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).

Hello and welcome! I am a dedicated physics and mathematics tutor with extensive experience (5+ years) in helping students excel in their studies. Whether you're preparing for standardized tests like the SAT, SAT Subject Tests, AP-Physics, AP-Calculus, or pursuing advanced coursework like VWO, A-levels, OMPT-A, OMPT-B, OMPT-C, OMPT-D, or OMPT-F, I'm here to provide you with top-quality online tutoring sessions that cater to your specific needs. With my academic background (Ph.D. in Physics [ongoing], M.Sc. in Nanoscience, and B.Sc. in Physics and Mathematics) and a passion for teaching, I have successfully assisted students in mastering physics and mathematics for years. I understand that test preparation can be challenging and stressful, but with proper guidance and support, it can be conquered easily. I aim to help you develop a robust foundation by clarifying fundamental concepts. Course Highlights: 1. Physics Topics: - Mechanics - Electricity and Magnetism - Waves and Optics - Thermodynamics - Modern Physics - Quantum Mechanics - And more, tailored to your requirements! 2. Mathematics Topics: - Algebra - Geometry - Trigonometry - Calculus (AP and beyond) - Probability and combinatorics - Problem-solving techniques - Customized to suit your level and objectives! Whether you're seeking to boost your scores on standardized tests or aiming for excellence in your coursework, I am here to guide you. I tailor sessions to your learning needs. Feel free to suggest any additional topics or specific concepts to cover. We'll work together to improve weaknesses and enhance strengths, preparing you for the future. Interested? Contact me now for personalized online tutoring. *Note that the sessions will be held online (via Discord/Teams/Zoom).