Notes, summaries, assignments, exams, and exercises for Mathematics for Baccalaureate

Organizations and Management

Organizations would: exist in all organizations. Organizations would manage resources, plan, coordinate, organize and control. Organizations must be well managed, doing the right things at the right time. They produce goods and services using factors of production: natural resources, capital (money, machinery, technology) and time and information (time that allows efficiency).

The Objective of the Company

The objective of the company is to satisfy the needs of consumers, generate profit and endure over time. Accounting is necessary to determine whether the company generates the expected profits.

The Company and the Environment

The company and environment: companies generate value for both internal and external stakeholders....

Population vs. Sample

The population represents the total universe of all possible observations, whether real or theoretical, while a sample is a subset of those observations. In experimental research, it is crucial to draw a representative, random sample that is not biased.

Frequency Distribution

A frequency distribution provides a numerical representation of data, helping to create a mental picture of how linguistic phenomena perform.

Descriptive Statistics

• Mode: The most frequent mark. It is quick to identify with a frequency distribution and is applicable to categorical data.
• Median: The score in the middle of an ordered list. It divides data into halves. It does not account for the values of all scores, only those in the middle position, making

Project Management Fundamentals: PERT and CPM

HL (Total Slack) is the time that can delay the completion of an activity without affecting the start of another and the final term. HM (Marginal Slack) refers to the most unfavorable slack case in the book.

The Critical Path

The Critical Path is the longest and most winding route. It defines the sequence that marks the current and critical events in a double-arrow network. An activity is considered critical when it has zero slack time. An event is critical when its TE (Earliest Time) and TL (Latest Time) are equal. It is essential to pay attention to critical paths, as any delay can affect the entire project. Both initial and final events are critical.

PERT: Probabilistic System

PERT is a probabilistic...

CME 315 - Midterm 1

1 — Solve using a bracket or initial guess. root = fzero(f, [xLower guess xUpper guess]); root = fzero(f, x0);

Minimum & Maximum: fminbnd

1 — Minimum candidate. [xMinCandidate, fMinCandidate] = fminbnd(f, a, b);

2 — Maximum candidate. xMaxCandidate = fminbnd(@(x) -f(x), a, b); fMaxCandidate = f(xMaxCandidate);

Linear Systems & Mass Balances

1 — Start from the balance. % Accumulation = In - Out + Net generation. % Steady state: In - Out + Net generation = 0

2 — Arrange equations into A*x = b. Rows = equations; columns = unknowns. Move known terms to the right.

3 — Diagnostics. n = size(A,2); Aug = [A b]; rA = rank(A); rAb = rank(Aug); d = det(A); % Square A only c = cond(A);

Gaussian Elimination

1 — Setup. N =...

Converting Decimal to 8-Bit Floating Point

Example 1: Convert 2.625 to 8-Bit Format

1. The integral part is calculated as: 2₁₀ = 10₂. For the fractional part:

   0.625	× 2 =	1.25	1	Generate 1 and continue with the rest.
   0.25	× 2 =	0.5	0	Generate 0 and continue.
   0.5	× 2 =	1.0	1	Generate 1 and nothing remains.

   So, 0.625₁₀ = 0.101₂, and 2.625₁₀ = 10.101₂.
2. Add an exponent part: 10.101₂ = 10.101₂ × 2⁰.
3. Normalize: 10.101₂ × 2⁰ = 1.0101₂ × 2¹.
4. Mantissa: 0101
5. Exponent: 1 + 3 = 4 = 100₂.
6. Sign bit is 0.

The result is 0 100 0101. Represented as hex, that is 45₁₆.

Example 2: Convert -4.75 to 8-Bit Format

1. The integral part is 4₁₀ = 100₂. The fractional part:

   0.75	× 2 =	1.5	1	Generate 1 and continue with the rest.
   0.5	× 2 =	1.0	1	Generate 1 and nothing remains.

   So, 4.75₁₀ = 100.11₂.
2. Normalize: