Engineering Maths and Modelling 1B
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The paper covers.
- Functions and trigonometric equations
- More calculus, particularly integration, with applications to engineering problems.
- An introduction to statistics
In particular we will look at how to
- Setup and solve trigonometric equations.
- Describe features of waves and oscillations (amplitude, period, wavelength, phase, phase difference, ...)
- Describe what a function is/does. Be able to draw its graph. Decompose a function into even and odd parts.
- Apply differentiation to determine the maximum and minimum of functions, solve "related rates" problems, including in engineering applications, and produce accurate sketches of functions.
- Calculate Taylor series for simple functions.
- Calculate indefinite and definite integrals of simple functions. Interpret integrals.
- Integrate using the methods of substitution, integration by parts, and partial fractions. Be able to recognize which technique to use.
- Use integration to help setup and solve engineering applications and problems.
- Use the properties of the logarithm and exponential functions, particularly in solving engineering-based problems.
- Solve problems involving first-order separable differential equations.
- Work with second order equations for conic sections (circle, ellipse, hyperbola, parabola)
- Use the integral definition of the average of a function.
- Calculate measures of location and spread
- Calculate probabilities using the normal distribution
- Understand key statistical theories - strong law of large numbers and the central limit theorem
- Perform statistical inference procedures for means and proportions - hypothesis tests, confidence and prediction intervals
The paper is divided into four sections each taking a week or so. Each section (other than the first) starts on a Tuesday and finishes on the following Monday with an in class test. On test days the first hour will be a tutorial and the second hour will be the test.
On non-test days we will be using the two hours as a lectorial presenting theory interspersed with problems to be done in class. There will be assessed problems in class every day that we don't have a test. These may take a variety of forms. They could be done in groups or individually and could consist of multichoice or short answer questions.
Students who successfully complete the paper should be able to:
Students should be able to demonstrate understanding of mathematical ideas and notation in calculus and statistics:
Understand foundational mathematical concepts, notation and ideas to a sufficient level to recognise, understand and work with these concepts as they arise in engineering texts, applications, and other engineering papers. (WA1, WA9, WA11)Linked to the following assessments:• 4x Weekly Tests (1)• 4x Weekly Problem Sets (2)
Students should be able to recognise the application of mathematics, especially calculus and statistics, to engineering applications. They should also appreciate how these ideas can be used as a tool in an engineering context and thus formulate an appropriate mathematical description of engineering problems. (WA2, WA4)Linked to the following assessments:• 4x Weekly Tests (1)• 4x Weekly Problem Sets (2)
Students should be able to use appropriate mathematical tools from calculus and statistics to solve problems. In particular they should be able to recognise and use appropriate mathematical techniques for engineering problems formulated in mathematical terms (WA3, WA5)Linked to the following assessments:• 4x Weekly Tests (1)• 4x Weekly Problem Sets (2)
The paper is divided into four sections each taking approximately a week.
Each week there is a test worth 15% and some problems worth 10%.
The problems will consist of in class assessment of some sort. There will be some assessment attached to every class. A variety of assessment types will be used. We may ask you to work in small groups to answer a question, or ask you submit a written answer to a very short assignment. The workload is not intended to be heavy, but you we expect you to participate and do some work every day.
There is no final examination for this paper.
The four tests are items of compulsory assessment. A clear pass in this paper requires that in the four tests you achieve an average score of at least 40%.
The internal assessment/exam ratio (as stated in the University Calendar) is 100:0. There is no final exam. The final exam makes up 0% of the overall mark.
The internal assessment/exam ratio (as stated in the University Calendar) is 100:0 or 0:0, whichever is more favourable for the student. The final exam makes up either 0% or 0% of the overall mark.
Error: Assessment components must add up to 100%
At least one Assessment Component needs to be entered
|Component Description||Due Date||Time||Percentage of overall mark||Submission Method||Compulsory|
|1. 4x Weekly Tests||
|2. 4x Weekly Problem Sets||
Required and Recommended Readings*
Higher Engineering Mathematics, John Bird, 8th Edition, Routledge
If the 8th edition cannot be found, the 9th edition is acceptable.
A standard Casio FX82 scientific calculator or similar is needed for tests. Graphing and CAS calculators are not permitted.
Octave is a free (GPL ) implementation of MATLAB which we encourage students to download and play with. Matlab is specifically designed to carry out matrix calculations. You can search for it online. Links for download will also appear on Moodle.
Microsoft Excel may be used to perform tasks in the statistics part of the course. Microsoft Office 365 is available and free to all enrolled University of Waikato students. Instructions to download can be found through the following link:
Online learning is not supported. Many students end up in this class precisely because online learning has failed them. This paper is the opposite - an intensive and immersive learning experience. Students are expected to be in class and a roll will be taken every day.
The Moodle page for this paper is the main forum for notices and information.
It is also where things like sample problems and formula sheets can be accessed.
The gradebook for this paper can also be accessed through Moodle. It is your responsibility to check that your marks are correctly entered.
There are 10 'contact' hours each week for a total of 52 contact hours. Students are also expected to spend considerable additional time studying. This is an intensive paper taught over a short time period and the workload is not compatible with full time employment. In particular you are expected to be available from 10-12 every day of the week. If you cannot make that commitment you should not be enrolled in this paper.
Linkages to Other Papers*
Prerequisite papers: ENGEN101
Restricted papers: MATHS101, MATHS102, ENGEN183, ENGEN184