . Complex analysis i:-. concerned with complex analytic functions as defined in Sec. . Checking for analyticity is done by the Cauchy-Riemann equations (Sec. ). These equations are of basic importance, also because of their relation to Laplace's equation. The remaining sections of the chapter are devoted to elementary complex functions (exponential, trigonometric, hyperbolic, and logarithmic .
