Korea Advanced Institute of Science and Technology(KAIST) via Coursera
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.
Some points apply to every course of this kind; see how we rank.
Korea Advanced Institute of Science and Technology is in Tier 2: excellent universities and the companies that build the technology of our institution ranking (86/100).
Instructor(s): Tom Leighton, Marten van Dijk This course covers elementary discrete mathematics. Mathematical definitions and proofs are emphasized. Topics include formal logic, induction, graph theory, asymptotic notation and growth of functions, counting principles, and discrete probability.
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