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Start of the Integration Course from scratch for students and teachers. Course: Integration From Scratch General Objective: Guide the student from the basics to a solid mastery of indefinite and definite integrals, techniques, and applications. Module 1: Previous Foundations and Motivation Goals: Understand the concept of area under the curve as a motivation for the integral. Establish a basis with functions and derivatives. Contents: 1. What is integration? (visual intuition) 2. Review of functions (linear, quadratic, exponential) 3. Derivative and its relationship with the integral 4. Introduction to the integration symbol Exercises: Identify areas under simple curves (visually). Relate known derivatives with antiderivatives. Module 2: Indefinite Integrals Goals: Learn to calculate antiderivatives of common functions. Contents: 1. Definition of indefinite integral 2. Integration rules: Constant Powers Addition/subtraction 3. Integration by substitution 4. Integration by parts (simple introduction) Exercises: 15 graded exercises with feedback. Module 3: Definite Integrals and Fundamental Theorem Goals: Calculate exact areas under curves using definite integrals. Understand and apply the fundamental theorem of calculus. Contents: 1. Definition of definite integral 2. Geometric interpretation 3. Properties (linearity, additivity) 4. Fundamental Theorem of Calculus Exercises: 10 visual exercises + 10 algebraic exercises. Module 4: Integration Techniques Goals: Use advanced techniques to integrate more complex functions. Contents: 1. Trigonometric substitution 2. Partial fractions 3. Integration by parts (formal) 4. Numerical methods: trapezoidal rule Exercises: 20 problems per technique, with guided solutions and free practice. Module 5: Applications Goals: Apply integration to real-world problems. Contents: 1. Calculation of areas between curves 2. Volume of solids of revolution 3. Work and energy 4. Physical and economic problems Exercises: 10 practical problems with real-life context. Module 6: Evaluation and Final Challenges Goals: Measure learning and reinforce skills. Contents: 1. Final multiple-choice exam and development 2. Level-based challenges 3. Corrections in video or PDF Additional resources: Formula notebook Bank of integrals Explanatory videos Downloadable PDFs with theory and exercises

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Many students lose confidence in math during the school year due to stress, fast-paced classes, or gaps in understanding. This summer program helps students rebuild confidence, strengthen fundamentals, and prepare calmly for the next academic year. This program is designed for students who want to: - catch up on difficult topics - prepare for the next school year - improve grades and confidence - build strong problem-solving skills - prepare for exams and entrance tests Lessons are adapted individually for each student and explained step-by-step in a clear and patient way. I focus not only on solving exercises, but also on helping students truly understand concepts and think independently. After the first lesson, I create a personalized study plan based on the student’s level, goals, and areas that need improvement. Lessons are interactive, organized, and supportive, with homework and additional practice materials when needed. Suitable for: - Middle school students - High school students - IB students - Students preparing for exams ! ! ! Summer availability is limited to ensure individual attention for each student.

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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 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).

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I hold a PhD in Mechanical Engineering and currently work as a post-doctoral researcher in the Aerospace Engineering Faculty at TU Delft (Delft University of Technology). Key topics that I teach for this course include: • Calculus: Differentiation & integration, Multivariable calculus • Linear Algebra: Matrices, vectors, systems of equations, Eigenvalues and eigenvectors • Differential Equations: First- and second-order ODEs, Laplace transforms • Complex Numbers: Polar form, Euler’s formula • Vector Calculus: Gradient, divergence, curl, Line and surface integrals • Series & Transforms: Taylor series, Fourier series I understand that not all teachers excel in teaching Engineering and Mathematics courses and explaining their importance to students. Courses with strong mathematical backgrounds may become boring for students who lack a solid mathematical basis. To address this, I take a student-centered approach, starting from the basics to actively engage all students, including those with weaker mathematical backgrounds. I also provide practical examples to demonstrate the real-world significance of what they are learning, inspiring and fostering their interest in the subject matter. If you have any additional questions before starting a class, please feel free to ask me. I am here to assist! :)

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Seven years of experience in the mission of providing academic support to students in ESO or Bachillerato (Science or Social Sciences), university students in the first year and students of the IGCSE, Alevel and IB programs (Ed Excel or Cambridge), In addition to the classes themselves, I offer permanent online support for students' queries via WhatsApp (especially important during study periods prior to exams), guidance in the use of technological tools (programs, videos or web pages) that can contribute to improving the student's training in Mathematics. We educate to train the student in Mathematics. University courses I have recently supported include Business Mathematics for students at IE Business School, Rey Juan Carlos University, European University of Madrid, CUNEF, and Carlos III University. I also provide support for programs in Probability and Statistics, Financial Mathematics, and Mathematical Programming (experience with students from the School of Economics at the Autonomous University of Madrid). My hourly rate decreases as the session length increases. The most cost-effective rate is for a two-hour session.