Mathematical Theory and Its applications: Calculus and Introduction to Analysis

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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).

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