Mathematics Tutor - Specializing in Advanced Math for Special Needs

The Tutor and Student worked extensively on solving second-order linear differential equations, covering both homogeneous and non-homogeneous types. They practiced finding general solutions, particular solutions, and applying initial conditions to solve initial value problems, with a brief introduction to boundary value problems and advanced solution methods.

The Tutor and Student extensively practiced calculating areas enclosed by and between polar curves. They covered the formula for polar area, determining integration bounds, and distinguishing between common interior and bounded areas. The Student also worked on finding intersection points and applying symmetry for area calculations, with plans to receive additional homework problems.

The session focused on advanced calculus topics, including limits with absolute values, various integration techniques like substitution and partial fractions, and applications of the Fundamental Theorem of Calculus. The tutor and student worked through practice problems, and the tutor provided additional practice questions via email for future study.

The student and tutor worked through several calculus problems. They covered definite integrals, evaluating limits of piecewise functions, polynomial long division for integration, related rates, and the definition of Riemann sums. The student was encouraged to review integration formulas.

The Tutor and Student worked on solving second-order linear homogeneous differential equations with constant coefficients. They covered identifying homogeneous vs. non-homogeneous equations, the superposition principle, linear independence of functions, and three cases for solving differential equations based on the roots of the characteristic equation (distinct real, repeated real, and complex conjugate roots). The next session will focus on finding the constants c1 and c2 using initial and boundary value problems.

The student and tutor reviewed AP Calculus BC topics, focusing on related rates and optimization problems. They practiced setting up and solving related rates problems for conical shapes and worked through an optimization problem to maximize light intensity. The session concluded with a discussion about the Mean Value Theorem and plans to address more problems in the future.