# DE4102 – Engineering Mathematics 1

Module code
DE4102
Module title
Engineering Mathematics 1
Prescription
To develop mathematical skills, concepts and understanding in order to perform calculations and solve problems within engineering contexts
Programmes
• EN1603
• EN1803
• SC1101
NZQA Level
Level 4
NZQA Credits
15
Delivery method
• Not Web enabled
Learning hours
Directed hours
90
Self directed hours
60
Total learning hours
150
Resources required
Learning Outcomes
On successful completion of this course, the student should be able to:
1.Manipulate and solve algebraic expressions and equations.
2.Solve, manipulate and apply mathematical functions, including application of graphs where appropriate.
3.Apply the rules and principles of trigonometry using both degree and radian measure.
4.Demonstrate knowledge of differentiation and integration techniques and apply them to solve engineering problems.
5.Demonstrate knowledge and application of one of the following:
5.1 Complex numbers, logic expressions and numbers OR
5.2 Basic statistical concepts and techniques.
Content
Rules for simplifying, factorising, exponents and fractions; Simple manipulation of surds; Linear equations
Basic functions: linear-, quadratic-, exponential-, logarithmic functions; Solve quadratic, exponential and log equations; Solve simultaneous equations; Graphs: linear-, polynomial-; exponential-, logarithmic-, simple rational functions; Amplitude, frequency, period, phase displacement and time displacement of a graph
Trigonometric identities and formulae; Degree and radian measure; Solve trigonometric equations; Graph trigonometric functions; Calculation of areas and volumes
Differentiation and integration rules and concepts; Applications of differentiation: tangent to a curve, minima and maxima, optimisation techniques, rate of change of time dependent variables, growth and decay rates; Applications of integration: Area under a curve, mean value, RMS (non-trigonometric only), first and second moments of area, Simpson's rule.
Complex numbers: rectangular and polar conversion, quadratic equations with complex roots, Logic expressions and numbers: Conversions between and operations on binary, hexadecimal, decimal and binary coded decimal numbers; Boolean algebraic expressions.
Mean, median, range, standard deviation, Scatter diagrams, Regression analysis, Correlations.