Complex Variables and Applications (9th Edition) by James Ward Brown & Ruel V. Churchill — An in-depth introduction to the theory and applications of complex variables, covering complex numbers, analytic functions, contour integrals, residue theory, confo

Complex Variables and Applications (9th Edition) by James Ward Brown and Ruel V. Churchill is a well-established and widely used textbook offering a rigorous yet accessible treatment of the theory of functions of a complex variable along with their applications in engineering, physics, and mathematics. Agorism +1 The book begins with the basics of complex numbers—algebraic and geometric representation, modulus and argument, exponential form, roots of complex numbers and regions in the complex plane. Building on that foundation, the text develops the concept of analytic functions—limits, continuity, the Cauchy-Riemann equations, harmonic functions, and properties of analytic functions. Agorism +1 Subsequent chapters cover elementary functions of a complex variable—exponential, logarithmic, trigonometric and hyperbolic complex-valued functions—and show how these extend classical real analysis into the complex domain. The subject of integration of complex functions is treated in depth: contour integrals, the Cauchy-Goursat theorem, Cauchy integral formula, Morera’s theorem, and integrals over general paths. Residue theory is then introduced for evaluating real integrals, dealing with poles, branch points and essential singularities. A major strength of the text is its emphasis on applications: conformal mapping and boundary-value problems, potential flow in fluid mechanics, heat conduction, and other areas where complex variable methods yield elegant solutions. Branch cuts, multi-valued functions, Laurent series and singularity classification are treated with clarity. Flipkart +1 Throughout the book, the authors provide numerous worked examples and exercises, allowing students to apply theory immediately to practical problems. The 9th edition brings enhancements: improved explanations, new examples, reorganized sections for clearer progression of topics, and expanded problem sets to accommodate different student backgrounds. Flipkart This text is highly suitable for upper-level undergraduate or beginning graduate courses in complex variables, as well as for engineering curricula where complex function methods are applied in electromagnetics, signal processing, fluid mechanics or structural mechanics. Instructors will appreciate the balance of mathematical theory and applied problem solving; students will value the clarity of exposition and structured progression from foundational topics to advanced methods. In summary, whether you aim to master analytic function theory or apply complex variable techniques in engineering and physics, Complex Variables and Applications (9th Edition) provides a robust, well-organized, and application-oriented framework. Its proven track record and comprehensive coverage make it a reliable choice for courses and self-study alike.