Mastering Complex Variables: A Comprehensive Guide to Brown & Churchill (7th Edition) скачать в хорошем качестве

Mastering Complex Variables: A Comprehensive Guide to Brown & Churchill (7th Edition)

This video provides a complete, structured walkthrough of Complex Variables and Applications (7th Edition) by James Ward Brown and Ruel V. Churchill, one of the most trusted textbooks for Engineering Mathematics and Pure Mathematics. Module 1: Foundations of Complex Numbers 00:00 – Introduction to Brown & Churchill (7th Edition) 02:15 – Sums, Products & Algebraic Properties 05:40 – Modulus, Triangle Inequality & Geometry 08:20 – Complex Conjugates & Properties 12:10 – Polar Form & Euler’s Formula 15:45 – Roots of Complex Numbers & Roots of Unity 🔹 Module 2: Analytic Functions 20:30 – Complex Functions & Mappings 24:15 – Limits, Continuity & Differentiability 28:50 – Cauchy-Riemann Equations (Cartesian & Polar) 35:10 – Sufficient Conditions for Analyticity 40:05 – Analytic vs Entire Functions 44:30 – Harmonic Functions & Conjugates 🔹 Module 3: Elementary Functions 48:20 – Complex Exponential Function 52:15 – Trigonometric & Hyperbolic Functions 58:40 – Logarithmic Function & Branch Cuts 01:05:10 – Complex Powers 𝑧 𝑐 z c 🔹 Module 4: Integrals & Cauchy Theory 01:12:00 – Definite Integrals of Complex Functions 01:18:30 – Contours & Contour Integrals 01:25:00 – Cauchy–Goursat Theorem 01:32:45 – Cauchy Integral Formula & Derivatives 01:40:20 – Liouville’s Theorem & Fundamental Theorem of Algebra 🔹 Module 5: Series & Residues 01:48:00 – Taylor & Laurent Series 01:55:10 – Power Series Differentiation & Integration 02:05:30 – Singularities: Poles & Essential 02:15:20 – Residue Theorem (Step-by-Step) 02:25:40 – Evaluating Improper Integrals Using Residues 🔹 Module 6: Conformal Mapping & Applications 02:35:00 – Conformal Mapping & Angle Preservation 02:42:15 – Möbius (Linear Fractional) Transformations 02:50:00 – Schwarz–Christoffel Transformation 03:00:00 – Applications in Heat Conduction & Fluid Flow