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Calculus and Linear Algebra (High School and University Level)
From 87 € /h
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).
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).
Location
At teacher's location :
- Groningen, Netherlands
- Cologne, Germany
Online from Netherlands
About Me
Welcome!
I have recently obtained my Master's degree in Nanoscience (w/ cum Laude) at the University of Groningen and started my Ph.D. journey in Physics at the University of Cologne, Germany. Before that, I completed my Bachelor's degree in Physics and Mathematics at Jacobs University Bremen. I already have 6+ years of experience tutoring students as both a teaching assistant and a private tutor. I adapt my tutoring individually for each student so you can get the most out of it.
With me, you can expect the following advantages:
+ 100% attention and support
+ Safe and judgment-free learning environment
+ Learning pace and content adjusted to your needs
+ Identification, solving, and overcoming of problem topics/tasks
+ Elimination of knowledge gaps
+ Flexible lessons possible (also on weekends and public holidays)
+ Lessons for high school and university students
I look forward to hearing from you and working together to help you achieve your study goals. If you have any further questions, please do not hesitate to contact me.
I have recently obtained my Master's degree in Nanoscience (w/ cum Laude) at the University of Groningen and started my Ph.D. journey in Physics at the University of Cologne, Germany. Before that, I completed my Bachelor's degree in Physics and Mathematics at Jacobs University Bremen. I already have 6+ years of experience tutoring students as both a teaching assistant and a private tutor. I adapt my tutoring individually for each student so you can get the most out of it.
With me, you can expect the following advantages:
+ 100% attention and support
+ Safe and judgment-free learning environment
+ Learning pace and content adjusted to your needs
+ Identification, solving, and overcoming of problem topics/tasks
+ Elimination of knowledge gaps
+ Flexible lessons possible (also on weekends and public holidays)
+ Lessons for high school and university students
I look forward to hearing from you and working together to help you achieve your study goals. If you have any further questions, please do not hesitate to contact me.
Education
Regarding my academic qualification, I have been pursuing a Ph.D. in Physics at the University of Cologne, Germany, since 2023. Quite recently, I obtained my M.Sc. Nanoscience degree (w/ cum Laude) at the University of Groningen in the Netherlands. In 2021, I completed my Bachelor's in Physics and Mathematics from Jacobs University Bremen, Germany, with a 1.05 GPA. During my Bachelor's, I took various specialization courses such as Condensed Matter Physics and Devices, Advanced Quantum Mechanics, Elementary Particles and Fields, Advanced Optics, etc.
Experience / Qualifications
- 6+ years of private tutoring for high school and university-level students
- 3+ years teaching assistant at Jacobs University for Bachelor's courses such as Classical Physics, Modern Physics, Analytical Mechanics, and Quantum Mechanics. Additionally, worked as a teaching lab assistant at the University of Groningen for the 'electricity and magnetism' course. Currently, I am also working as a teaching lab assistant at the University of Cologne for a master's course in condensed matter.
- Organized MINT workshop in Physics for high school students around the Bremen area
- Actively involved in Physics and Math societies during my studies
- Participated in the International Physics Olympiad (IPhO 2016, Switzerland and Liechtenstein) and the University Physics Competition (UPC 2018, 2019, 2020)
- 3+ years teaching assistant at Jacobs University for Bachelor's courses such as Classical Physics, Modern Physics, Analytical Mechanics, and Quantum Mechanics. Additionally, worked as a teaching lab assistant at the University of Groningen for the 'electricity and magnetism' course. Currently, I am also working as a teaching lab assistant at the University of Cologne for a master's course in condensed matter.
- Organized MINT workshop in Physics for high school students around the Bremen area
- Actively involved in Physics and Math societies during my studies
- Participated in the International Physics Olympiad (IPhO 2016, Switzerland and Liechtenstein) and the University Physics Competition (UPC 2018, 2019, 2020)
Age
Teenagers (13-17 years old)
Adults (18-64 years old)
Student level
Beginner
Intermediate
Advanced
Duration
60 minutes
90 minutes
The class is taught in
English
Reviews
Availability of a typical week
(GMT -05:00)
New York
At teacher's location and via webcam
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
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 Mathematics A and/or B so that you can enter the university. This course will be tailored to your specific needs, and we can 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. Algebra and combinatorics
2. Functions and their graphs
3. Trigonometric functions
4. Logarithmic functions
5. Inverse functions
6. Transformations
7. Coordinate geometry
8. Quadratic equations
9. Equalities and inequalities
10. Vector and the dot product
11. Vector representation of a line
12. Algebraic methods in planar geometry
13. Parametric equations
14. Sequence and series
15. Limits and asymptotes
16. Derivatives and integral calculus
17. Probability and statistics
18. Normal and binomial distribution
19. Hypothesis testing
And many more...
*Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).
This class aims to prepare you for the CCVX and James Boswell entrance examination in Mathematics A and/or B so that you can enter the university. This course will be tailored to your specific needs, and we can 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. Algebra and combinatorics
2. Functions and their graphs
3. Trigonometric functions
4. Logarithmic functions
5. Inverse functions
6. Transformations
7. Coordinate geometry
8. Quadratic equations
9. Equalities and inequalities
10. Vector and the dot product
11. Vector representation of a line
12. Algebraic methods in planar geometry
13. Parametric equations
14. Sequence and series
15. Limits and asymptotes
16. Derivatives and integral calculus
17. Probability and statistics
18. Normal and binomial distribution
19. Hypothesis testing
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).
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).
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