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.