Hi! Welcome! I am a Ph.D. researcher in Physics at the University of Cologne, Germany. Recently, I graduated from the University of Groningen in the Netherlands with a Master's degree in Nanoscience (w/ cum Laude). I offer private tutoring (for high school and/or university-level students) so you can understand the fundamental concepts and excel in your studies. I have teaching experience of 5+ years in Physics and Mathematics to both high school and university-level students.
This class aims to provide an overview of calculus and linear algebra and focuses on the fundamental mathematical tools and concepts, such as limits, differentiation, and integration. Building on these basic concepts, we will review methods for solving problems related to optimization, linear differential equations, and matrix algebra.
Outline of the course:
1. Calculus:
1.1 Limits of functions
1.2 Continuity, types of discontinuities, intermediate value theorem
1.3 Differentiation (or derivative), slope, secant, tangent
1.4 Rules and theorems for differentiation, power rule, product rule, chain rule
1.5 Derivatives of exp, log, and trigonometric functions
1.6 Implicit differentiation and derivative of inverse functions
1.7 Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function
1.8 First and second derivative tests, inflection points
1.9 Anti-derivative, indefinite integral, integration by substitution, integration by parts
1.10 Definite integral and its application (area between curves, application in physics)\
1.11 Optimization and linear differential equations
2. Linear Algebra:
2.1 Vectors and scalars in Euclidean space, vector arithmetic, scalar product, cross product
2.2 Equations for lines and planes, vector spaces, linear independence, span, basis, dimension
2.3 Linear transformations, coordinates, and representation of linear transformations by matrices
2.4 Matrix operations: matrix multiplication, transpose, determinant, inverse, and Hermitian conjugate
2.5 Systems of linear equations, Gaussian elimination
2.6 Eigenvalues and eigenvectors
2.7 Range, kernel, and rank-nullity theorem
and many more...
*Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).
