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Course: MATH 11218, Fall 2009
School: Allan Hancock College
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MATH11218 Engineering Foundation Mathematics Autumn Term 2003 Course Summary This course introduces the fundamental concepts necessary for further studies in engineering. Topics covered are vector algebra, matrix algebra and linear equations, complex numbers, elementary functions, function notation and the elements of statistics. MATLAB, where appropriate, will be used to support the learning process. Course...

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MATH11218 Engineering Foundation Mathematics Autumn Term 2003 Course Summary This course introduces the fundamental concepts necessary for further studies in engineering. Topics covered are vector algebra, matrix algebra and linear equations, complex numbers, elementary functions, function notation and the elements of statistics. MATLAB, where appropriate, will be used to support the learning process. Course Profile The course profile is available on the Infocom toolkit CD and on the web at http://www.infocom.cqu.edu.au/Courses/2004/T2/MATH11218/ Prescribed textbook You must purchase or have access to the textbook: James, G. 2001, Modern Engineering Mathematics, 3rd edition, Prentice Hall. Course timetable (Rockhampton only) Lectures: Wednesday 10-11 (in 18/G.40), 2-3, 3-4 (in 32/1.28). Tutorials (from week 2): to be selected from Monday 8-9, 9-10 (in 33/2.11), Wednesday 4-5 (in 7/1.23) 5-6, 6-7 (in 18/LG.08) or Thursday 2-3 (5/G.06) or Friday 12-1* (in 7/1.17). Labs: details to be announced later. Course contact details Course coordinator: Mike Drumm, office 19/3.29, phone 4930 9475, email m.drumm@cqu.edu.au. Course assessment details Three class tests (15% of assessment each) in weeks 4, 8, 11. The final examination (50%) is a two hour open book (unrestricted) The remaining 5% of assessment is based on tutorial attendance. Note that announcements (eg for tests, computer labs) will be made at lectures and posted to the course website. It is the student's responsibility to keep informed of such announcements. Test 1, to be held in week 4, is based on the material covered in weeks one to three as detailed below. Week 1 Sections 1.1-4 of James. Skim Section 1.1 Introduction Section 1.2 Number and arithmetic Reviews some of the rules of basic arithmetic from high school. Most of the material of this section is assumed and is not directly tested. The following topics may however be tested: rules for exponents, simplification of expressions involving inequalities. Skip example 1.7, pages 8-9. Section 1.3 Algebra Section 1.4 Geometry Skip section 1.4.4 (Conics), pages 33 to 37. Week 2 Sections 1.5-6 and 2.1-3 of James. Section 1.5 Numbers and accuracy Skip pages 46 to 48. Section 1.6 Engineering applications Skip...

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Allan Hancock College - MATH - 11218
MATH11218 Engineering Mathematics 1A Week 2 Lecture Notes James, 1.5, Numbers and accuracy.Autumn Term 2004We next examine mechanisms for the representation of numbers. We begin by reviewing the way we write the most elementary data type, namely
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 2 Lecture Notes - Part 2 James, 2.1, Functions - basic definitionsAutumn Term 2004A function shows how one quantity relates to or depends on another, essentially a cause and effect relationship. T
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 3 Lecture Notes Linear and quadratic functions (James, 2.3) We next review linear and quadratic functions.Autumn Term 2004Recall that a linear function is one that may be written in the form y = m
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 3 Lecture Notes - Part 2 Partial fractions (James, 2.5) We next consider rational functions of the form f (x) = p(x) q(x)Autumn Term 2004where the functions p(x) and q(x) are polynomials. We say t
Allan Hancock College - MATH - 11218
MATH11218 Engineering Mathematics 1A Week 4 Lecture Notes James, 2.6, Circular functionsAutumn Term 2004Circular functions are dened in terms of the right angle triangle shown below.Figure 1: Right angle triangle For the angle (ie ACB, assumed
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 4 Lecture Notes - Part 2 James, 2.6, Exponential and associated functionsAutumn Term 2004We are already familiar with the exponential function of the form y = ax for a given constant value a. Some
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 5 Lecture Notes Complex numbers (James, 3.2)Autumn Term 2004When solving quadratic equations it is apparent that sometimes a quadratic will have two zeros and sometimes it will have no zeros. Is t
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 6 Lecture Notes Vectors (James, 4.2)Autumn Term 2004We here treat the topic of vectors. So far, in considering real and complex numbers, we have considered scalars, that is quantities possessing m
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 6 Lecture Notes - Part 2 The scalar product (James, 4.2.7)Autumn Term 2004For the vectors a and b we define their scalar product as a b = |a|b| cos where (0 ) is the angle between the vector
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 7 Lecture Notes Matrix Algebra (James, 5.2)Autumn Term 2004In the present section we treat the topic of matrices and matrix operations. Systems of linear equations result from many situations wher
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Week 7 Lecture Notes - Part 2Autumn Term 2004Example Consider the situation where we rotate coordinate axes in a clockwise direction through an angle . If the original coordinates are (x, y) and the ro
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 1 Croft &amp; Davison, Chapter 6, Blocks 1-6Autumn Term 20051. Plot the graphs of each the functions given below. In each case state the domain and range of the function. (i) f (x) = 2x 1 1 x 4
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 1 SolutionsAutumn Term 2005Croft &amp; Davison, Chapter 6, Functions, Blocks 1-6 1. (i) For the function f (x) = 2x 1 with domain 1 x 4 we tabulate the values x 1 0 1 2 3 4 y = f (x) 3 1 1 3 5
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 2 Croft &amp; Davison, Chapter 6, Blocks 7-8Autumn Term 20051. Find the equation of the straight line such that (i) the line passes through the points (1, 4) and (2, 5), (ii) the line passes throu
Syracuse - CSE - 687
Handouts/CSE687/code/DrawingOnCppWinFormSimple WinForm Drawing in C+\CLI Purpose:Illustrate basic techniques you will need for Project #4:Jim Fawcett CSE687 Object Oriented Design Spring 2009
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 3 Croft &amp; Davison, Chapter 7Autumn Term 20051. Solve each of the following equations for their respective variable. (i) 5x - 2 = 8, (ii) 3x - 2 = 8 - 2x, (iii) x2 + 3x - 4 = 0, (iv) 2x2 - 4x -
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 3 SolutionsAutumn Term 20051. (i) x = 2, (ii) x = 2, (iii) x = 1 or x = -4, (iv) x = -1 or x = 3. 2. (i) (x - 2)(x + 5), (ii) 2(x + 1)(x - 3). 3. Since the equation has a solution x = 1 the le
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 4 Croft &amp; Davison, Chapter 8 1. Simplify the following expressions. (i) e2x ex , (ii) (ex )2 ex ,Autumn Term 2005(iii) e3x (2ex e2x ) + ex ,2. Evaluate the following expressions. (i) e0.02
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 4 SolutionsAutumn Term 20051. (i) e2x e-x = e2x-x = ex , (ii) (ex )2 e-x = e2x e-x = ex , (iii) e3x (2e-x - e-2x ) + ex = 2e3x e-x - e3x e-2x + ex = 2e2x - ex + ex = 2e2x . 2. To three signifi
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 5 SolutionsTerm 1 20051. (i) Here we merely change the sign of y in the identity sin(x + y) = sin x cos y + cos x sin y to obtain sin(x y) = sin x cos y cos x sin y (ii) Writing y = x
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 6Term 1 2005(Questions marked * are slightly more involved.) 1. Given a = (1, 0, 2) and b = (1, 1, 1) calculate (i) b 2a, (ii) |a b|, (iii) a. 2. Show that the points with position ve
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 7Term 1 20051. Suppose that ABC is a right angle triangle with a right angle at C as in figure 1 below. (i) Find B given a=12 cm and c=16 cm. (ii) Find A given a=6 cm and c=11 cm. (iii)
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 7 SolutionsTerm 1 2005(Intermediate working below is to four significant figures and final values are quoted to three figures. Please report errors to m.drumm@cqu.edu.au.) 1. (i) B = cos
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 8 1. Given the matrices , C = Term 1 2005a=1 0 2 1 , b = 3 2 4 11 0 2 0 1 3, D=1 0 2 1 3 1 1 0evaluate each of the following expressions or indicate that one
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 8 SolutionsTerm 1 20051. For matrix addition to be a valid operation the matrices involved must be of the same size (that is have the same number of rows and the same number of rows). Op
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 9 1. Consider the system Ax = b where A= 0 1 1 -1 ,b= 2 -1 .Term 1 2005Solve the system (i) using Cramer's rule, (ii) using the inverse of A as calculated in question 9 of tutorial sheet
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 9 Solutions 1. (i) Cramer's rule gives 2 1 -1 -1 0 1 1 -1 0 2 1 -1 0 1 1 -1 -1 = 1, -1Term 1 2005x==y==-2 = 2. -1(ii) Using the inverse matrix from Tutorial Sheet 8, Exercise 9
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 10 Solutions 1. (i) (3 + 4j) - (2 - 6j) = (3 - 2) + (4 + 6)j = 1 + 10j. (ii) (3 + 4j)(2 - 6j) = 6 - 18j + 8j - 24j 2 = 30 - 10j. 9 (iii) 3+4j = 3+4j 2+6j = -18+26j = - 20 + 13 j. 2-6j 2-6j 2
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 11Term 1 20051. The speeds of thirty vehicles travelling on an isolated stretch of a major highway with a 100 kph limit are recorded as follows 85 106 98 93 102 94 88 102 76 95 99 98 102
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 11 SolutionsTerm 1 20051. We first calculate xi = 1910, x2 = 183 320. The sample mean is then i x = 95.5 and the variance 183 320 - 20 1910 202= 45.75.The sample standard deviation
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation MathematicsAutumn Term 2004Tutorial 1 Note that questions marked * are slightly more involved. James, section 1.2 1. Simplify each of the following expressions (ie giving your answers without indices). (i) 16-1/2
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 1 Solutions 1. Simplifying we have 1 (i) 1 , (ii) 64 (iii) 1 . 2 2 2. (i) Squaring the bracket (3 + 2 5)2 = (3 + 2 5)(3 + 2 5) = 29 + 12 5 (ii) Rationalising 1 325 3 1 2 3+2 5 = 3+2 5 32 5
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial 2 James, section 1.5Autumn Term 20041. Find the decimal equivalent to the binary number 111012 . 2. Find the binary equivalent to the decimal number 15910 . 3. Using exact arithmetic, compute
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundations Mathematics Tutorial Sheet 3 James, section 2.4 1. Factorise the polynomials (i) x3 - 3x + 2, (ii) x4 + 2x3 + x2 - 2x - 2.Autumn Term 20042. Use synthetic division to express each of the following polynomials as
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundations Mathematics Tutorial Sheet 3 SolutionsAutumn Term 20041. (i) Clearly x3 - 3x + 2 has a zero at x = 1 and so has a factor (x - 1). Synthetic division gives 1 1 1 We therefore have x3 - 3x + 2 = (x - 1)(x2 + x - 2)
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 4 Questions marked * are slightly more involved. James, section 2.6Autumn Term 20041. Use the identity sin(x + y) = sin x cos y + cos x sin y to establish the following identities. (i) s
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 4 SolutionsAutumn Term 20041. (i) Here we merely change the sign of y in the identity sin(x + y) = sin x cos y + cos x sin y to obtain sin(x - y) = sin x cos y - cos x sin y (ii) Writing
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 6 James, section 4.2 (excluding triple products)Autumn Term 20041. Given a = (1, 0, 2) and b = (-1, 1, 1) calculate ^ (i) b - 2a, (ii) |a - b|, (iii) a. 2. Show that the points with posi
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 6 SolutionsAutumn Term 2004 6, (iii)1. (i) b - 2a = (-3, 1, -3), (ii) a - b = (2, -1, 1), so |a - b| = 1 ^ |a| = 5 so a = 5 (1, 0, 2).2. For the three points a, b and c to lie on a t
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 7 James, section 5.2 1. Given the matrices , C = Autumn Term 2004a=1 0 -2 1 , b = 3 2 4 -11 0 -2 0 1 3, D=1 0 2 1 3 -1 1 0evaluate each of the following expre
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation MathematicsAutumn Term 2004Tutorial Sheet 8 (Questions 1 to 4 repeat Tutorial Sheet 7) James, section 5.3 1. Find the determinants of the matrices A= 0 1 1 -1 ,B= 1 -1 2 1 1 0 1 , C = 2 -1 0 -1 0 1 2. Show
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 8 Solutions 1. We have |A| = 0 1 1 -1 = -1, |B| = 1 -1 2 1Autumn Term 2004= 3,|C| =1 0 1 2 -1 0 -1 0 1=12 -1 2 0 -1 0 +1 +0 -1 1 -1 0 0 1= -1 + 0 - 1 = -2 2. We first have AB =
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 9Autumn Term 20041. Determine the first five terms (ie rn for n = 1, 2, . . . 5) given by the recurrence relation rn+1 = 3rn - 1 where r0 = 1. Next compute5n rn .n=02. Newton's met
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 9 SolutionsAutumn Term 20041. The first five terms are r1 = 2, r2 = 5, r3 = 14, r4 = 41 and r5 = 122. We then have5n rn = 0 r0 + 1 r1 + 2 r2 + 3 r3 + 4 r4 + 5 r5n=0= 0 1 + 1
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 10Autumn Term 20041. The speeds of thirty vehicles travelling on an isolated stretch of a major highway with a 100 kph limit are recorded as follows 85 106 98 93 102 94 88 102 76 95 99 9
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Tutorial Sheet 10 SolutionsAutumn Term 20041. The stem and leaf plot of the data shown below is based on intervals of length 5. The corresponding histogram would exhibit a similar profile. class interv
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Matlab Tutorial 1 Operations with matricesAutumn Term 2004Matlab is in many respects similar to other algorithmic programming languages such as Fortran and Pascal. In particular, the way arithmetic com
Allan Hancock College - MATH - 11218
MATH11218 Engineering Foundation Mathematics Matlab Tutorial 2 Curve and surface sketchingAutumn Term 2004In the present tutorial we see how Matlab can be used to draw the graphs of curves in the plane and curves and surfaces in three dimensions.
Stanford - CS - 205
CS205b/CME306Lecture 11IntroductionThe goal of this class is to cover numerical simulation of PDEs, serving both the CME306 and CS205b groups, with the goal of changing the old CME306 style. The old CME306 went through compressible flow only,
Stanford - CS - 205
CS205b/CME306Lecture 311.1Smoothed Particle Hydrodynamics (SPH)Representation and SimulationIn the previous lecture, we showed how to dene density throughout space by smearing out masses at discrete points in space. (x) = mi W (x xi )iWe
Stanford - CS - 205
CS205b/CME306Lecture 41Time IntegrationWe now consider several popular approaches for integrating an ODE.1.1Forward Eulern+1 n nForward Euler evolution takes on the form x v = x v + t v a .Because forward Euler is unstable when the sy
Stanford - CS - 205
CS205b/CME306Lecture 711.1Finite Element MethodGeometric Calculation of StrainThis section uses a significant amount of text from Teran et al., Finite Volume Methods for the Simulation of Skeletal Muscle, 2003, with permission of the author.
Syracuse - CSE - 681
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NATIONAL TECHNOLOGICAL UNIVERSITY IC 792CA Fall 2001 Introduction to MEMS (UC Berkeley EECS 245) Homework Assignment #4 (Due Oct. 11th) Problem 1: Strength of Silicon a) If you want to make a solid thread of silicon that will hold up your body weigh
Colorado College - EC - 341
Then and now: A quick look at Colorado history and current controversies relevant to Sustainable Economics field trip Readings edited by Christopher Juniper, October 2002Table of Contents: 1. Transportation 1.1 History 1.1.1 Early Rail History 1.2 C
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SSILA Annual Meeting, Atlanta, January 25, 2003Reconstructing Achumawi and Atsugewi: Proto-Palaihnihan revisitedJeff Good,Teresa McFarland, and Mary Pasterjcgood@socrates.berkeley.edu, terefar@socrates.berkeley.edu, paster@socrates.berkeley.edu
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EECS 245 - FALL 2001 Introduction to MEMS Homework Assignment #6 (Due Nov. 8th) Problem 1: Comb-Drive Array Below is a typical comb-drive resonator. Design, using your CAD tool of choice, an array of comb-drive resonators using layer poly1 in the MC
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NATIONAL TECHNOLOGICAL UNIVERSITY IC 792CA SPRING 2000 Introduction to MEMS (UC Berkeley EECS 245) Homework Assignment #6 Solutions Since this problem relies heavily on your own design there is no one right answer, so these solutions are just a road
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NATIONAL TECHNOLOGICAL UNIVERSITY IC 792CA Fall 2001 Introduction to MEMS (UC Berkeley EECS 245) Homework Assignment #7 (Due Nov. 29th) Problem 1: Actuator in DRIE process Assuming a DRIE aspect ratio S, a minimum feature size l, a ma
Bergen Community College - N - 245
NATIONAL TECHNOLOGICAL UNIVERSITY IC 792CA Fall 2001 Introduction to MEMS (UC Berkeley EECS 245) Homework Assignment #7 (Due Nov. 29th) Problem 1: Actuator in DRIE process Assuming a DRIE aspect ratio S, a minimum feature size l, a material density
Bergen Community College - N - 245
NATIONAL TECHNOLOGICAL UNIVERSITY IC 792CA Fall 2001 Introduction to MEMS (UC Berkeley EECS 245) Homework Assignment #7 (Due Nov. 29th) Problem 1: Actuator in DRIE process Assuming a DRIE aspect ratio S, a minimum feature size , a material density ,