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

Key Concepts in Engineering Economics

Engineering Economics is the science dealing with quantitative analysis techniques for selecting the most preferable alternative from several technically viable options.

Fundamental Principles

Four fundamental principles must be applied in all engineering economic decisions:

• The time value of money
• Differential (or incremental) cost and revenue
• Marginal cost and revenue
• The trade-off between risk and reward

Core Terminology Explained

Ethics

A set of principles that guides a decision-maker in distinguishing between right and wrong.

Market Interest Rate

The interest rate quoted by financial institutions, which refers to the cost of money for borrowers or the earnings from money for lenders.

Interest Rate

The cost, or price,

Inheritance Tax Base Reductions

We highlight three primary types of base reductions:

Kinship-Based Reductions

The amount of reduction varies depending on the heir's kinship group. There are four standard groups:

• Group I: Descendants under 21 years old.
• Group II: Descendants aged 21 and older, ascendants, and the spouse.
• Group III: Second and third-degree collateral relatives by affinity.
• Group IV: Fourth-degree or more distant collateral relatives, and strangers.

Life Insurance Reductions

If the beneficiary is a spouse, ascendant, or descendant, a 100% reduction applies, up to a maximum limit.

Primary Residence Reductions

If the heir is a spouse, descendant, or ascendant and inherits the primary residence, a 95% reduction applies, up to a specific ceiling....

Precision Measurement Techniques and Instruments

Action

This is the procedure of comparing a magnitude, known as drive power, with another of the same nature to find the relation between them.

Magnitude

Everything is likely to be measured, such as length, mass, or time.

Metrology

The science that studies the measurement of magnitudes. It is currently attempting to standardize so that it will be unique for everyone, and called the International System of Units (SI).

Accuracy of Measurement

Accuracy of measurement is determined by its degree of approximation to the actual value of the magnitude or conventional that is measured. Accuracy is the ability of a measuring instrument to give results with very high accuracy.

Weighing

1. A) Direct measurement: We

Working Papers

These are the documents in which the auditor records the data and information obtained during their review, as well as the results of the tests performed.

Summary Warrant

A sample of major accounts that are an item.

Worksheet

This is the card that shows the groups or items that comprise the financial statements.

Decree of Detail

The items that comprise an account balance of a major account or any other account.

Certificates of Verification

The work performed to verify the correctness of an item or transaction.

Situations for Audit Work Plan

• Ensure that the service is clearly controlled.
• Be fully aware of what is being offered.

Conditions to Perform the Audit

• Maintain independence of mind regarding the specific client.
• Possess the ability to

Saw-Tooth Diagram for Inventory Management

The Saw-Tooth Diagram is a design used for input control and monitoring of stock. This graph serves to manage inventories, ordering, and the volume of flow itself.

The optimal quantity is determined according to the purchase price, storage costs, and handling volume. The optimal lot (often related to the Economic Order Quantity or EOQ, here referred to as PDID) includes the purchase price, carrying costs, PDID costs, overhead costs, and costs incurred until the item reaches the point of sale or placement.

Henry Gantt and the Gantt Chart

Henry Gantt was an American engineer belonging to the classical school of organization who planned American military transport during World War I, using bar-line graphs....

The Architecture of Basilica San Lorenzo

The Basilica San Lorenzo was built during the Quattrocento by the architect Filippo Brunelleschi, with construction conducted between 1422 and 1470. It is inspired by the Church of the Holy Cross (Gothic). The structure is divided into three naves and lateral chapels. In the middle of the transept is a cupola, which is surrounded by chapels. Opposite the middle of the transept is the main chapel.

Geometric and Mathematical Design

Its plan is a Latin cross with three naves and side chapels, forming a basilica that is almost extremely longitudinal. In the transept, which has little development, he set a dome with a lantern. The space was mathematically and geometrically modulated by the circle inscribed in

Boolean Algebra Fundamentals

Formulating Expressions: SOP and POS

Sum of Products (SOP) Formulation Steps

1. Circle rows in the truth table where the output $Y = 1$.
2. Identify the minterms corresponding to the circled rows.
3. Sum (OR) the selected minterms to form the final expression.

Product of Sums (POS) Formulation Steps

1. Circle rows in the truth table where the output $Y = 0$.
2. Identify the maxterms corresponding to the circled rows.
3. Multiply (AND) the selected maxterms to form the final expression.

Order of Evaluation in Boolean Algebra

Operations are evaluated in the following sequence:

1. Parentheses
2. NOT (Complementation)
3. AND (Multiplication)
4. OR (Addition)

Fundamental Boolean Laws and Theorems

• Identity Laws

  • $A + 0 = A$
  • $A \cdot 1 = A$

• Null Laws

  • $A + 1 = 1$
  • $A \cdot

Loan Amortization and EAR: You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

Using a financial calculator: N=60, I/YR=8/12=0.6667, PV=-40,000, FV=0. Solve for PMT: $811.06.

To calculate the EAR: EAR = (1 + nominal rate/m)^m - 1. In this case, EAR = (1 + 0.08/12)^12 - 1.0 = (1.00667)^12 - 1.0 = 8.30%.

Loan Amortization Example: Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, with semiannual payments beginning next June 30. Next year, Jan must report...

Statistics: The Science of Organizing Data

Statistics is the science of organizing data to draw conclusions or answer questions.

Descriptive Statistics

Descriptive statistics describe data through numerical summaries and graphs.

Variables

Variables are characteristics of individuals within the population.

Discrete and Continuous Variables

Discrete variables are counted, while continuous variables are measured.

Nominal and Ordinal Variables

Nominal variables are named, while ordinal variables are ranked or ordered.

Interval and Ratio Variables

Interval variables have no meaningful zero and equal intervals between values, while ratio variables have a meaningful zero.

Types of Variables in a Study

The response variable is what is being studied, the explanatory...

Map Generalization

Types of Symbols

• Line Symbols: Represent real-life objects with a linear path.
• Point Symbols: Represent objects occurring at a single point on Earth's surface using a dot.
• Area (Polygon) Symbols: Represent real-life objects spread over Earth's surface using geometric shapes.

Generalization Techniques

Reality contains too much information for a single 2D map. Generalized geometry and content make a map useful. A good map suppresses less important information to highlight what needs to be seen.

• Selection: Only relevant line, point, and area features are chosen.
• Classification: Grouping similar features and using a common symbol to represent them.
• Simplification: Reduction of unnecessary detail.
• Smoothing: Smoothing out abruptly joined