Calculus I II & III

The Study of Infinitesimals

Physics has given me a thorough understanding of both the material found in calculus classes as well as how to apply it to physical and scientific problems. Calculus is another language of math to learn and so getting a good foundation in the fundamentals of Calculus makes the class that much more manageable. I have taught all three levels of calculus (which includes both AP Calc AB and BC) many times and am very successful at imparting the understanding needed in these classes. Whether it’s helping you prepare for an AP test or working with you through the semester on your Calculus class, I would love to work with you in mastering your goals!

~ Finding limits (numerical and analytic)

~ One-sided and indeterminate limits

~ Continuity

~ The definition of the derivative

~ Differentiation (power, product, quotient, chain rules)

~ L’Hôpital’s rule and differentiability

~ First and second derivative tests

~ Slopes and tangent lines

~ Second derivative test and concavity

~ Related rates problems

~ Mean and intermediate value theorems

~ Riemann sums and areas under curves

~ Indefinite/definite integrals and antiderivatives

~ The fundamental theorem of calculus

~ Average values

~ Displacement, velocity and acceleration

~ Areas between curves

~ Volumes of revolution and cross-sections

~ Arc lengths and parameterizations

~ Exponential growth

~ Basic Differential Equations

~ Convergence and divergence tests

~ Arc length

~ Intro to vector calculus

~ Improper integrals

~ Polar coordinates and calculus

~ Equations of lines, planes and surfaces

~ Planar geometry and 3D representations

~ Multivariable and vector functions

~ Spherical polar and cylindrical coordinates

~ Partial derivatives

~ Derivatives and rules in multiple dimensions

~ Directional derivatives

~ Tangent planes and lines in 3D

~ The gradient vector operator

~ Lagrange Multipliers

~ Double integrals and the Jacobian in various coordinates

~ Surface area and volume

~ Vector fields and line integrals

~ Green’s theorem

~ Curl and divergence

~ Surface integrals

~ Stoke’s theorem

~ Divergence theorem