Mathematics for Engineers

Basic Principles

• Understand the basic principles of algebra including simplifying expressions, solving equations, and rearranging formulas.
• Familiarise yourself with trigonometry, focusing on understanding sine, cosine and tangent and their applications, including solving triangles and working with radian measure.
• Develop a solid understanding of geometry, particularly how to calculate areas and volumes of complex shapes and studying angles between lines and planes.
• Become proficient at calculus. This includes differentiating and integrating functions and understanding how this connects to real-world engineering scenarios, like ndetermining rates of change and calculating areas under curves.

Engineering Context

• Use your mathematical understanding in engineer-specific contexts. This involves understanding physical quantities and units of measure, for example, torque, force, power and energy.
• Implement graphical techniques to represent engineering situations, such as plotting and interpreting data, and understanding how to read and generate engineering drawings.
• Apply principles of statistics and probability to engineering situations. This includes using statistical measures like mean, median, mode and standard deviation to analyse data, and using probability to analyse risk.
• Use vectors and matrices in engineering contexts. This involves understanding how vectors describe magnitude and direction, and how to perform operations on them. It includes understanding what a matrix is, and how to perform operations like addition, subtraction and multiplication.

Applied Techniques

• Develop an understanding of complex numbers and how they're used in electrical engineering contexts.
• Apply Fourier series to signal analysis, used in the field of telecommunications engineering.
• Use the Laplace transform technique to solve differential equations, commonly used in control engineering.

Computational Methods

• Practice using calculators and computer software to solve complex problems. This includes using engineering-specific software for problem-solving, and understanding the difference between exact answers and approximate answers given by calculators and computers.
• Consider the advantages and disadvantages of different computation methods. Manual calculations might be more accurate, but they're often slower and more prone to human error.
• Understand that not every problem has a single 'right' solution. In engineering, there are often trade-offs to consider. Different solutions may be better in different circumstances, so it's important to understand how to evaluate options critically.