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1. Mathematics and Physics Topics
2. Mathematics
   1. Algebra
      1. Arithmetic Rules
      2. Fractions and Percentages
      3. Powers
      4. Standard Form
      5. Simplification and Factorization
      6. Equations and Formula Manipulation
         1. Solving First and Second Degree Equations
         2. Solving Systems of Equations with Two Unknowns
         3. Adjusting and Transforming Formula Expressions
   2. Trigonometry and Geometry
      1. Area, Perimeter, Volume, and Surface Area
      2. Pythagorean Theorem
      3. Trigonometry in Right-Angled Triangles
      4. Vectors in the Plane
   3. Functions
      1. Linear Functions
      2. Polynomial Functions
      3. Exponential Functions
      4. Derivatives of Polynomial Functions
      5. Regression Using Digital Tools
3. Physics
   1. Introductory Topics in Physics
      1. Applying the SI System and Decimal Prefixes
      2. Concepts of Mass, Weight, and Density
      3. Uncertainty and Proper Use of Significant Figures
   2. Force and Straight-Line Motion
      1. Applying Newton's Laws
      2. Calculating Motion Equations with Constant Speed and Constant Acceleration
   3. Energy
      1. Calculating Work, Power, and Efficiency
      2. Calculating Kinetic and Potential Energy
      3. Applying Conservation of Energy
      4. First Law of Thermodynamics
   4. Study Program Specific Topics
      1. Briggsian Logarithms
      2. Combinatorics
      3. Probability and Statistics
      4. Phases and Phase Transitions
      5. Heat and Internal Energy
      6. Second Law of Thermodynamics
      7. Heat Capacity and Calorimetry
   5. Number Systems
   6. Algorithmic Thinking
4. Learning Outcomes
   1. Knowledge
   2. Skills
   3. General Competence

Mathematics and Physics Topics

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Mathematics and Physics Topics

This document covers various topics in mathematics and physics, with examples formatted in Markdown for rendering on GitHub. Each topic includes a link to the corresponding Wolfram Alpha computation.

Mathematics

Algebra

Arithmetic Rules

• Addition, subtraction, multiplication, and division of real numbers.
• Example: $a + b = c$ Wolfram Alpha Calculation

Fractions and Percentages

• Simplifying fractions, converting between fractions and percentages.
• Example: $\frac{a}{b} \times 100 = c%$ Wolfram Alpha Calculation

Powers

• Rules of exponents, calculations with powers.
• Example: $a^b = c$ Wolfram Alpha Calculation

Standard Form

• Expressing numbers in standard form.
• Example: $a \times 10^b = c$ Wolfram Alpha Calculation

Simplification and Factorization

• Combining like terms, factoring expressions.
• Example: $ax^2 + bx + c = 0$ Wolfram Alpha Calculation

Equations and Formula Manipulation

Solving First and Second Degree Equations

• Example: $ax + b = 0$ Wolfram Alpha Calculation
• Example: $ax^2 + bx + c = 0$ Wolfram Alpha Calculation

Solving Systems of Equations with Two Unknowns

• Example:

$$ \begin{cases} ax + by = c \ dx + ey = f \end{cases} $$

Wolfram Alpha Calculation

Adjusting and Transforming Formula Expressions

• Example: Rearrange $a = bc$ to solve for $c$ Wolfram Alpha Calculation

Trigonometry and Geometry

Area, Perimeter, Volume, and Surface Area

• Example: Area of a circle $A = \pi r^2$ Wolfram Alpha Calculation

Pythagorean Theorem

• Example: $a^2 + b^2 = c^2$ Wolfram Alpha Calculation

Trigonometry in Right-Angled Triangles

• Example: $\sin(\theta) = \frac{opposite}{hypotenuse}$ Wolfram Alpha Calculation

Vectors in the Plane

• Example:

$$ \mathbf{A} = \begin{pmatrix} a \ b \end{pmatrix} $$

Wolfram Alpha Calculation

Functions

Linear Functions

• Example: $y = mx + b$ Wolfram Alpha Calculation

Polynomial Functions

• Example: $f(x) = ax^n + bx^{n-1} + \ldots + c$ Wolfram Alpha Calculation

Exponential Functions

• Example: $y = a \cdot e^{bx}$ Wolfram Alpha Calculation

Derivatives of Polynomial Functions

• Example: $f'(x) = \frac{d}{dx}(ax^n + bx^{n-1} + \ldots + c)$ Wolfram Alpha Calculation

Regression Using Digital Tools

• Example: Linear regression Wolfram Alpha Calculation

Physics

Introductory Topics in Physics

Applying the SI System and Decimal Prefixes

• Example: Convert 5000 grams to kilograms Wolfram Alpha Calculation

Concepts of Mass, Weight, and Density

• Example: Density $\rho = \frac{mass}{volume}$ Wolfram Alpha Calculation

Uncertainty and Proper Use of Significant Figures

• Example: Calculate with significant figures Wolfram Alpha Calculation

Force and Straight-Line Motion

Applying Newton's Laws

• Example: $F = ma$ Wolfram Alpha Calculation

Calculating Motion Equations with Constant Speed and Constant Acceleration

• Example: $v = u + at$ Wolfram Alpha Calculation

Energy

Calculating Work, Power, and Efficiency

• Example: $P = \frac{W}{t}$ Wolfram Alpha Calculation

Calculating Kinetic and Potential Energy

• Example: $KE = \frac{1}{2}mv^2$ Wolfram Alpha Calculation

Applying Conservation of Energy

• Example: Total energy $E = KE + PE$ Wolfram Alpha Calculation

First Law of Thermodynamics

• Example: $\Delta U = Q - W$ Wolfram Alpha Calculation

Study Program Specific Topics

Briggsian Logarithms

• Example: $\log_{10}(x)$ Wolfram Alpha Calculation

Combinatorics

• Example: $nCr = \frac{n!}{r!(n-r)!}$ Wolfram Alpha Calculation

Probability and Statistics

• Example: Mean of a data set Wolfram Alpha Calculation

Phases and Phase Transitions

• Example: Phase transition of water Wolfram Alpha Calculation

Heat and Internal Energy

• Example: $Q = mc\Delta T$ Wolfram Alpha Calculation

Second Law of Thermodynamics

• Example: Entropy change

Wolfram Alpha Calculation

Heat Capacity and Calorimetry

• Example: $C = \frac{Q}{\Delta T}$ Wolfram Alpha Calculation

Number Systems

• Binary, decimal, and hexadecimal number systems
• Example: Convert $1010_2$ to decimal Wolfram Alpha Calculation

Algorithmic Thinking

• Boolean algebra and simple algorithm programming
• Example: Boolean expression $A \land B$ Wolfram Alpha Calculation

Learning Outcomes

Knowledge

The candidate:

• has knowledge of mathematics and physics as tools within their field.
• understands mathematical and physical concepts, theories, analyses, strategies, processes, and tools used in the field.
• can perform calculations, estimates, and problem-solving relevant to dimensioning and other issues within their study program.
• can evaluate their work according to mathematical and physical laws.
• can expand their knowledge and understand their own development opportunities within mathematics and physics.
• knows the nature and role of mathematics and physics in society.

Skills

The candidate:

• can explain the choice of calculation methods used to solve professional problems.
• can explain the choice of digital tools used for problem-solving in mathematics and physics.
• can use digital aids to solve equations and other mathematical tasks.
• can assess calculation results, reflect on their professional practice, and adjust under guidance.
• can find and refer to relevant information and professional materials in formula collections, tables, and textbooks.
• can map a situation and identify mathematical and physical issues.
• is familiar with and can apply basic physical laws and physics methodologies.
• can interpret and use models used in mathematics and physics.

General Competence

The candidate:

• can plan and carry out work tasks and projects alone and as part of a group by applying mathematics and physics in line with ethical requirements, guidelines, and the needs of the target group.
• understands the assumptions and simplifications made in their calculations.
• understands the scope and limitations of the methods used.
• can exchange viewpoints and collaborate on subject-specific issues with mathematics and physics as a cross-disciplinary foundation with peers and thus contribute to organizational development. +++