PenjiJan 11, 20204 minPhase Diagrams and Lever RuleAt first glance, there seems to be a lot going on in a two-phase diagram. There are temperatures, percentages, different elements, and sy...

PenjiJan 11, 20203 minDC Steady State AnalysisFirst thing to address is what is D.C. Steady State. Basically, all that means is that the circuit has been active/running for a long ti...

PenjiJan 11, 20202 minEmpirical vs. Molecular FormulasOverview When going through introductory chemistry courses, a common problem that you will run into is your professor asking for either e...

PenjiDec 10, 20191 minImaginary Numbers and Euler’s Formulas ReviewA lot of people seem to freak out when they see an i in math or j in electrical engineering. So hopefully this will help. The first thin...

PenjiDec 10, 20193 minVolume of a Solid of Known Cross SectionFind the volume of the solid with these parameters. Since we have been given both boundaries for a base and the general shape of the cro...

PenjiDec 10, 20193 minMesh Analysis with SupermeshFind the value of i in the circuit below using mesh analysis. The first thing you should notice about this circuit is that there are two ...

PenjiDec 10, 20193 minHuman Anatomy Final Exam Tips and Example ProblemAnatomy can be a difficult topic to study for- especially when you have a whole semester’s worth of memorization and re-learning to cover...

PenjiDec 10, 20195 minUnderstanding Coffee Cup CalorimetryIntroduction to Coffee Cup Calorimetry When I first heard about a calorimeter, I had no idea what it was or what relevance it would have ...

PenjiDec 10, 20194 minProtein StructureProteins are macromolecule polymers, composed of a long chain of amino acid residues. One of the fundamental building blocks of life, pro...

PenjiDec 10, 20196 minAcid/Base Titration: An ExampleAs a student, when I was taught titration, it was accompanied by a long laundry list of scenarios: titration of a strong acid with a stro...

PenjiDec 10, 20193 minRoller Coaster LoopsAs with any problem, we must decide what lens/perspective we will look at the problem with. Will it be energy or kinematics? In this case...

PenjiDec 10, 20193 minDouble and Triple IntegralsWhen I was first taught integrals, I was told they are like area. More specifically, $$int_{0}^{1} f(x) d x$$ represents the infinite sum...

PenjiDec 10, 20196 minInspiration for Calculus Students: The Things We Take for Granted“Alright class, let’s take a look at a really interesting example today. This question is much too hard to be on the test, but I think i...

PenjiDec 10, 20191 minChemical Equilibrium – ICE TablesEquilibrium Review When a reaction is allowed to ‘run’ for some time, at some point it will no longer be favorable to continue forward or...

PenjiDec 10, 20193 minPointers in CWhat is a pointer? A pointer is simply a variable that stores the address of another variable. An address of a variable is where the vari...

PenjiDec 10, 20197 minYour Integral Calculus ToolboxMy favorite metaphor for a math and science education is the toolbox metaphor: every technique you learn is like a tool, which can be use...

PenjiDec 10, 20192 minInfinity and DNE in LimitsThe best way to approach why we use infinity instead of does not exist (DNE for short), even though they are technically the same thing, ...

PenjiDec 10, 20195 minPhase Planes and Solutions Curves: Qualitative AnalysisWhen I took MAT 22B, one of the topics I heard the most complaints about was Qualitative Analysis. But I thought Qualitative Analysis wa...

PenjiDec 10, 20194 minSeparable Differential Equations: Exponential DecayWhen I was in high school, my chemistry teacher presented me with a radioactive decay problem, and a formula that read: $$Q=Q_{0} * e^{-r...

PenjiDec 10, 20193 minHexadecimal Addition/Subtraction and 2’s ComplementThis article will cover unsigned addition and subtraction, and 2’s complement addition and subtraction in base 16 (hexadecimal). This art...