OpenLLM-France/wikimedia huggingface dataset:
# Physics with Calculus/Appendix 2/Examples of Derivatives

< Physics with Calculus

#### Motion

For x(t), position as a function of time
Velocity: The rate of change of position with respect to time
    ${\begin{matrix}\mathbf {v} (t)=f'(t)={dx \over dt}\end{matrix}}$
Acceleration: The rate of change of velocity with respect to time
    ${\begin{matrix}\mathbf {a} (t)=\mathbf {v} '(t)=f''(t)={d^{2}x \over dt^{2}}\end{matrix}}$
Jerk: The rate of change of acceleration with respect to time
    ${\begin{matrix}\mathbf {j} (t)=\mathbf {a} '(t)=f'''(t)={d^{3}x \over dt^{3}}\end{matrix}}$
Jerk is not commonly used in first year motion. Its main application is in dealing with travel of large objects that change their weight as they move due to a change in mass. One example might be a rocket travelling up from rest. As it burns fuel, its centre of gravity changes and as such, its acceleration is not constant (violation of Newton's Second Law).

#### Mechanics (Statics)

Given the details of the loading of a beam, we can represent it on a diagram of the beam with arrows indicating forces, curved arrows indicating moments (resistance to torque) and shaded regions representing universally varying or distributed loads. We can use this diagram (commonly known as a free body diagram) and the information contained within it to draw a diagram representing the shear forces (V in the beam, and can also derive an equation that represents these. The equation may not be as simple as a polynomial, and is quite often a series of continuous functions with endpoints at the points on the beam where the forces occur.
We can perform an indefinite integral on each of these segments of the beam to get more information on it. The indefinite integrals combine to form a diagram of the bending moments in the beam. Bending moments are a special type of moment, as the beam is most likely to fail where the bending moments are at a relative extrema. By definition, any indefinite integral will contain a constant, C. In the case of the bending moment diagram, our C is merely the endpoint of the previous segment. The only exception being when we have a moment, we add or subtract its value (depending on direction).
Hence, differentiating the bending moment model will give us the shear force.
Differentiating the shear force model brings us back to our loading diagram, and differentiating that will give us the shape of the deflection of the beam under the loading.
For any bending moment model b, as a function of distance from the end of the beam, x,
    ${\begin{matrix}b'(x)&=&V(x)\\b''(x)&=&V'(x)&=&\operatorname {FBD} (x)\\b'''(x)&=&\operatorname {FBD} '(x)&=&f(x)\end{matrix}}$
Where f(x) is a function describing the deflection of the beam.
# Physics with Calculus/Electromagnetism/Continuous Charge Distributions

If N charges is present, the electric field is obtained by summing over the contributions of each charge. This can be converted into an integral:
$\mathbf {E(\mathbf {r} } )=k_{e}\sum _{n=1}^{N}{\frac {q_{n}}{|\mathbf {r} -\mathbf {r} _{n}|^{2}}}{\frac {\mathbf {r} -\mathbf {r} _{n}}{|\mathbf {r} -\mathbf {r} _{n}|}}\rightarrow k_{e}\int d^{3}r'{\frac {\rho (\mathbf {r} ')}{|\mathbf {r} -\mathbf {r} '|^{2}}}{\frac {\mathbf {r} -\mathbf {r'} }{|\mathbf {r} -\mathbf {r} '|}},$
where $\rho$ is charge density, and
${\frac {\mathbf {r} -\mathbf {r'} }{|\mathbf {r} -\mathbf {r} '|}}$
is a unit vector pointing from the source point at $\mathbf {r} '$ to the field point at $\mathbf {r}$.
# MapleStory/Thief Guide/Armor

* MapleStory
* Complete Table of Contents
* Jobs
* Locations
* Shops
* Monsters
* Quests
* FAQs
* Glossary
* Authors list
* Beginner
* Warrior
* Bowman
* Thief
* Magician
* Skills
* Builds
* Weapons
* Armor

## Common Shield

| Name | Type | Requirements | Stats | Location | EMV | Additional Comments |
| Stolen Wooden Fence | Common Shield | Lvl 5 | 5 wDef | Lith Harbour | 1000 mesos | Cheap and effective |
| Pan Lid | Common Shield | Lvl 10 | (8-12) wDef | Very Rare Drop from Green Mushrooms | 300k to 500k mesos | Currently best shield for Bandit |

## Thief Shields

| Name | Requirements | Stats | Location |
| Seclusion Wristguard | Level 22 | Weapon Def. +17-21 Luk +1 | dropped by Green Trixter |
| Jurgen Wristguard | Level 22 | Weapon Def. +17-21 Dex +1 | dropped by Zeta Gray |
| Nimble Wristguard | Level 22 | Weapon Def. +17-21 Str +1 | dropped by Mateon |
# MapleStory/Quests/Exchange Quest

* MapleStory
* Complete Table of Contents
* Jobs
* Locations
* Shops
* Monsters
* Quests
* FAQs
* Glossary
* Authors list
* Quests
* Jump Quests
* Party Quests
* Exchange Quest
There's a man in Orbis named Staff Sergeant Charlie who is accepting etc drops from specific Ossyria monsters for 500 experience and will give you some rewards.
A list of the tradable items and possible rewards is already compiled on Hidden-Street here.
Some items are more efficient when comparing the gained exp to the exp gained while hunting the monsters. Specifically, the Solid Horns from the Jr. Kitties have the best ratio, as the only other monsters weaker in Ossyria are not accepted in the exchange quest. Other items, like Bain Collars and Lycanthrope Toenails, are merely a novelty exchange, as the reward likely pales in comparison to the items gained while hunting down the monsters.
Some items are also bought in large quantities in use of levelling lower level characters. Though a character levelled by this method needs to be a minimum level 10 to reach Orbis, training is incredibly fast, gaining 500 exp in a matter of seconds. At higher levels, however, this method becomes less efficient. Eventually the exchange becomes merely a way to clear useless etc items for usable items, though selling them for pure meso is always an option. Solid horns are usually preferred to level up a lower-level character, due to the number of players training on the Jr. Kitties at any one time. Zombie Teeth are more expensive, but the chance of getting a Fairy Wing as a reward can offset this extra cost. Also, players train on Zombies far longer than Jr. Kitties. Jr. Yeti Skins fall in between, more expensive from a higher-level monster, and providing better potions than Solid Horns, but nothing too special.
Every exchangable etc item has a specific scroll type (usually 10%) that has a small chance of being given as a reward for a trade-in. However, there are a few exceptions. Solid horns provide Return to Nearest Town scrolls, while Luster Pixie's Sunpieces provide the expensive 60% Cape INT scroll, contributing to the higher-than-average Sunpiece price. Some trade-ins also have special rare items. Notable examples are Ancient Scrolls from Hector Tails, Icicles from Werewolf Toenails (though rarely traded in), and the aforementioned Fairy Wings from Zombie's Lost Teeth.
# MapleStory/Thief Guide/Weapons

* MapleStory
* Complete Table of Contents
* Jobs
* Locations
* Shops
* Monsters
* Quests
* FAQs
* Glossary
* Authors list
* Beginner
* Warrior
* Bowman
* Thief
* Magician
* Skills
* Builds
* Weapons
* Armor

## Assassin

MY advice for this is to just get the weapons from the shop and kill what the guide told you. Upgrade your claws(like titan to mithril titan, gold if rich). Then make Meba and get +7. If your a bandit-thief then stay with the most up-datable weapons(try to get above average if cheap).

## Throwing Stars

| Star | Qty/Refill | Effects | Availablility |
| Subi | 500/150 | Attack +15 | Jr.Sentinel,Trixter,All Item Department Stores |
| Wolbis | 500/200 | Attack +17 | Jr.Cellion,Leatty,Fire Boar |
| Snowball | 800/800 | Attack +17 | Lupin, Tick |
| Mokbi | 700/350 | Attack +19 | Drum Bunny,Jr. Wraith, Jr. Pepe,Cold Eye,Green Trixter, Jr.Cerebes,Lunar Pixie, Luster Pixie, Stone Gollem |
| Wooden Top | 800/800 | Attack +19 | Dark Axe Stump |
| Kumbi | 500/300 | Attack +21 | Chirppy,Fire Boar,Jr. Lioner,Jr. Grupin,Lupin, Helly,Chronos,Drake,Hector,Stone Gollem |
| Icicles | 800/800 | Attack +21 | Cold Eye,Grupin,Yeti & Pepe, Exchange Quest |
| Maple Star | n/a | Attack +21 | GM event items |
| Tobi | 1000/700 | Attack +23 | Chronos,Master Chronos,Grupin,White Pang,Dark Stone Gollem, Mix Gollem,Wild Cargo,Dark Yeti & Pepe,Bain |
| Steely | 1000/700 | Attack +25 | Red Drake,Tauromacis,Yeti & Pepe,Dark Klock,Dual Ghost Pirate |
| Ilbi | 800/640 | Attack +27 | Mushmom, Lycanthrope, Spirit Viking |
| Hwabi | 800/? | Attack +27 | Zombie Mushmom |
# MapleStory/TOC

MapleStory
* Table of Contents
* Jobs
** Beginner
*** Builds
*** Weapons
*** Armor
** Warrior
*** Alternative Fighter Guide
*** Skills
*** Builds
*** Weapons
*** Armor
** Bowman
*** Skills
*** Builds
*** Weapons
*** Armor
** Thief
*** Skills
*** Builds
*** Weapons
*** Armor
** Magician
*** Alternative Ice/Lightning Magician Guide
*** Skills
*** Builds
*** Weapons
*** Armor
* Towns
** Training Location Guide
** Maple Island
*** Amherst
*** Southperry
** Victoria Island
*** Lith Harbor
*** Ellinia
*** Henesys
*** Kerning City
*** Perion
*** Sleepywood
** Ossyria
*** Orbis
*** El Nath
*** Aquarium
*** Ludibrium
*** Omega Sector
* Monsters
* Quests
** Jump Quests
** Party Quests
** Exchange Quest
* Items
** Use
** Etc.
* FAQs
* Glossary
* Authors list
# Piano/Accidentals

An accidental, in music theory, is a musical notation that is used to raise or lower the pitch of a note. There are a handful of accidentals - sharps, flats, naturals, double sharps, and double flats. In piano, when an accidental precedes a note, it tells the pianist to play a different note from the original. When an accidental appears in a measure, every note that is the same as the note being changed is changed the same way. In a key signature, accidentals retain their effects for the entire piece (unless a natural has been used to cancel it).
In this image, a sharp, a flat, and a natural accidental, respectively, can be seen.

## Sharps

A sharp raises the note by a half-step (or one key precisely to the right of the note being raised). They can written as #. A sharp does not necessarily mean a black key as sharps raise a note by a semitone, whether if it is a black or white key. An example of a sharp: B sharp sounds the same as, or is enharmonically equivalent to a C natural. G sharp becomes an A flat and so on.

## Flats

A flat lowers the note by a half-step (or one key precisely to the left of the note being lowered). They can be written as b. Flats also do not mean the presence of a black key as e of all flats lower a note by a semitone, regardless if it is a black or white key. An example of a flat: C flat is enharmonically equivalent to B natural. G flat sounds the samed as F sharp.

## Naturals

Naturals are used to cancel the effects of any accidental.

## Double Sharps

Double sharps raise the affected note by a whole-step (or two keys precisely to the right of the affected note).

## Double Flats

Double flats lower the affected note by a whole-step (or two keys precisely to the left of the affected note).
To remember the order of the flats or the sharps, keep in mind these mnemonics:
For the order of the flats: Battle Ends And Down Goes Charles' Father
For the order of the sharps: Father Charles Goes Down And Ends Battle
This page brought to you by Sage Jim (talk) 02:33, 28 March 2008 (UTC)
# Piano/Alternative Notation: Klavar

By far the easiest music notation to work with is Klavar (full name Klavarskribo). Klavar is easy to learn and easy to play particularly with keyboard instruments such as piano, organ or synthesizer. The system was invented by a Dutchman called Cornelis Pot.
Some time in the early 1930s Pot had a brilliant idea: he imagined black lines extending upwards from the black keys of a piano keyboard. He realized that if he could transfer that image onto paper and write dots on the lines or spaces formed by the pattern he could write music in a simple, practical way: it would show the performer exactly which notes to play. Pot published his ideas in 1931 and called his system of writing music Klavarskribo which is Esperanto for "Keyboard Writing". Here I will simply refer to it as 'Klavar'.
# Physiotherapy Assessment/Neurology

Neurology Assessment:

### Observation

General observations This begins from the moment you lay eyes on the patient. what type of gait they are acquiring while entering to the cubicle? what posture they are acquiring while standing or sitting on the chair? whether they are using any devices or not? Do they walk with a limp, how pronounced is it? Do they lean to one side? Once you're in the cubicle you're still observing their movements. Are they guarded, wincing, nervous, etc.?

### Local observations

Once you've asked them to remove any relevant clothing in an appropriate manner (wolf whistles are almost never called for), you can take a closer look at the area in question. Do you see any bruising (haematoma), swelling, inflammation, cuts (lacerations), stitches, bony abnormalities, etc. Sometimes the clues will be more apparent than others. One lady I saw had a ruptured head of biceps (she came in with 'shoulder pain'), which meant that her biceps muscle ended up being bunched up near her elbow. She complained more of discomfort than pain and couldn't remember any traumatic injury to the area. Needless to say, it wasn't difficult to find the source of her 'shoulder pain'.

### Palpation

The therapist must carefully select the structures to palpate from the clinical findings they acquired from the subjective interview and physical examination. Targeted palpation detects variation in temperature, pain, tissue structure and tenderness over certain anatomical features (such as tendons, ligaments and muscle).
# Paediatric assessment

The important thing to remember when assessing a very young child is that they probably don't want to be there (especially if they're in hospital). In fact, most adults don't want to be there either but at least they're able to recognise that it's probably in their best interests to attend. A child attends because somebody made them.
Play is going to be an important aspect of your assessment (as well as your treatment). If you can distract them with balls, trampolines, toys and wedges you'll get a lot further than with instructions, commands and regimes. Children want to climb up onto things. They want to throw balls and hang from beams. If you can make their trip to you a little more fun and a little less scary, you'll end up not only getting a better response to your treatment, but you may find yourself enjoying your job!

## Equipment
### Balls

(Keywords)Throwing, kicking, rolling, sitting, bouncing. Postural control, strengthening, co-ordination.

### Wedges

(Keywords)Wedges are good for stretching muscles, placing limbs into normal positions and props for climbing over, under and around.

### Trampolines

There is some controversy over the use of mini-trompolines (Rebound therapy) in rehabilitation programmes for children. Research in the US, UK and New Zealand has shown that the number of A&E admissions after trompoline-related injury is staggeringly high. Most conclude with a statement calling for a complete ban on the sale of recreational trampolines. However, they also found that most injuries came about as a result of unsupervised activity, which hopefully would never occur in a physio gym. The use of trampolines has (perhaps surprisingly) been shown to be effective in assisting with sputum clearance, among other, more well-documented effects.

### Mats

(Keywords)Rolling, tumbling, falling safely, clean.
# Pokémon/Pokédex/Komala
## Description

A Koala-like Pokémon.

## Base Statistics

A Normal type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Komala: fighting Moves that deal 0% of their damage to Komala: ghost
# Pokémon/Pokédex/Kricketune
## Base Statistics

A bug type

## Type Matching

Moves that deal 200% of their damage to Kricketune: fire, flying, rock Moves that deal 50% of their damage to Kricketune: grass, fighting, ground
# Pokémon/Pokédex/Krookodile
## Description

A crocodile-like Pokémon.

## Base Statistics

A Ground and Dark type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Krookodile: water, grass, ice, fighting, bug, fairy Moves that deal 50% of their damage to Krookodile: poison, rock, ghost, dark Moves that deal 0% of their damage to Krookodile: electric, psychic
# Pokémon/Pokédex/Kyogre
## Basic Statistics

* National Index: 382
* Johto Index: 382
* Hoenn Index: 198
* Stage: Basic
* Height: 4.5m/14'9"
* Weight: 352kg/776.0lb
* Gender Distribution: Genderless
* Ability: Drizzle
* Type: Water
* Species: Sea Basin
* Egg Group: Unbreedable
* Hatch Steps: 30720
* Catch Rate: 5
* Base Experience: 218
* Max Experience: 1250000
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | - | - | - | - | - | - |
| Base Stats (RS/FL/E) | 100 | 100 | 90 | 90 | 150 | 140 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | - | - | - | - | - | - |
| Max Stats (RS/FL/E) | 404 | 328 | 306 | 306 | 438 | 416 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are super effective on Kyogre: Electric, Grass
Move types which are not very effective on Kyogre:Fire, Ice, Steel , Water
All other move types are normal effectiveness on Kyogre.

## Moveset

| Level | Ruby / Sapphire | Fire Red / Leaf Green |
| Start | Water Pulse | Water Pulse |
| 5 | Scary Face | Scary Face |
| 15 | Ancientpower | Ancientpower |
| 20 | Body Slam | Body Slam |
| 30 | Calm Mind | Calm Mind |
| 35 | Ice Beam | Ice Beam |
| 45 | Hydro Pump | Hydro Pump |
| 55 | Rest | Rest |
| 60 | Sheer Cold | Sheer Cold |
| 65 | Double-Edge | Double-Edge |
| 75 | Water Spout | Water Spout |

### TM/HM

* RS/FL: Blizzard, Brick Break, Calm Mind, Dive, Double Team, Earthquake, Facade, Frustration, Hail, Hidden Power, Hyper Beam, Ice Beam, Protect, Rain Dance, Rest, Return, Roar, Rock Smash, Rock Tomb, Safeguard, Secret Power, Shock Wave, Strength, Surf, Thunder, Thunderbolt, Toxic, Water Pulse, Waterfall

## Variant Forms
### Primal Kyogre

Introduced in Pokémon Omega Ruby and Alpha Sapphire.

## Trading Cards

* EX Team Magma vs Team Aqua #3 - Team Aqua's Kyogre
* EX Hidden Legends #94 - Kyogre EX
# Pokémon/Pokédex/Kricketot
## Base Statistics

A bug type

## Type Matching

Moves that deal 200% of their damage to Kricketot: fire, flying, rock Moves that deal 50% of their damage to Kricketot: grass, fighting, ground
# Pokémon/Pokédex/Krokorok
## Description

A crocodile-like Pokémon.

## Base Statistics

A Ground and Dark type Pokémon.

## Type Matching

Moves that deal 200% of their damage to Krokorok: water, grass, ice, fighting, bug, fairy Moves that deal 50% of their damage to Krokorok: poison, rock, ghost, dark Moves that deal 0% of their damage to Krokorok: electric, psychic
# Pokémon/Pokédex/Lairon
## Basic Statistics

* National Index: 305
* Johto Index: 305
* Hoenn Index: 71
* Stage: Stage 1
* Height: 0.9m/2'11"
* Weight: 120kg/265.0lb
* Gender Distribution: 50% Male
* Ability: Sturdy/Rock Head
* Type: Steel/Rock
* Species: Iron Armor
* Egg Group: Monster
* Hatch Steps: 8960
* Catch Rate: 90
* Base Experience: 152
* Max Experience: 1250000
* Hold Item in Advance: Hard stone: 5%
| | HP | Attack | Defense | Speed | Special Attack | Special Defense |
| Base Stats (RB/Y) | - | - | - | - | - | - |
| Base Stats (GS/C) | - | - | - | - | - | - |
| Base Stats (RS/FL/E) | 60 | 90 | 140 | 40 | 50 | 50 |
| Base Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Base Stats (BW/B2W2) | – | – | – | – | – | – |
| Base Stats (XY/ORAS) | – | – | – | – | – | – |
| Base Stats (SM/USUM) | – | – | – | – | – | – |
| Base Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Max Stats (RB/Y) | - | - | - | - | - | - |
| Max Stats (GS/C) | - | - | - | - | - | - |
| Max Stats (RS/FL/E) | 324 | 306 | 416 | 196 | 218 | 218 |
| Max Stats (DP/PT/HGSS) | – | – | – | – | – | – |
| Max Stats (B/W/B2W2) | – | – | – | – | – | – |
| Max Stats (X/Y/ORAS) | – | – | – | – | – | – |
| Max Stats (SM/USUM) | – | – | – | – | – | – |
| Max Stats (Sword/Shield/BDSP) | – | – | – | – | – | – |
| Effort Points (Sword/Shield/BDSP) | – | – | – | – | – | – |

## Type Matching

Move types which are very good on Lairon: Fighting, Ground Move types which are good on Lairon: Water Move types which are bad on Lairon: Bug, Dark, Dragon, Ghost, Ice, Psychic, Rock Move types which are bad on Lairon: Flying, Normal Move types which don't effect Lairon: Poison

## Where to Catch

Lairon can be evolved from Aron at Level 32, and can also be caught in Victory Road.

## How to Evolve

Lairon evolves at level 42.

## Moveset

| Level | Ruby / Sapphire/ Emerald/ XD/ Colosseum | Fire Red / Leaf Green |
| Start | Tackle Harden Mud-Slap Headbutt | Tackle Harden Mud-Slap Headbutt |
| 4 | Harden | Harden |
| 7 | Mud-Slap | Mud-Slap |
| 10 | Headbutt | Headbutt |
| 13 | Metal Claw | Metal Claw |
| 17 | Iron Defense | Iron Defense |
| 21 | Roar | Roar |
| 25 | Take Down | Take Down |
| 29 | Iron Tail | Iron Tail |
| 37 | Protect | Protect |
| 45 | Metal Sound | Metal Sound |
| 53 | Double-Edge | Double-Edge |

### TM/HM

* RS/FL: Aerial Ace, Attract, Cut, Dig, Double Team, Earthquake, Facade, Frustration, Hidden Power, Iron Tail, Protect, Rain Dance, Rest, Return, Roar, Rock Smash, Rock Tomb, Sandstorm, Secret Power, Shock Wave, Strength, Sunny Day, Toxic, Water Pulse

### Evolution

* RS/FL: Body Slam, Endeavor, Smellingsalt, Stomp

## Trading Cards

* EX Ruby & Sapphire #36 - Lairon
* EX Ruby & Sapphire #37 - Lairon
* EX Sandstorm #41 - Lairon
* EX Team Magma vs Team Aqua #20 - Team Magma's Lairon
* EX Team Magma vs Team Aqua #36 - Team Magma's Lairon
| Basic: Aron | Stage 1: Lairon | Stage 2: Aggron |