Engineering

Engineering Principles

# Maths for engineering

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Maths for engineering

**Maths for Engineering Principles**

**Basic Maths**

- Understand and apply the basic principles of arithmetic, including
**addition**,**subtraction**,**multiplication**, and**division**. - Demonstrate understanding of fractions, decimals, and percentages, and the conversion between these.
- Apply principles of
**ratio**and**proportion**to practical engineering problems. - Recognise the importance of
**significant figures**and**decimal places**in calculations.

**Algebra**

- Work confidently with
**algebraic expressions**and**equations**. - Know how to implement
**indices**and**logarithms**in equations. - Recognise and manipulate
**linearity**, understanding direct and inverse relationships. - Understand how to solve simultaneous equations.
- Apply principles of
**inequalities**.

**Geometry and Trigonometry**

- Identify and calculate properties of basic geometric shapes: triangles, quadrilaterals, pentagons, hexagons, and circles.
- Understand and apply
**Pythagoras' theorem**and trigonometric ratios (**sine**,**cosine**,**tangent**) to solve problems in 2D and 3D shapes. - Utilise
**circle theorems**and properties of angles in polygons. - Apply principles of vectors and matrix arithmetic in engineering contexts.

**Calculus**

- Understand and apply principles of
**differentiation**to find gradients and tangents of curves, rates of change, and optimisation problems. - Use
**integration**to find areas under curves and solve problems related to displacement, velocity, and acceleration. - Understand and apply the fundamental theorem of calculus.

**Statistics & Probability**

- Understand definitions and calculation methods for
**mean**,**median**,**mode**, and**range**. - Use probability to predict outcomes in an engineering context.
- Interpret statistical data in relation to distributions and population.
- Understand and apply principles of
**standard deviation**and**variance**to measure risk and variability.

**Complex Numbers**

- Understand and apply principles of
**i**(imaginary unit) in complex number calculations. - Demonstrate an ability to perform addition, subtraction, multiplication, and division with complex numbers.
- Implement
**Euler's Formula**to exponentiate complex numbers in certain types of rotating objects or oscillating systems.

Remember, it's not just about knowing how to complete the calculations and solve problems – it's about understanding the underlying principles and being able to apply them to a variety of engineering concepts, from mechanics and materials, to circuits and systems.