VL 23: Extremwertaufgaben mit Nebenbedingungen -TU Dortmund Höhere Mathematik II (BCI/BW/MLW)

Here is the twenty-third lecture for Higher Mathematics II (BCI/BW/MLW). We continue with multidimensional mathematics and now ask ourselves: How do we find local or global extrema of a multivariate function subject to given constraint(s), i.e., with a restricted domain? The answer lies in the Lagrange multiplier theorem, our necessary criterion for extrema with constraint(s). Note: The rank condition is crucial here! Keywords: Extrema subject to constraints, Lagrange multiplier theorem, necessary criterion, Lagrange multipliers, Lagrange function, rank condition. ... Timeline: 00:00 - Intro 00:06 - Lecture on Optimization Problems with Constraints 34:18 - Exercise on Optimization Problems with Constraints 1:00:30 - Outro Questions / suggestions / constructive criticism / comments are welcome at [email protected]