Applied Complex Analysis and Differential Equations for Scientists and Engineers

To excel in the mathematical sciences, you must bridge the gap between abstract mathematical theory and practical problem-solving. This course offers a structured, text-based approach to mastering complex analysis and differential equations, designed to build your confidence from the ground up. You will transition from understanding foundational definitions to independently solving rigorous mathematical problems. What you'll learn: Understand the fundamentals of complex variables, analytic functions, and Cauchy-Riemann equations; Apply integration theorems, including Cauchy's integral formula and residue calculus, to evaluate complex integrals; Solve first-order and higher-order ordinary differential equations using systematic, step-by-step methods; Practice solving linear differential equations with constant coefficients and explore power series solutions; Learn modern numerical approximation concepts and stability basics applicable to real-world mathematical modeling. This course begins with essential terminology and foundational definitions before moving into structured, step-by-step problem-solving guides and practical exercises. It is specifically designed for beginners and students preparing for scientific examinations, requiring no advanced prerequisites. Start reading today to sharpen your mathematical reasoning and master these essential topics.