DE4102                             ENGINEERING MATHEMATICS 1

Level 4                                             Credits 15                                            Version July 2010

  

RECOMMENDED PRE-REQUISITE
Nil

RECOMMENDED CO-REQUISITE
Nil

AIM/PURPOSE
To develop mathematical skills, concepts and understandings in order to perform calculations and solve problems within engineering contexts.

 

 

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.

  

INDICATIVE 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; Boolian algebraic expressions.
  • Mean, median, range, standard deviation, Scatter diagrams, Regression analysis, Correlations.
  • Use spreadsheets throughout as appropriate.