Applied Math for Materials Science and Engineering (Part 2)

Build the mathematical toolkit you need for materials science and engineering. This course covers three essential areas, multivariable calculus, infinite series, and complex numbers, and connects each topic directly to physical and engineering applications. You'll start with multiple integration across Cartesian, cylindrical, and spherical coordinate systems. You'll learn how the Jacobian and scale factors enable correct transformations between systems, and you'll apply these tools to calculate solid angles, moments of inertia, and other physical properties for symmetric geometries. Next, you'll study infinite series and convergence criteria using the comparison, ratio, and integral tests. You'll work with Taylor and power series to approximate complex physical laws, including relativistic mechanics models, and perform term-by-term calculus operations to solve advanced problems. Finally, you'll explore complex numbers in both Cartesian and polar form, connect them through Euler's formula, and apply complex impedance methods to solve differential equations for LCR electrical circuits. Who this is for: First- and second-year undergraduates in engineering or science, advanced high school students, and working professionals seeking to strengthen their applied mathematics foundations.