Mathematics Tutor - Specializing in Advanced Math for Special Needs

The Tutor and Student reviewed the Divergence Theorem, its relationship to other calculus theorems, and its application in calculating surface integrals via volume integrals. They practiced several problems involving vector fields, surfaces, and volumes, with the goal of preparing the Student for an upcoming test.

The Tutor and Student worked through AP Calculus BC problems, focusing on vectors, parametric equations, and motion along a curve. They practiced finding velocity, speed, acceleration, slope of the tangent line, total distance traveled, and position using calculus principles and the Fundamental Theorem of Calculus. The Tutor also provided an overview of important AP Calculus BC topics.

The Student and Tutor worked through problems related to power series, geometric series, Taylor series, derivatives of series, and differential equations. The Student practiced determining convergence, finding coefficients, and solving for particular solutions. Follow-up was scheduled to further discuss differential equations after the Student's upcoming test.

The student and tutor worked on problems related to infinite series, Taylor series, and power series in preparation for an upcoming AP Calculus BC test. They covered topics such as finding intervals of convergence, determining coefficients in Taylor series, and using the ratio test. The tutor will send additional practice problems focusing on Taylor series and error bounds for the student to work on independently.

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.