Notes, summaries, assignments, exams, and problems for Other courses

First Stage: Gum Pad (Birth to 2 Years)

This stage lasts from birth until the completion of the deciduous maxillary gum pad.

• Maxillary Gum Pad: Horseshoe shape.
• Mandibular Gum Pad: U shape.
• Transverse Division: Elevated ridges are divided into segments for future deciduous teeth.
• Lateral Sulcus: Located distal to the canine area.

Gum Pad Occlusion

Gum Pad at Rest: The pads are not in contact, and the tongue is projecting.

Occlusal relationships are described in three dimensions:

1. Anteroposteriorly (Overjet): Anterior overjet; the mandibular lateral sulcus is posterior to the maxillary.
2. Vertically: Anterior open bite; posterior segments (Segment D) touch.
3. Transversely: The maxillary gum pad is wider than the mandibular (resulting in overjet).

Second Stage:

Human Anatomy: English-Spanish Vocabulary

• Mouth / Boca
• Knee / Rodilla
• Ears / Orejas
• Lower Arm / Forearm / Antebrazo
• Breast / Pecho
• Eyes / Ojos
• Ankle / Tobillo
• Elbow / Codo
• Waist / Cintura
• Face / Cara
• Calf / Gemelos
• Fingers / Dedos
• Thorax / Chest / Pecho
• Lips / Labios
• Heel / Talón
• Upper Arm / Arm / Brazo
• Nose / Nariz
• Eyebrows / Cejas
• Navel / Umbilicus / Ombligo
• Eyelids / Párpados
• Abdomen / Abdomen
• Forehead / Frente
• Thigh / Muslo
• Hand / Mano
• Back / Espalda
• Cheek / Mejilla
• Toe / Dedo del pie
• Eyelashes / Pestañas
• Leg / Pierna
• Foot / Pie
• Mandible / Jaw / Mandíbula

Medical Symptoms and Signs: English-Spanish

• Fatigue (Symptom) / Fatiga
• Fever (Sign) / Fiebre
• High Blood Pressure (Sign) / Presión Arterial Alta
• Skin Rash (Sign) / Erupción Cutánea
• Lump (Sign) / Bulto
• Color (Sign) /

Essential English Language Skills & Vocabulary

Effective Communication Vocabulary

• Make contact / Get in touch: Ponerte en contacto
• Keep up to date: Mantenerse al día
• Speak fluently: Hablar fluidamente
• Use mainly slang: Usar expresiones características
• Become bilingual
• Have a strong accent
• Native speaker: Hablante nativo
• Mother tongue: Lengua madre
• Second language
• Discussion: Debate

Common Language Pitfalls & Similarities

False Friends

Words that look or sound similar in two languages but have different meanings.

• Advertise: (Not "advertir" - to warn)
• Argument: (Not "argumento" - a plot or summary)

Cognates

Words that have a common origin and similar meaning across languages.

• Dialogue: Dialogar
• Comment on: Comentar

English Idioms & Expressions

• She puts

Equity and Financial Concepts

Free Cash Flow (FCF)

FCF_t = EBIT + DEP - CAPEX - ΔWC - TAX

ΔWC = Δreceivables + Δinventories - Δpayables + Δother items

TAX = (EBIT-Y_t)*T = EBIT*T - Y_tT

FCFE = FCF_t - Y_t - PRINC_t

FCF_t^u = FCF_t - Y_tT

Y = k_dD₀ (interest paid is cost of debt*value of debt)

Standard WACC

k_s=(1-L)k_e + Lk_d(1-T) | Use Standard WACC with FCF_u | ITS is not included in both FCF_u & k_s | Need Constant Target Leverage Ratio (L)

k_e = reflects operating and financial risk faced by investors | k_u = unlevered cost of equity (if firm had no debt), reflects operating risk

V₀ = U₀ + I₀ (Enterprise Value = value of operations + value of ITS) | Leave space for Standard WACC equation if k_its = k_d OR k_its = k_u

Standard WACC model implicitly assumes k_its... Continue reading "Understanding Equity, WACC, and Discount Rates in Finance" »

Morphological Analysis

This section details the morphological characteristics observed in early Middle English texts.

Nouns

Examples include: boc (book), Englisca boc (English book), Latin (Latin), Albin (Albin), Austin (Austin), feire (fair), fulluht (baptism), Frenchis clerc (French clerk), quene (queen), kinges (king), leaf (leaves). Note that boc (book) uses the singular form, while leaf (leaves) is the plural form. The pluralization of leaf does not follow the modern -s or -es form, illustrating historical variation.

Verbs

Examples include: bi-won (obtained), nom (took), makede (made), broute (brought), leide (laid), wende (turned). bi-won (obtained) shows the prefix bi-, which is less common in Modern English. The past tense forms nom (took)... Continue reading "Early Middle English Linguistic Analysis" »

Mastering Reported Speech: Tense Transformations

When reporting what someone said, the tenses often shift. Here's a breakdown of common tense changes:

• Present Simple (makes) → Past Simple (made)
• Present Continuous (is making) → Past Continuous (was making)
• Past Simple (made) → Past Perfect (had made)
• Past Continuous (was making) → Past Perfect Continuous (had been making)
• Present Perfect (has made) → Past Perfect (had made)
• Present Perfect Continuous (has been making) → Past Perfect Continuous (had been making)
• Past Perfect (had made) → Past Perfect (had made) (no change)
• Past Perfect Continuous (had been making) → Past Perfect Continuous (had been making) (no change)
• Future Simple (will make) → Conditional Simple (would make)
• Future

Vocabulary

• Being admired by the people around you
• Being part of a loving family
• Doing really well in your studies or work
• Having enough money to live well
• Having friends
• Having a lot of time to spend on the things I love doing
• Living in a nice neighborhood

Achieve, Carry Out, and Devote

• Achieve: *conseguir/lograr* (It helped her to achieve her aim of improving her family's happiness)
• Carry out: *llevar a cabo* (Susan's concerns prompted her to carry out her own research)
• Devote: *dedicar* (We know devoting more time...)

Stay, Spend, and Pass

• Stay: *permanecer, estar tiempo* (I stayed 2 hours listening to the radio)
• Spend: *pasar/gastar* (I have spent my life studying)
• Pass: *pasar tiempo*

Make, Cause, and Have

• Make: *hizo que* (The bad sound made the film difficult

Numerical Methods for Solving Equations

1.1 Solving an Algebraic System

This code defines a function f(V) and then solves the system f([x,y,z]) = [x,y,z] to find its fixed points using the algsys command.

faux(x,y,z) := [(x^2)/2 + 1/3, x+y+z/4, x^2-y^2+(z^2)/4];
f(V) := faux(V[1], V[2], V[3]);

ecus : f([x,y,z]) - [x,y,z];
algsys(ecus, [x,y,z]), numer;

1.2 Fixed-Point Iteration Method

This block implements the fixed-point iteration method. It starts with an initial guess (seed) and iteratively applies the function f until the norm of the difference between successive iterations is smaller than a given tolerance (10^-14).

nor(V) := sqrt(V.V);
fpprec:100;

block(
  semilla:[0,0,0],
  while nor(f(semilla)-semilla) > 10^(-14) do 
    semilla:bfloat(