# My Math Book

## (Basics of Trig, Calculus, & Physics)

This post is s page by page table of contents with links. Cumulatively, this post makes the electronic/online version of one of my three hand written math books.

These are not intended to replace, but may supplement standard math texts. When I went through electrical engineering school after the army, I found I really struggled to understsnd the math concepts. My professors would explain things one way, Khan Academy would break it down another way, etc. I made it through school because whenever I found an explanation that clicked for me, I put it in my little book, which I referenced all the way up to the end. Some of the simpler concepts like dimensional analysis will probably stick forever once I get it - but others (like integration by partial fractions) I will most likely *never* commit to memory.

Anyway, this is the base-level book. It covers introductory concepts like SI prefixes and dimensional analysis, and works up through several of the basic concepts of physics.

Feel free to reference as needed, or jump around according to your interests. @mcsamm the hydraulic ram pump on PG52 might be useful for you as you tackle the challenges of delivering water to communities around Ghana. This design harnesses the powers of water pressure and momentum to deliver water to a location uphill from the original source. Or @cahlen, you might be in a good position to confirm, deny or just try the physics of spear fishing as illustrated on PG71. All I’m saying is, physics is cool and I’ve tried in this small volume to honor that legacy :)

I’d like to say that the individual pages will be updated with more notes as they come up, but I don’t really use this math much in real life, so I’m posting this mostly for preservation.

If you’re just checking it out for the heck of it, I recommend the physics applications. I tried to put these together in a way that was fun and informative. Most of these will have fun illustrstions and other non-mathy nuances to make it aesthetically pleasing for any passers-by.

Pages/Sections

- SI PREFIXES
- SI BASE UNITS & PHYSICAL QUANTITIES
*( Not Used )*- DIMENSIONAL ANALYSIS
- EXPONENTIAL, LOGARITHM, SQ ROOTS & QUADRATIC FORMULA
- TRIGONOMETRY: UNIT CIRCLE w RADIANS
- TRIGONOMETRY: UNIT CIRCLE w FUNCTIONS
- TRIGONOMETRY: UNIT CIRCLE w SIN & COS
- TRIGONOMETRY: CONSTRUCTION OF A SINUSOID
- TRIGONOMETRY: CHARACTERISTICS OF TRIG FUNCTIONS
- TRIGONOMETRY: TRIGONOMETRIC IDENTITIES
- TRIGONOMETRY: TYPES OF TRIANGLES
- TRIGONOMTRY: SOLVING TRIANGLES
- CALCULUS: THE DERIVATIVE OF
*f(x)* *( Above )*- CALCULUS: INTEGRAL OF
*f(x)* *( Above )*- CALCULUS: INTEGRATION WITH
*u*SUBSTITUTION *( Above )*- CALCULUS: INTEGRATION BY PARTS
*( Above )*- VECTORS: BASIC DESCRIPTION
- VECTORS: BASIC VECTOR OPERATIONS
- VECTORS: QUANTITATIVE CALCULATIONS
- VECTORS: MAGNITUDE & SCALAR MULTIPLICATION
- VECTORS: CALCULATING DOT PRODUCT
- VECTORS: CALCULATING CROSS PRODUCT
- CALCULUS: PARTIAL DERIVATIVES
- CALCULUS: PARAMETERIZED CURVES IN CUBIC REGION
- CALCULUS: SECOND DERIVATIVE TEST
- CALCULUS: CONSTRAINED OPTIMIZATION/LaGRANGE MULTIPLIERS
- CALCULUS: INTEGRATION BY PARTIAL FRACTIONS
*( Above )*- CALCULUS: INTEGRATION w/ TRIG SUBSTITUTION
*( Above )*- QUADRATICS PT2: COMPLETING THE SQUARE
- CALCULUS: L’HÔPITAL’S RULE
- PHYSICS: CLASSICAL MECHANICS
- PHYSICS: NEWTON’S 1st & 2nd LAWS
- PHYSICS: NEWTON’S 3rd LAW & COLLISIONS
- PHYSICS: 1D KINEMATICS
*(& PROJECTILE EQNS)* - PHYSICS APPLICATIONS: DISTANCE OF PROJECTILE
- PHYSICS APPLICATIONS: MAX
*h*OF PROJECTILE - PHYSICS APPLICATIONS: DISTANCE OF CAR OVER CLIFF
- PHYSICS APPLICATIONS: BALL KICK & ROCK RACE
- PHYSICS APPLICATIONS: NICE MAN PULLS SLED
- PHYSICS APPLICATIONS: MASS UP RAMP (FREEBODY)
- PHYSICS APPLICATIONS: SATELLITE ORBITS EARTH…
- PHYSICS: NEWTON’S LAWS & FREEBODY DIAGRAMS
- PHYSICS: UNIFORM CIRCULAR MOTION
*( Not Used )*- PHYSICS: HYDRAULIC RAM PUMP
*( Above )*- PHYSICS: FINDING THETA
- PHYSICS: TRANSVERSE MOTION (WAVES & SOUND)
- PHYSICS: TRANSVERSE MOTION: WAVE EQN, SPEED OF SOUND
- PHYSICS APPLICATIONS: SOUND WAVES
- PHYSICS APPLICATIONS: HARMONICS/FUNDAMENTALS OF GUITAR
- PHYSICS: MUSICAL FREQUENCY FORMULA
- PHYSICS APPLICATION: CLOSED END RESONATOR
- PHYSICS: BEAT FREQUENCIES/DEFINITION OF HARMONIC vs OVERTONE
- PHYSICS: DOPPLER EFFECT
*( Above )*- PHYSICS: SOUND LEVEL & INTENSITY
- PHYSICS: BASICS OF SOUND/ENERGY IN WAVES
- PHYSICS: BASICS OF WAVE MOTION
*( Above )*- PHYSICS: SIMPLE HARMONIC MOTION (BULLETS, BLOCKS & SPRINGS)
- PHYSICS: PLOT OF
*f(x)*AND 1st TWO DERIVATIVES - PHYSICS: DRAWING RAY DIAGRAMS (LENSES)
- PHYSICS APPLICATION: SPEAR FISHING (REFRACTION)
- PHYSICS: REFLECTIONS
- PHYSICS: MAXWELL’S EQNS
- TRANSCENDENTALS: pi,
*e*, phi - TRANSCENDENTALS: pi
- TRANSCENDENTALS:
*e* - TRANSCENDENTALS: phi

@mes I think I may have mentioned this book to you in one of our conversations in the comments - anyway I wanted to do this a while back but gave up due to the logistical challenges at the time - your STEM posts really inspired me to finalize this effort, so thank you for lighting the fire!

PS @adysscheryl Sorry the individual pages/posts weren’t properly tagged. I added tags to the last couple pages I uploaded, after seeing your comment. I may also go through over time and update them all to have tags. This was a pretty big undertaking and I’ve been trying for a few months to think of a better way to go about it, but so far creating the AZL INDEX support community was the best method I came up with. I apologize to anyone who was inconvenienced by the uploads required to pull this all together - I know it was intense, and I do not plan on repeating that any time soon.

Thanks for checking out some more of my work! As always, I hope you enjoyed witnessing as much as I enjoyed creating!

© Photos and words by @albuslucimus, except where otherwise indicated.

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