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I strongly agree that students have very different learning styles and skill levels so depending on what works best for the students, I can be energetic and fun, patient and calm, or professional and precise. By helping the the student feel comfortable, they are more likely to open up and ask questions on the little and big things they don't yet understand. I have been tutoring for 5 years. I pay very close attention to details, hence I have perfected my teaching approach to most all issues in the subjects I specialize in (algebra, trigonometry, calculus, geometry, SAT, ACT math, differential calculus).
Typically, I can advance a student's understanding at a rate of about one chapter per hour. I have privately tutored 250 students all with different situations yet none have expressed their dissatisfaction.
From my point of view, it would be impossible to talk about calculus without taking in consideration differential equations. It has its applications in real life situations, such as radioactive decay and radio carbon dating, newton's law of cooling, natural growth equation just to name a few examples. There are differential equations of first and second degree orders, where solving a differential equation means finding an equation with no derivatives that satisfies the given differential equation. This procedure always involves one or more integration steps.
Linear Algebra is the branch of mathematics dedicated to the study of dimensional vector spaces, system of linear equations, matrices, eigenvalues and eigenvectors. Combined with calculus linear algebra facilitates the solution of linear systems of differential equations. The use of linear algebra has been proven in analitic geometry, engineering, physics, natural sciences and linear programming.
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