Mathematics Tutor - Specializing in Advanced Math for Special Needs

The Student and Tutor reviewed concepts related to Taylor polynomials, error bounds (Lagrange error bound), and the interval and radius of convergence for power series. They practiced calculating error bounds, determining the degree of Taylor polynomials, and applying the ratio test to find convergence intervals. The Tutor also provided practice problems to reinforce these topics.

The Tutor and Student reviewed and practiced applying the Fundamental Theorem of Calculus, Part One, for differentiation of integrals and converting Riemann sums into definite integrals. They also worked on finding intervals of increasing/decreasing functions and approximating integrals using right Riemann sums. The Student confirmed they have a formula list for integration and derivatives.

The tutor and student worked through various algebra and quantitative reasoning problems, including word problems, currency exchange, systems of equations, ratios, algebraic identities, and rationalizing denominators. The student practiced setting up equations, applying formulas, and solving for unknown variables, with a plan to reinforce these concepts through further practice problems.

The tutor and student reviewed concepts related to power series, including finding the radius and interval of convergence, and then moved on to Taylor polynomials and error bounds using the Lagrange remainder. They worked through several example problems to solidify understanding of these topics.

The session focused on multivariable calculus topics including divergence, curl, and Green's Theorem. The student practiced applying these concepts to calculate work done, area, and flux, and also worked on identifying conservative vector fields. The tutor recommended further review of Green's Theorem for an upcoming test.

The session covered GMAT quantitative reasoning topics including real numbers, absolute value, factors, multiples, division, and mean/median. The Student practiced identifying factors and multiples, applying division theorems, and calculating means and medians in the context of word problems. The tutor assigned practice questions from the class and will provide a PDF of the class notes.