Blog and Discussion
Contact

Subscribe

New posts weekly.

Thank you!

Based in the Seattle Area.

Free study guides and discussions about various topics in Mathematics. Thanks for stopping by!

My Math Teacher is Terrible! (I can help.)

Jun 27
Jun 27 Summer homework for Algebra 2 students: Terrence Howard's claims

Phil Petrocelli

You can wade into this controversy as someone who has taken Algebra 2. I would really really like you to.

Nov 29
Nov 29 Trig integral two ways: Something interesting happens!

Phil Petrocelli

Seeing multiple ways to solve a problem is one of the beautiful things about using the tools of Mathematics in creative ways. This integral, done two different ways, reveals something interesting about two inverse trig functions.

Nov 28
Nov 28 A system of exponential and logarithmic equations

Phil Petrocelli

Systems of linear equations are part of high school Mathematics studies. But what about other types of systems of equations? Here, we'll look at a system that mixes exponential and logarithmic equations.

Oct 25
Oct 25 Flex your trig identity muscles with this tricky trig limit!

Phil Petrocelli

The use of trigonometric identities to rephrase problems in Calculus is a very important skill. In this limits problem, it really really helps!

Aug 25
Aug 25 Interesting series question - the notation saves us!

Phil Petrocelli

Sometimes a simple change in perspective helps us solve a problem quicker. Here, a simple change in the original, somewhat daunting notation is just what we need.

Aug 22
Aug 22 An advanced factoring trick for a tough limit problem

Phil Petrocelli

Sometimes, limit problems can be difficult. This is one such limit where an advanced factoring trick unlocks the solution.

Jul 20
Jul 20 An infinite series problem, two ways

Phil Petrocelli

Sometimes there are multiple ways to do a problem. This one can be approached somewhat systematically, with intuition helping us out.

Apr 11
Apr 11 A challenging trig limit with a cool algebra trick

Phil Petrocelli

Sometimes a Calculus problem is about non-obvious algebra. Here is one such instance. Let’s get into it!

Jan 1
Jan 1 A really cool discussion of indeterminate forms

Phil Petrocelli

For Calculus students, this topic can be very tricky. Here is a discussion that can help.

Sep 27
Sep 27 Properties of integrals and u-substitution: 2 problems from Reddit

Phil Petrocelli

Integration rules are simple. Sometimes, the rules show up in very interesting ways.

Sep 19
Sep 19 Free Calculus study guide: Difficult Limits

Phil Petrocelli

The season for difficult limits is upon us, Calculus I students! This guide is a big help! Download it!

Apr 26
Apr 26 A really great related rates problem from the College Board

Phil Petrocelli

A student brought this to a tutoring session recently. It's a really great question from the AP Calculus Exam prep materials. Nice one, College Board!

Apr 23
Apr 23 An interesting integration question: dividing an area in half with a line

Phil Petrocelli

Another cool integration question from the front lines of Calc I / AP Calc.

Apr 20
Apr 20 A tough trigonometric integral, solved multiple ways

Phil Petrocelli

This one is reduced to something super easy once we flex our integration muscles! King Property! Weierstrass substitution! Odd/even properties! Trig identities! One of my favorite articles to date!

Apr 14
Apr 14 A free Odd-Even function workbook - now on Desmos!

Phil Petrocelli

Here is a link to a Desmos workbook I made that allows us to decompose any function into its odd and even components. Super useful for various integration problems in Calculus.

Mar 29
Mar 29 My favorite math video right now

Phil Petrocelli

Papa Flammy isn’t kidding. This is an absolutely beautiful result, as is the path to getting there.

Mar 25
Mar 25 Solving a 2nd order ordinary differential equation using Variation of Parameters

Phil Petrocelli

Here is a problem from a first-year DiffEq class with a straightforward solution.

Mar 18
Mar 18 A cool second-order differential equation problem

Phil Petrocelli

Having a look at the machinations of how solving problems works sometimes results in a deeper understanding of what solving certain types of problems is all about. This differential equation problem is interesting, in that regard.

Feb 25
Feb 25 An infamous question from an MIT entrance exam, 1876

Phil Petrocelli

Via Popular Mechanics, this problem was more about making choices that ease solution by abstracting away some details we might not know what to do with, so as not to derail us as we work. This is my take, mostly an application of function notation.

Nov 19
Nov 19 The chirping crickets problem from Australia

Phil Petrocelli

This is a classic final exam question where it tests multiple things and asks us to jump between Math topics in order to correctly solve it. This is how we do this, Internet!

Load More
 

Powered by Squarespace