calculus and elements of linear algebra i

taught in Fall of 2024, under Professor Sören Petrat

This is a methods-based Calculus class, with great focus on applications. The final three weeks entail a glimpse into some of the main foundations of Linear Algebra. Nevertheless, rigor is utilised in the treatment of the course. Below you may find topics covered in my tutorials, week by week.

  1. Numbers, Quadratics and Polynomials
  2. Binomial Coefficients, Polynomial Division & Sketching
  3. Continuity, Limits, Asymptotes, Induction
  4. Extreme Value Theorem, Bisection Method and the Squeeze Law
  5. Derivatives with Examples, Implicit Differentiation, and the Oscillating Circle
  6. First-and-Second Derivative Analysis, Sketching
  7. A Full Sketch of \(f(x)=\frac{x^2}{4-x^2}\), Integration Methods
  8. Riemann Integration, Integral Mean Value Theorem, Partial Fractions
  9. Area between Curves, The Fundamental Theorem of Calculus, Taylor’s Series
  10. Separable Differential Equations
  11. Span, Linear Independence, and Basis Vectors
  12. Vector Spaces, Matrices as Linear Maps, Composition of Matrices
  13. Systems of Linear Equations – Solutions & Geometric Interpretation

The following series contains 100 videos, amassing 19 hours and 30 minutes of simple walkthrough tutorials to the course’s weekly problem sets.

mini-tutorials



In addition to the standard tutorials, I gave two exceptional lectures on behalf of Professor Petrat. They are included below, accompanied by recordings of some tutorials.

recordings