Notes, summaries, assignments, exams, and problems for University

Material Properties and Heat Treatment

• 2.1: Toughness
• 2.2: 14 × 10⁴, 90 × 10⁴
• 2.3: Stiffness
• 2.4: Toughness
• 2.5: Hardness
• 2.6: Malleability
• 2.7: 3–4% Carbon
• 2.8: Grey cast iron with ultimate tensile strength 300 N/mm²
• 2.9: Plain carbon steel (0.35–0.45% C, 0.7–0.9% Mn)
• 2.10: Mild steel
• 2.11: Less than 0.3% carbon
• 2.12: Sulphur
• 2.13: Chromium
• 2.14: Chromium
• 2.15: Above upper critical temperatures, cooled in still air
• 2.16: Case-hardening
• 2.17: Cyaniding
• 2.18: Case-carburising

Manufacturing and Tolerances

• 3.1: Aluminium
• 3.2: Fibre lines arranged in a predetermined way
• 3.3: Very small fillet radius
• 3.4: Easy removal of forged part from die cavities
• 3.5: Tolerances given on both positive and negative sides
• 3.6: Tolerance zone of hole and shaft overlap
• 3.7:

Versatile Writing Templates for Every Situation

This document provides structured templates for various communication scenarios, ranging from personal messages to formal complaints and narrative accounts.

1. Personal and Professional Correspondence

I am writing this because I recently experienced a situation related to this topic. It is essential to consider how these events affect our daily lives.

2. Structuring Your Narrative

On the one hand, everything seemed fine at first. However, circumstances changed, leading to unexpected challenges that required patience or immediate attention.

3. Addressing Unexpected Problems

On the other hand, a strange problem occurred. Whether dealing with public transport issues, customer service failures, or personal... Continue reading "Mastering Formal and Informal Writing Templates" »

Probability Basics

• Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
• Complement Rule: P(A') = 1 - P(A)
• Conditional Probability: P(B | A) = P(A ∩ B) / P(A) (if P(A) > 0)
• Law of Total Probability: P(B) = Σ P(B | A_i)P(A_i)
• Bayes' Theorem: P(A_k | B) = P(B | A_k)P(A_k) / Σ P(B | A_i)P(A_i)
• Independence: P(A ∩ B) = P(A)P(B) → then P(A | B) = P(A)

Counting Principles

• Multiplication Rule: n₁ × n₂ × ...
• Permutation (Order Matters): nPr = n! / (n - r)!
• Combination (No Order): C(n, r) = n! / (r!(n - r)!)
• Distinguishable Permutations: n! / (n₁! n₂! ...)
• Probability (Equal Outcomes): P(A) = (# favorable) / (# total)

Discrete Distributions

Mean: E[X] = Σ x f(x)   Variance: Var(X) = E[X²] - (E[X])²

• Binomial(n, p): P(X = x) = C(n, x)p^x(1 - p)^{n - x}, E = np, Var

Fruits and Vegetables

Fruits: Grape, strawberry, pineapple, apple, banana, melon, orange, pear, avocado.

Vegetables: Pea, carrot, onion, pepper, tomato, cucumber, potato.

Singular and Plural Forms

Use a before consonants and an before vowels.

• a: Cucumber, pineapple, grape, pea, potato, banana, melon, pear, strawberry, carrot, pepper, tomato.
• an: Apple, orange, avocado, onion.

Plural Nouns

• Pepper → Peppers
• Strawberry → Strawberries
• Tomato → Tomatoes
• Onion → Onions
• Carrot → Carrots
• Pineapple → Pineapples
• Avocado → Avocados
• Grape → Grapes
• Melon → Melons
• Pea → Peas
• Pear → Pears
• Apple → Apples
• Banana → Bananas
• Orange → Oranges
• Potato → Potatoes
• Cucumber → Cucumbers

Calendar and Dates

Months of the Year

There are 12 months in a year.

• Which month

Phonetic vs. Phonological Perspectives

Looking at syllables from a phonetic point of view is different from the phonological perspective. Phonetically, syllables are described according to how they are produced and how they sound.

A syllable normally has a central part, which has little or no obstruction to the airflow and sounds louder. This central part is usually a vowel. Before and after this centre (that is, at the beginning and end of the syllable), there is more obstruction to the airflow and the sounds are usually less loud.

The Articulatory Approach

One phonetic approach tries to define syllables according to the articulatory effort needed to produce them. The psychologist R. H. Stetson suggested that syllables are related to chest pulses,... Continue reading "Phonetic Analysis of Syllable Structure and Division" »

Data Types and Vector Creation

• Nominal → names
• Ordinal → order
• Interval → equal spacing
• Ratio → real math possible

Creating Vectors

c(1, 2, 3) # numeric
c("a", "b") # text
c(TRUE, FALSE) # logical

Vector Functions

numeric(5) # 0 0 0 0 0
rep(2, 5) # 2 2 2 2 2
seq(1, 10) # 1 to 10

Matrix Operations

A matrix is a table of numbers: matrix(1:12, nrow=3)

• + → add
• %*% → matrix multiply
• t() → transpose
• solve() → inverse
• det() → determinant

Note: Standard deviation is the square root of the variance.

Understanding trim=0.10 in R

It means to trim 10% from each end of the dataset.

Reading Data

return <- fund_return[,1]

Descriptive Statistics Functions

length(return)

Gives the number of observations (e.g., 76).

mean(return)

Calculates the ordinary average.

median(

The Bear Came Over the Mountain: Identity and Loss

The Themes: Loss of identity when entering the care home. Fiona's memory loss is serious and dangerous (using sticky notes, calling Grant for directions). Meadowlake is seen as comfort and renewal but contrasts with the emotional reality inside the institution, which lacks good emotional care. Kristy compares Fiona to a child, suggesting the elderly are viewed as children. Grant dreams about a letter, reflecting guilt and unresolved remorse; her illness forces him to confront his unfaithfulness and the need to repair. He promises her a new life, yet there is a pervasive fear of aging and loss of dignity.

Grant's Emotional Disorientation and Aubrey

Grant gets lost in the corridors of the residence,... Continue reading "Literary Analysis: Aging, Memory, and Sacrifice" »

Data Warehouse

A Data Warehouse (DW) is a centralized, integrated repository designed for analysis rather than transaction processing. It consolidates data from multiple OLTP systems to support reporting, dashboards, and advanced analytics, serving as a single source of truth for strategic decision support.

Key Properties

The data is curated to be subject-oriented, integrated, time-variant, and non-volatile, ensuring data quality and consistency. Unlike OLTP, the DW is built for read-heavy analytics and historical trends, providing the governance needed for managers to trust the KPIs.

Process Context

Data flows via ETL (Extract-Transform-Load) into the DW, typically in scheduled batches (e.g., nightly). This process standardizes and cleanses data,... Continue reading "Data Warehousing and Business Intelligence Essentials" »

Unit 7: Civil War and Reconstruction

• Causes: Sectional tension over slavery; Popular Sovereignty (local voting on slavery) led to "Bleeding Kansas."
• John Brown: Radical abolitionist; the 1859 Harpers Ferry raid signaled imminent war.
• Abraham Lincoln: Won the 1860 election on a "Free Soil" platform, triggering Southern secession.
• The War: Shifted from "preserving the Union" to "abolition" after the Emancipation Proclamation (1863).
• Turning Point: Gettysburg (1863); Lincoln’s Gettysburg Address defined the "new birth of freedom."
• Reconstruction Amendments: 13th (ends slavery), 14th (citizenship/equal protection), and 15th (Black male suffrage).
• Conflict: President Johnson (lenient) vs. Radical Republicans (strict/Military Reconstruction).

Unit 8: Jim

Network Delay and Performance Metrics

Understanding the components of network delay is essential for optimizing data transmission:

• d-proc (Processing Delay): Checks for bit errors and determines the output link; typically less than a microsecond.
• d-queue (Queuing Delay): Time spent waiting at the output link for transmission, heavily dependent on network congestion.
• d-prop (Propagation Delay): Calculated as Link Length / (2 x 10⁸).

Key Variables: a = average packet arrival rate, L = packet length, R = link bandwidth.

DNS Record Types

The Domain Name System (DNS) uses Resource Records (RR) in the format: (name, value, type, ttl).

• Type A: Name is the hostname; value is the IP address.
• Type CNAME: Name is an alias for a canonical name; value is the actual