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 the high school and university-level students. This class aims to provide an overview of calculus 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 their applications. Note that this course will be tailored to your specific needs, and we could mainly focus on the topics you are struggling with. Furthermore, please feel free to contact me and suggest any other topics you would like me to cover and teach. Outline of the course: ----------------------------------------------------------------------------------------------------------------------------------------------- 1.1 Limits of functions 1.2 Evaluate the limits using L'Hospital's rule (for 0/0, ∞/∞) 1.3 Continuity, types of discontinuities, intermediate value theorem ----------------------------------------------------------------------------------------------------------------------------------------------- 1.4 Introduction to differentiation (or derivative) 1.5 Tangent line to a curve, slope, instantaneous velocity 1.6 Rules and theorems for differentiation: power rule, product rule, chain rule 1.7 Derivatives of exp, log, and trigonometric functions 1.8 Implicit function and implicit differentiation 1.9 Derivative of inverse functions 1.10 Second and higher-order derivatives 1.11 Application of derivatives 1.12 Geometrical interpretation of the derivative of a function 1.13 Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function 1.14 First and second derivative tests, inflection points ----------------------------------------------------------------------------------------------------------------------------------------------- 1.15 Anti-derivative, indefinite integral 1.16 Techniques of integration: integration by substitution, integration by parts 1.17 Definite integral and its application (area between curves, application in physics) 1.18 Area as a definite integral 1.19 Areas between two curves and many more... *Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).

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).

Hi! 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 they can understand the fundamental concepts and excel in their studies. I have teaching experience of 5+ years in Physics and Mathematics to both high school and university-level students. I have expertise in the following courses: 0. All high school topics 1. Classical Physics (Newtonian mechanics, linear motion, rotational motion, collision theory, angular momentum, and many more) 2. Modern Physics (Electrostatics, Maxwell's law, motion of electrons in electric and magnetic fields, Quantum theory of light, Compton scattering, photoelectric effect, and many more) 3. Optics (Ray optics, wave mechanics, reflection and refraction, Fresnel's law, polarizer, matrix optics, interference, diffraction, and many more) 4. Quantum Mechanics (Schrödinger equation, Heisenberg uncertainty principle, commutation relation, the addition of angular momentum, matrix representation, density matrix, and many more) 5. Solid-state Physics (Crystal structure, wave diffraction, and the reciprocal lattice, crystal vibrations (phonons), the density of states, semiconductor physics, pn junction, transistors, and many more) *Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).

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 the high school and university-level students. This class aims to prepare you for the CCVX and James Boswell entrance examination in Physics so that you can enter the university. This course will be tailored to your specific needs, and we could mainly focus on the topics you are struggling with. Furthermore, please feel free to contact me and suggest any other topics you would like me to cover and teach. Topics of the course: 1. Mechanics 2. Oscillations and waves 3. Electrical circuits 4. Electric fields 5. Magnetic fields 6. Electromagnetic induction 7. Ray Optics 8. Pressure 9. Fluids and gases 10. Heat and thermodynamics 11. Sensors and automatic systems 12. Radiation and matter 13. Radioactivity and medical imaging 14. Nuclear energy 15. Light waves 16. Model of the atom 17. Basics of quantum mechanics and many more... *Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).