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.