As part of my teaching experience, I had the opportunity to lead one of the exercise groups (60 hours over one semester) for an undergraduate course in mathematical analysis for IT students at the University of Warsaw, taught by Professor Paweł Strzelecki. The course covered a broad range of foundational and (more) advanced topics, including higher-order derivatives and Taylor’s formula, power series and the Cauchy-Hadamard theorem, the geometry and applications of definite integrals, and an introduction to the topology of Euclidean spaces. We also explored partial derivatives, critical point analysis, and touched on modern measure theory and Lebesgue integration.
Below are (most) of the exercises that I have given my group. Those include even more advanced questions, as the lecture was only 30h.
Series 2, Taylor’s expansion and Newton’s method
Series 3, Taylor’s expansion-repetition
Series 5, Power series-continuation
Series 6, Basics of uniform convergence
Series 7, Introduction to integration
Series 12, Limits in multiple dimensions
Series 13, Norms, limits, and partial derivatives
Series 14, Multidimensional derivative. Inverse and Implicity function theorems
Series 15, Minima and maxima in multiple dimensions
Series 16, Minima and maxima in multiple dimensions-continuation
Series 17, Taylor’s expansion, and Lagrange’s multipliers theorem
Series 18, Basics of measure theory
Series 19, Measure theory-continuation, and introduction to limits of integrals
Series 20, Limits of integrals