Differential and integral calculus, vector calculus, Differential Equations EDO

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).

Mathematics is all about learning basic elements with which you can create explosions, interactions and much more desired computations. It is the heart of every science known and without it, even the text that I am writing right now would not work (recall binary numbers). I have always been passionate about Math and during primary and high school I attended many Regional Math Olympiads where I usually won the top 5 places. During this period, I got the chance to be trained by university professors and gained knowledge of many complex math concepts at a really young age. This made it possible for me to afterward be able to explain these concepts in a brief and clear manner to my fellow students. I aspire to visualize everything with everyday life and when students see this connection, the puzzle is finally solved. We can cover all of the branches of mathematics together at the desired level and degree level. Starting from Algebra, Geometry, Calculus, Probability, Trigonometry and much more, we will build that mathematic intuition in no time!

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Being a fanatics of Mathematics, I love doing things related to Maths. For that reason, I feel pleasure to share my Mathematical knowledge with others. I would be happy to give tuition for Mathematics for high school or university students (HAVO, HBO, VWO) using my experience of more than 10 years. Most of the Dutch universities ask for OMPT-A OMPT-E OMPT-F or OMPT-D (online mathematics placement test) for specific Bachelors courses. If you need to achieve OMPT (online mathematics placement test), I can help you. My lessons are comprehensive, clear and person-specific. I make sure that the students learn quickly with minimum number of lessons.

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