1 Infinite Series, Power Series 2 Complex Numbers 3 Linear Algebra 4 Partial Differentitation 5 Multiple Integreals 6 Vector Analysis 7 Fourier Series And Transforms 8 Ordinary Differential Equations 9 Calculus Of Variations 10 Tensor Analysis 11 Special Functions 12 Series Solutions Of Differential Equations; Legendre, Bessel, Hermite, And Laguerre Functions 13 Partial Differential Equations 14 Functions Of A Complex Variable 15 Probability And Statistics expand_more
14.1 Introduction 14.2 Analytic Functions 14.3 Contour Integrals 14.4 Laurent Series 14.5 The Residue Theorem 14.6 Methods Of Finding Residues 14.7 Evaluation Of Definite Integrals By Use Of The Residue Theorem 14.8 The Point At Infinity; Residues At Infinity 14.9 Mapping 14.10 Some Applications Of Conformal Mapping 14.11 Miscellaneous Problems expand_more
Problem 1P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 2P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 3P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 4P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 5P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 6P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 7P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 8P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 9P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 10P: Evaluate the following line integrals in the complex plane by direct integration, that is, as in... Problem 11P: Evaluate C(z3)dz where C is the indicated closed curve along the first quadrant part of the circle... Problem 12P: 01+2iz2dz along the indicated paths: Problem 13P: In Chapter 6, Section 11, we showed that a necessary condition for abFdr to be independent of the... Problem 14P: In finding complex Fourier series in Chapter 7, we showed that 02einxeimxdx=0,nm Show this by... Problem 15P: If f(z) is analytic on and inside the circle z=1, show that 02eifeid=0. Problem 16P: If f(z) is analytic in the disk z2, evaluate 02e2ifeid. Problem 17P: Use Cauchys theorem or integral formula to evaluate the integrals in Problems 17 to 20. Csinzdz2z... Problem 18P: Use Cauchys theorem or integral formula to evaluate the integrals in Problems 17 to 20. Csin2zdz6z... Problem 19P: Use Cauchys theorem or integral formula to evaluate the integrals in Problems 17 to 20. e3zdzzln2 if... Problem 20P: Use Cauchys theorem or integral formula to evaluate the integrals in Problems 17 to 20 .... Problem 21P: Differentiate Cauchys formula (3.9) or (3.10) to get f(z)=12iCf(w)dw(wz)2orf(a)=12iCf(z)dz(za)2. By... Problem 22P: Use Problem 21 to evaluate the following integrals. Csin2zdz(6z)3 where C is the circle z=3. Problem 23P: Use Problem 21 to evaluate the following integrals. Ce3zdz(zln2)4 where C is the square in Problem... Problem 24P: Use Problem 21 to evaluate the following integrals. Ccoshzdz(2ln2z)5 where C is the circle z=2. format_list_bulleted