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Integration course from scratch for students and teachers
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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
Extra information
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I have videos and online classesLocation
Online via webcam
At student's location: Around Glendale, AZ, United States









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About Me
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I am Miguel Ángel, a Master of Mathematical Sciences graduate with a solid track record teaching mathematics and physics at the university, high school, and professional levels. My passion is helping students understand the most complex concepts through a clear, structured approach tailored to each student's pace.Throughout my career, I have worked with students of various levels, offering personalized tutoring, problem-solving, exam preparation, and ongoing support with assignments and projects. I specialize in areas such as Calculus, Algebra, Differential Equations, Probability, Statistics, Complex Variables, and Physics (Levels I, II, and III).
I work both in person and virtually, and I always strive to ensure that my classes not only clarify doubts but also strengthen students' confidence in their own abilities.
Education
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I have a Bachelor's degree in Mathematics from the Universidad de Oriente, Santiago de Cuba, year 2005 and a Master's degree in Mathematical Sciences from the University of Havana, year 2017.Experience / Qualifications
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I have more than 20 years of experience teaching Mathematics and Physics. I worked as a professor at the Universidad de Oriente, Santiago de Cuba until 2019, then I moved to Mexico in 2022 and was at the Autonomous University of Guerrero, where I gave several lectures and courses.Reviews (1)
He is a super good teacher!
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I'm Miguel Ángel, a Master of Science in Mathematics with extensive teaching experience. I provide personalized tutoring and tutoring classes in Mathematics and Physics, both online and in-person, tailored to any academic level.
I specialize in helping students understand everything from basic to advanced topics with clear explanations, ongoing support, and strategies that actually work.
What do I offer?
100% personalized advice
Support with homework, exams, and projects
Preparation for midterms and finals
Practical and theoretical classes
I work with all academic levels: secondary, pre-university, university, and graduate.
Subjects I cover
Basic Mathematics and Geometry
Differential and Integral Calculus
Linear and Nonlinear Algebra
Series and Differential Equations
Complex Variable
Numerical Mathematics
Probabilities and Statistics
Laplace, Fourier and Z transforms
Physics I, II and III
Do you want to learn Differential Equations from scratch?
This course is for you!
What will you learn?
Basic concepts and what is a differential equation
Simple methods for solving ordinary differential equations
Practical applications in real life (physics, biology, economics)
Step-by-step exercises to help you understand everything easily
Who is it addressed to?
Students beginning advanced mathematics
Professionals who want to strengthen their foundations
Anyone interested in understanding these key tools
Why choose this course?
Clear and uncomplicated explanations
Personalized support during the course
Study material and practical exercises included
Don't wait any longer and take the first step toward mastering differential equations!
Reserve your spot now!
Ask a question
Send a message explaining your needs and Miguel Angel will reply soon:
The more detail, the better.
Ex. "Hi, when are you available to meet for a lesson?"
Ex. "Hi, when are you available to meet for a lesson?"
Availability of a typical week
(GMT -04:00) New York
Mon | Tue | Wed | Thu | Fri | Sat | Sun | |
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0 | Monday at 0:00 | Tuesday at 0:00 | Wednesday at 0:00 | Thursday at 0:00 | Friday at 0:00 | Saturday at 0:00 | Sunday at 0:00 |
1 | Monday at 1:00 | Tuesday at 1:00 | Wednesday at 1:00 | Thursday at 1:00 | Friday at 1:00 | Saturday at 1:00 | Sunday at 1:00 |
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11 | Monday at 11:00 | Tuesday at 11:00 | Wednesday at 11:00 | Thursday at 11:00 | Friday at 11:00 | Saturday at 11:00 | Sunday at 11:00 |
12 | Monday at 12:00 | Tuesday at 12:00 | Wednesday at 12:00 | Thursday at 12:00 | Friday at 12:00 | Saturday at 12:00 | Sunday at 12:00 |
13 | Monday at 13:00 | Tuesday at 13:00 | Wednesday at 13:00 | Thursday at 13:00 | Friday at 13:00 | Saturday at 13:00 | Sunday at 13:00 |
14 | Monday at 14:00 | Tuesday at 14:00 | Wednesday at 14:00 | Thursday at 14:00 | Friday at 14:00 | Saturday at 14:00 | Sunday at 14:00 |
15 | Monday at 15:00 | Tuesday at 15:00 | Wednesday at 15:00 | Thursday at 15:00 | Friday at 15:00 | Saturday at 15:00 | Sunday at 15:00 |
16 | Monday at 16:00 | Tuesday at 16:00 | Wednesday at 16:00 | Thursday at 16:00 | Friday at 16:00 | Saturday at 16:00 | Sunday at 16:00 |
17 | Monday at 17:00 | Tuesday at 17:00 | Wednesday at 17:00 | Thursday at 17:00 | Friday at 17:00 | Saturday at 17:00 | Sunday at 17:00 |
18 | Monday at 18:00 | Tuesday at 18:00 | Wednesday at 18:00 | Thursday at 18:00 | Friday at 18:00 | Saturday at 18:00 | Sunday at 18:00 |
19 | Monday at 19:00 | Tuesday at 19:00 | Wednesday at 19:00 | Thursday at 19:00 | Friday at 19:00 | Saturday at 19:00 | Sunday at 19:00 |
20 | Monday at 20:00 | Tuesday at 20:00 | Wednesday at 20:00 | Thursday at 20:00 | Friday at 20:00 | Saturday at 20:00 | Sunday at 20:00 |
21 | Monday at 21:00 | Tuesday at 21:00 | Wednesday at 21:00 | Thursday at 21:00 | Friday at 21:00 | Saturday at 21:00 | Sunday at 21:00 |
22 | Monday at 22:00 | Tuesday at 22:00 | Wednesday at 22:00 | Thursday at 22:00 | Friday at 22:00 | Saturday at 22:00 | Sunday at 22:00 |
23 | Monday at 23:00 | Tuesday at 23:00 | Wednesday at 23:00 | Thursday at 23:00 | Friday at 23:00 | Saturday at 23:00 | Sunday at 23:00 |
from 70.55 QAROnline via webcam
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If you are not satisfied after your first lesson, Apprentus will find you another instructor or will refund your first lesson.
Online reputation
- Instructor since January 2024
- Phone number verified
- Google connected
- Linkedin connected
Availability of a typical week
(GMT -04:00) New York
Mon | Tue | Wed | Thu | Fri | Sat | Sun | |
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0 | Monday at 0:00 | Tuesday at 0:00 | Wednesday at 0:00 | Thursday at 0:00 | Friday at 0:00 | Saturday at 0:00 | Sunday at 0:00 |
1 | Monday at 1:00 | Tuesday at 1:00 | Wednesday at 1:00 | Thursday at 1:00 | Friday at 1:00 | Saturday at 1:00 | Sunday at 1:00 |
2 | Monday at 2:00 | Tuesday at 2:00 | Wednesday at 2:00 | Thursday at 2:00 | Friday at 2:00 | Saturday at 2:00 | Sunday at 2:00 |
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11 | Monday at 11:00 | Tuesday at 11:00 | Wednesday at 11:00 | Thursday at 11:00 | Friday at 11:00 | Saturday at 11:00 | Sunday at 11:00 |
12 | Monday at 12:00 | Tuesday at 12:00 | Wednesday at 12:00 | Thursday at 12:00 | Friday at 12:00 | Saturday at 12:00 | Sunday at 12:00 |
13 | Monday at 13:00 | Tuesday at 13:00 | Wednesday at 13:00 | Thursday at 13:00 | Friday at 13:00 | Saturday at 13:00 | Sunday at 13:00 |
14 | Monday at 14:00 | Tuesday at 14:00 | Wednesday at 14:00 | Thursday at 14:00 | Friday at 14:00 | Saturday at 14:00 | Sunday at 14:00 |
15 | Monday at 15:00 | Tuesday at 15:00 | Wednesday at 15:00 | Thursday at 15:00 | Friday at 15:00 | Saturday at 15:00 | Sunday at 15:00 |
16 | Monday at 16:00 | Tuesday at 16:00 | Wednesday at 16:00 | Thursday at 16:00 | Friday at 16:00 | Saturday at 16:00 | Sunday at 16:00 |
17 | Monday at 17:00 | Tuesday at 17:00 | Wednesday at 17:00 | Thursday at 17:00 | Friday at 17:00 | Saturday at 17:00 | Sunday at 17:00 |
18 | Monday at 18:00 | Tuesday at 18:00 | Wednesday at 18:00 | Thursday at 18:00 | Friday at 18:00 | Saturday at 18:00 | Sunday at 18:00 |
19 | Monday at 19:00 | Tuesday at 19:00 | Wednesday at 19:00 | Thursday at 19:00 | Friday at 19:00 | Saturday at 19:00 | Sunday at 19:00 |
20 | Monday at 20:00 | Tuesday at 20:00 | Wednesday at 20:00 | Thursday at 20:00 | Friday at 20:00 | Saturday at 20:00 | Sunday at 20:00 |
21 | Monday at 21:00 | Tuesday at 21:00 | Wednesday at 21:00 | Thursday at 21:00 | Friday at 21:00 | Saturday at 21:00 | Sunday at 21:00 |
22 | Monday at 22:00 | Tuesday at 22:00 | Wednesday at 22:00 | Thursday at 22:00 | Friday at 22:00 | Saturday at 22:00 | Sunday at 22:00 |
23 | Monday at 23:00 | Tuesday at 23:00 | Wednesday at 23:00 | Thursday at 23:00 | Friday at 23:00 | Saturday at 23:00 | Sunday at 23:00 |
from 70.55 QAROnline via webcam
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If you are not satisfied after your first lesson, Apprentus will find you another instructor or will refund your first lesson.
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