Applied Mathematics
Applied Mathematics in Engineering Principles
Basic Algebra
- Understand the importance of variables and constants in mathematical expressions and equations.
- Develop the ability to simplify algebraic expressions.
- Get confident with solving linear equations, using substitution and elimination methods.
- Practice factoring polynomial expressions as it's a common step in many engineering calculations.
Geometry and Trigonometry
- Use Pythagoras' theorem to solve engineering problems that involve right-angled triangles.
- Understand the principles of sine, cosine, and tangent and use them to calculate angles and distances in technical diagrams.
- Gain familiarity with circle geometry, including properties of chords, tangents, and sectors.
- Understand how to calculate the areas and volumes of basic and complex shapes, which is often required in materials and design processes.
Calculus
- Grasp the basic concepts of differentiation and integration, the two central operations in calculus.
- Use differentiation to determine the slope of a curve at a particular point.
- Use integration to calculate areas under curves and volumes of revolution.
- Understand and apply the concepts of instantaneous rate of change (derivative) and the accumulation of quantities (integral) in practical engineering problems.
Statistics and Probability
- Know how to present data using histograms, frequency polygons, bar charts, and pie charts.
- Understand the concept of central tendency and how to calculate the mean, median, and mode.
- Use statistical measures of spread, such as range, quartiles, and standard deviation, to analyse and interpret data.
- Understand basic principles of probability and how to calculate the probability of simple and combined events.
Vectors and Matrices
- Understand how vectors are used to represent quantities that have both direction and magnitude.
- Get familiar with operations with vectors, including addition, subtraction, and multiplication by scalars.
- Understand the concept of a matrix and how matrices can be used to represent and solve systems of linear equations.
- Practice operations with matrices, including addition, subtraction, multiplication, and determining the determinant and inverse of a matrix.
Complex Numbers
- Understanding the concept of complex numbers and their representation in form a+bi.
- Know how to perform arithmetic operations (addition, subtraction, multiplication, division) with complex numbers.
- Understanding the concept of complex conjugates and their application in engineering problems.
- Know how to graph complex numbers and how to find their absolute value/modulus and argument/angle.
Remember, regular application of these principles and concepts in problem-solving is essential to fully grasp their use in engineering principles.