Level 3 Engineering AQA

This subject is broken down into 42 topics in 8 modules:

  1. Engineering Principles 8 topics
  2. Engineering Product Design and Manufacture 8 topics
  3. Microcontroller Systems for Engineers 5 topics
  4. Calculus for Engineers 5 topics
  5. Further Engineering Science 4 topics
  6. Materials Technology and Science 4 topics
  7. Mechatronic Systems 4 topics
  8. Engineering Business Environment 4 topics
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  • 8
    modules
  • 42
    topics
  • 16,445
    words of revision content
  • 2+
    hours of audio lessons

This page was last modified on 28 September 2024.

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Engineering

Engineering Principles

Mathematics for Engineers

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Mathematics for Engineers

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.

Course material for Engineering, module Engineering Principles, topic Mathematics for Engineers

Engineering

Calculus for Engineers

Algebra

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Algebra

Basic Algebraic Concepts

  • Algebra is the branch of mathematics that deals with variables and the rules for manipulating these variables.
  • In algebra, letters (variables) often represent numbers; this technique simplifies problems and helps in handling situations where exact numbers are unknown.
  • Expressions are combined using mathematical operations such as addition, subtraction, multiplication, and division, as well as exponents and roots.
  • Understanding how to solve equations and inequalities is at the heart of algebra.

Algebraic Equations

  • A statement formed by setting two algebraic expressions equal to each other is known as an equation.
  • Simple linear equations look like

    ax = b

    , where

    a

    and

    b

    are constants. Solving them is usually a matter of isolating

    x

    on one side of the equation.
  • Quadratic equations, in the form

    ax^2 + bx + c = 0

    , might require methods such as factoring, completing the square, or using the quadratic formula.
  • Higher degree equations could require additional techniques for solving, such as synthetic division or polynomial long division.

Algebraic Manipulations

  • Transposition is the process of rearranging the equation by applying the same operation to both sides simultenously.
  • Factorisation is the process of breaking down expressions into product of its factors.
  • Understanding how to expand and simplify expressions is vital. This includes mastering the distributive law (

    a(b + c) = ab + ac

    ) and the rules for factoring.
  • Algebraic manipulation also involves understanding the laws of exponents (indices) and radicals (roots).
  • Practice manipulating variable expressions and substituting values in variable expressions to enhance problem-solving skills.

Algebra in Calculus

  • In calculus, algebra is particularly important for understanding functions and their properties, differential calculus, and integral calculus.
  • Functions are the heart of calculus. They chart the relationship or mapping between two sets where every input has a unique corresponding output.
  • Differential calculus deals with the concept of change in values, while integral calculus handles the accumulation of quantities.
  • Limits, the foundations of calculus, help develop the concept of continuity, differentiation, and integration of a function.

Those revising for their calculus-based engineering exams will need to reinforce their understanding of these fundamental algebraic principles, as they form the building blocks for understanding calculus in the context of engineering applications. Proper mastery of algebraic equations and manipulations will in turn lead to a smoother understanding of higher-level calculus concepts.

Course material for Engineering, module Calculus for Engineers, topic Algebra

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