Luis Armando Casso Echalar
Patient Math Tutor Who Makes Complex Topics Simple Through Visuals and Real-Life Examples
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Luis Armando Casso Echalar
Diploma degree
/ 55 min
Luis Armando - Know your tutor
My name is Luis Casso, students can call me Lucho. I've been an unofficial tutor for three years already, and my passion lies in teaching mathematics to anyone who needs help. I helped students from various academic levels, ranging from the last year of high school to undergraduate college students. I can help with any topic up to Calculus I, and I will find time for teaching and making sure that every student who requires my help finds all the sources they need. As a math major student, I got to understand how maths could be harder for any student and how that made every high school student to have some sort of rejection towards the topic, but I personally wanted to become a math teacher because I think that everyone can learn math, and math can be used to teach not only as a school subject, but a way to understand the world and how it works. That is why teaching is my passion.
Luis Armando graduated from American International School of Bolivia
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Class overview
My teaching style goes hand in hand with making sure students understand the why behind things. Every formula has a reason to exist, and students need to grasp the logical process behind the terminology for a more solid kind of learning — rather than just memorizing formulas they’ll likely forget. I’m very patient and interactive when teaching, and I always try to go at a pace that students find comfortable. The topics I can teach are varied in content, and I find it easy to identify areas of mathematics that require specific logical processes. At the same time, I can teach different strategies and tricks so that students learn through mnemonic devices or visual examples — helping them understand how to approach any exercise or problem they encounter. I have experience working with several students and have been able to connect with them in different ways to help them understand the problems presented. Once they become comfortable with the concepts, they reach the solutions much more quickly.
Luis Armando also teaches
Calculus
College Algebra
College Math
Elementary School Math
Geometry
High School Math
Mathematics concepts taught by Luis Armando
The Student and Tutor reviewed Calculus II concepts, primarily focusing on modeling with differential equations, verifying solutions, and analyzing complex models like the FitzHugh-Nagumo equation. They practiced finding critical points and intervals of increase/decrease for functions. The session also included a discussion of upcoming exam topics and general study strategies.
Analyzing Dynamic Systems: Critical Points and Behavior
Modulus Arithmetic: Beyond Standard Counting
Modeling Real-World Scenarios with First-Order Differential Equations
Verifying Solutions to Differential Equations
Verifying Solutions for Second-Order Differential Equations
The Student and Tutor reviewed and practiced problems related to arc length and the area of a surface of revolution. They worked through examples involving algebraic and trigonometric functions, focusing on differentiation, integration techniques like u-substitution, and the application of specific integral formulas. The Student has an exam next Thursday, and the next session will be a recap of covered topics.
Arc Length Formula
Surface Area of Revolution: Principles & Formulas
Strategic Simplification via Perfect Squares
U-Substitution with Integral Limit Adjustment
Integration of Trigonometric Functions & Standard Forms
General Problem-Solving Framework
The Student and Tutor practiced solving various types of improper integrals, including those with infinite limits and discontinuities. They focused on setting up limits, applying appropriate integration techniques like u-substitution, and evaluating the convergence or divergence of the integrals. For the next session, they plan to cover arc length and the surface area of revolution.
Complex Improper Integrals & U-Substitution Review
Type 2: Improper Integrals with Discontinuities
Type 1: Improper Integrals with Infinite Limits
Introduction to Improper Integrals
The Student and Tutor conducted an initial diagnostic session for SAT math preparation, identifying the Student's strengths in algebra and advanced math and a need for improvement in geometry and trigonometry. They practiced a factorization problem and a complex geometry problem, applying the Pythagorean theorem and trigonometric functions. The session highlighted the importance of time management and strategic problem-solving for the SAT.
Strategic Exam Preparation & Time Management
Factoring Differences of Squares
Geometry Problem Decomposition
Pythagorean Theorem Applications
Trigonometric Ratios & Inverse Functions
SAT Math Section Breakdown
The Student and Tutor reviewed a quiz problem on trigonometric substitution, working through the steps to simplify the integral and convert the solution back to the original variable. They then moved on to approximate integration, covering the trapezoidal, midpoint, and Simpson's rules, and practiced these methods on an example problem. The next session is scheduled for Tuesday.
Trigonometric Substitution (Form √(a² - x²))
Reverting Trig Substitution (Right Triangle Method)
Setting Up Data for Numerical Integration
Trapezoidal Rule for Approximating Integrals
Simpson's Rule for Higher Accuracy Integration
The Student and Tutor focused on practicing the integration of rational functions through partial fraction decomposition. They worked through two example problems, one of which also involved trigonometric substitution, to prepare for the Student's upcoming Calculus 2 exam. The Student expressed confidence in their understanding of the material.
Categorizing Denominator Factors for Decomposition
Introduction to Rational Functions & Partial Fraction Decomposition
Simplifying Logarithmic Expressions after Integration
Combining U-Substitution with Partial Fractions
Integrating Basic Partial Fractions
Strategies for Solving Unknown Coefficients (A
B
C...)
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