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Integration course from scratch for students and teachers
From 27.19 C$ /h
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
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
I have videos and online classes
Location
At student's location :
- Around Glendale, AZ, United States
Online from United States
About Me
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.
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
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
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.
Age
Children (7-12 years old)
Teenagers (13-17 years old)
Adults (18-64 years old)
Seniors (65+ years old)
Student level
Beginner
Intermediate
Advanced
Duration
45 minutes
60 minutes
90 minutes
120 minutes
The class is taught in
Spanish
English
Reviews
Availability of a typical week
(GMT -05:00)
New York
Online via webcam
At student's home
Mon
Tue
Wed
Thu
Fri
Sat
Sun
00-04
04-08
08-12
12-16
16-20
20-24
My name is Miguel Angel, and I offer tutoring and academic support in Mathematics and Physics. I'd be happy to help you with any courses you need in these subjects. I have over 25 years of experience preparing students of all levels.
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
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
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