...Laplace Transform The Laplace transform can be used to solve differential equations. Besides being a different and efficient alternative to variation of parameters and undetermined coefficients, the Laplace method is particularly advantageous for input terms that are piecewise-defined, periodic or impulsive. The direct Laplace transform or the Laplace integral of a function f (t) defined for 0 ≤ t < ∞ is the ordinary calculus integration problem ∞ 0 f (t)e−st dt, succinctly denoted L(f (t)) in science and engineering literature. The L–notation recognizes that integration always proceeds over t = 0 to t = ∞ and that the integral involves an integrator e−st dt instead of the usual dt. These minor differences distinguish Laplace integrals from the ordinary integrals found on the inside covers of calculus texts. 7.1 Introduction to the Laplace Method The foundation of Laplace theory is Lerch’s cancellation law ∞ −st dt 0 y(t)e = ∞ −st dt 0 f (t)e (1) L(y(t) = L(f (t)) implies or implies y(t) = f (t), y(t) = f (t). In differential equation applications, y(t) is the sought-after unknown while f (t) is an explicit expression taken from integral tables. Below, we illustrate Laplace’s method by solving the initial value problem y = −1, y(0) = 0. The method obtains a relation L(y(t)) = L(−t), whence Lerch’s cancellation law implies the solution is y(t) = −t. The Laplace method is advertised as a table lookup method, in which the solution y(t) to a differential equation...
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...called the Laplace transform. It is very effective in the study of initial value problem involving linear differential equation with constant coefficient. Laplace transform was first introduced by a French mathematician called Pierre Simon Marquis de Laplace about 1780’s. This method associated with the isolation of the original problem that is function ƒ(t) of a real variable and some function ƒ(s) of a complex variable so that the ordinary differential equation for the function ƒ(t) is transformed into an algebraic equation for ƒ(s) which in most cases can readily be solved. The solution of the original differential equation can be arrived at by obtaining the inverse transformation. The transformation and its inverse can be derived by consulting already prepared table of transform. This method is particularly useful in the solution of differential equation and has more application in various fields of technology e.g. electrical network, mechanical vibrations, structural problems, control systems. Meanwhile in this research work, I shall look into the Laplace transform, the properties of the Laplace transform and the use of this technique in solving delay differential equation will be looked into. 1.2 Statement of the Problem There are so many engineering and other related problems that can be expressed in the form of ordinary differential equations. But such problems cannot easily be solved using the elementary method of solution. In such cases, the Laplace transform...
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...MEEN 260 Introduction to Engineering Experimentation Homework 10: Laplace Transform, and Frequency Response Solution Assigned: Thursday, 9 Apr. 2009 Due: Thursday, 16 Apr. 2009, 5:00pm Learning Objectives: After completing this homework assignment, you should be able to: 1) 2) 3) 4) 5) Determine the Laplace Transform of a signal using the definition, tables, or properties of the Laplace Transform Utilize the Laplace Transform to find the Transfer Function of a dynamic system represented by a system of differential equations Utilize the Laplace Transform to solve for the transient response of a dynamic system Discuss the difference between the Laplace and Fourier Transforms and their respective uses Using the Transfer Function of a system, determine and plot the associated frequency response, and determine the steady state response of a system to a harmonic input signal Homework Problems: Problem 1) Definition of Laplace Transform Using the mathematical definition, compute the Laplace transform for the function: f (t ) = 3t + t cos(2t ) Solution: From the mathematical definition, we split the function into two pieces: 3 3 · We use u-v substitution (u=3t, dv=e-st) to get: ∞ 3 ∞ 3 3 0 0 The second piece of the function is more complicated. Recall that: · So we find: cos 2 We use u-v substitution (u=e-st, dv=cos(2t)) and get: sin 2 2 This does not give us a useful answer, so we perform a u-v substitution to the right hand side of the equation to obtain: cos 2 By rearranging...
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...desirable features: it can be estimated easily from data, it captures key empirical properties of order book dynamics, and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo Stock Exchange. Using simple matrix computations and Laplace transform methods, we are able to efficiently compute probabilities of various events, conditional on the state of the order book: an increase in the midprice, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Using high-frequency data, we show that our model can effectively capture the short-term dynamics of a limit order book. We also evaluate the performance of a simple trading strategy based on our results. Subject classifications: limit order book; financial engineering; Laplace transform inversion; queueing systems; simulation. Area of review: Financial Engineering. History:...
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...------------------------------------------------- ECET-402 Week 6 Lab Worksheet Name: John Natale Block Diagram Simplification and Step/Impulse Responses Please complete this worksheet and submit to week 6 lab dropbox This worksheet serves as coversheet 1. Determine the overall transfer function of the system given below by hand as discussed in pre-lab. Please show your work and type the equations if you can. TF=(Y(s))/(X(s))=((s^3+3s^2+3s+2)/(〖2s〗^4+6s^3+15s^2+12s+5))/(1+(s^3+3s^2+3s+2)/(〖2s〗^4+6s^3+15s^2+12s+5)×2/s)=(s^4+3s^3+3s^2+2s)/(2s^5+6s^4+17s^3+18s^2+11s+4) TF=(Y(s))/(X(s))=(s^4+3s^3+3s^2+2s)/(2s^5+6s^4+17s^3+18s^2+11s+4) 2. Determine the overall transfer function of the system shown above using MATLAB. Copy the MATLAB code and the overall transfer function obtained and paste them below: >> nG1 = [1 0]; >> dG1 = [1]; >> G1 = tf (nG1, dG1) Transfer function: >> nG2 = [1]; >> dG2 = [1 1]; >> G2 = tf (nG2, dG2) Transfer function: 1 ----- s + 1 >> nG3 = [1]; >> dG3 = [1 0]; >> G3 = tf (nG3, dG3) Transfer function: 1 - s >> nG4 = [1 2]; >> dG4 = [1 2 5]; >> G4 = tf (nG4, dG4) Transfer function: s + 2 ------------- s^2 + 2 s + 5 >> nG5 = [2]; >> dG5 = [1 0]; >> G5 = tf (nG5, dG5) Transfer function: 2 - s >> G6 = series (G1, G2) ...
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...No. 00, March 2008, 1{22 RESEARCH ARTICLE Laplace transform approach to the rigorous upscaling of the in¯nite adsorption rate reactive °ow under dominant Peclet number through a pore z Catherine Choquet a and Andro Mikeli¶c b ¤ aUniversit¶e P. C¶ezanne, LATP UMR 6632, Facult¶e des Sciences et Techniques de Saint-J¶er^ome, 13397 Marseille Cedex 20, FRANCE bUniversit¶e de Lyon, Lyon, F-69003, FRANCE; Universit¶e Lyon 1, Institut Camille Jordan, UFR Math¶ematiques, Site de Gerland, B^at. A, 50, avenue Tony Garnier 69367 Lyon Cedex 07, FRANCE (submitted on March 31, 2008) In this paper we undertake a rigorous derivation of the upscaled model for reactive °ow through a narrow and long two-dimensional pore. The transported and di®used solute par- ticles undergo the in¯nite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts' boundary conditions. The transport and reaction pa- rameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter " being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of " and guarantee the validity of the upscaled model. We use the Laplace transform in time to get better estimates than ...
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...Actually... Santa Claus is my grandfather! *The following story is purely based on my imagination. :) -------------------------------------------------------------------------------------------------------------------------------------- Present 1 (it just means chapter 1, instead of writing chap 1, I feel this is more interesting? XD ) 'Will you be my queen, princess?' he spoke with so much love and gentleness, it could melt any girl's heart. Yes! I longed to say yes. I don't really know why but I just have this feeling that I have to say yes. However, the sad thing is that I can only see a black silhouette of this 'king' or 'prince' kneeling in front of me. I couldn't see his face. 'Yes,' I whispered lightly and at the same time, I could feel blood gushed to my cheeks. He rose from his knee and lifted my chin to face him. As he leaned closer toward me, my heart was pounding rapidly against my ribcage. Of course, I am nervous and excited because I haven't had my first kiss yet. Hey! Don't you dare to laugh at me! I am just waiting for the right person to appear at the right moment for the one and only first kiss. Every girl has her right to dream. :P I closed my eyes and anticipated the moment where our lips touched. It was soft.... Wet and sticky... Hold on a minute! Wet and sticky??!! Eww!! This was superb freaking, disgusting and totally wasn't what I had expected. 'Rise and shine, dearie!' a sweet and warm voice called out. This voice sound...
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...reactions (internal, personal) to that subject. Figurative description relies on creating likenesses between objects, often through simile (e.g. like a snowflake...or fragile as a snowflake...) or metaphor. Such likenesses allow the reader to perceive the object more precisely. An objective sample: The kitchen table is rectangular, seventy-two inches long and thirty inches wide. Made of a two-inch-thick piece of oak, its top is covered with a waxy oilcloth patterned in dark red and blue squares against a white background. In the right corner, close to the wall, a square blue ceramic tile serves as the protective base for a brown earthenware teapot. A single white placemat has been set to the left of the tile, with a knife and fork on either side of a white dinner plate, around nine inches in diameter. On the plate are two thick pieces of steak. (Notice how "objective" the narrator in the piece is; his or her eyes scan the scene, but there is no emotional response provoked by the scene). A subjective sample: Our lives at home converged around the pleasantly-shaped kitchen table. It was the magnet that drew our family together quite warmly. Cut from the sturdiest oak, the table was tough, smooth, and long enough for my mother, my two sisters, and me to work or play on at the same time. Our favorite light blue ceramic tile, stationed in the right corner, was the table's sole defense against the ravages of everything from a steaming teapot to the...
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...Advantages. Specifilally,it sought answers to the following problem 1.What is the Advantages and Disadvantages of computers? 2.Is there a significant difference between advantages and disadvantages of computers? 3.Is there a significant between advantages and disadvantages of computers? IV.HYPOTHESIS Based on the aforementioned problems the following hypothesis were tested. 1.There is no significant difference between advantages and disadvantages of computer. 2.There is no significant relationship between advantages and disadvantages of computer. TABLE 1 : DISTRIBUTION OF RESPONDENTS ACCORDING TO GENDER GENDER | FREQUENCY | PERCENTAGE(%) | MALE | | | FEMALE | | | The table shown above desplets the distribution of respondence according to gender. TABLE 2: DISTRIBUTION OF RESPONDENTS ACCORDING TO AGE AGE...
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...Need your weekly work schedules each week; SUNDAYS OFF My office and restroom rules No longer is anyone allowed in my office while I’m not in it. No more food or drinks, cups, dishes and trash in my office. Only paper in my trashcan. No smoking contraband is allowed; if found it will be thrown away. Stay out of my drawers please; ask first before taking anything that belongs to me in my office. Whatever you bring into the house; take it all to your room. My office is not a rest stop. Take all hair, face, mouth accessories and products to your restroom; stop leaving your things in my restroom and take them to your room. Brush your teeth upstairs only no more toothpaste and brushes in my office or restroom. Paiton, toys, closes, shoes, diapers, trash are allowed unease its necessary. Your Restroom and hallway area No more seats in the restroom No more trash collections on the doors No more sheets, towels or clothes on the rail Secure all closet doors in hallway Clubbing A 24 hour notice is required if Paiton is left at home. If you put as much focus on going clubbing then you should put just as much emphases on Paiton or even more. You should put that same effort into Paiton as you do your own wardrobe and hygiene as you do yourself because you are both girls QUET Mondays, Wednesday, and Friday Only Full Kitchen duties includes the dishes, pots pans, countertops (the bar too) stove, microwave, fridge, floors, and trash. Your Restroom-...
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...Leonardo Castillo Enc 1101 M/W 5:00 pm 10/1/2012 Word count: 709 Descriptive Essay Rough draft It’s approximately four o’ clock in morning and I’m in the locker room changing my clothes. My colorless hands are chilly, my feet are weary and my body feels like is going to give up and collapse after working eight hours in a refrigerated warehouse. Even though my body just wants to give way, I manage to drag my feet all the way to my vehicle, and start rushing home which is the only thing I want to do after a long night of work. The best part of driving home at this hour of the day is that I have an open road almost all to myself. The streets are nearly empty, the drive nice and smooth and the best part is that there are no police so you can run through these streets like there’s no tomorrow. Also there are no rays of sunshine burning my eyes like in the day, the weather is nice and cool that I don’t even need to turn on my a/c which has been throwing nothing but burning air. As I get closer to home I could only think about going straight to comfy bed; however, it is not going to happen because this is the only free time during the day that I have time to study. As I am getting to the door my eyes feel unfocused and my eyelids are feeling heavy. Now that I made it to the white tarnished door, I am shuffling through my key chain to find the correct key. The darkness of the night makes it difficult to find the right one; thus, I lift my arm up toward the sky to see if...
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...Reinvention and Renewal Herman Miller Background SWOT Porters Five Forces Strengths Opportunities Weaknesses Threats Risk of Entry Rivalry Among Established Firms Bargaining Power of Buyers Bargaining Power of Suppliers Substitute Products Complementors Strategies Herman Miller's challenge is to continue to reinvent and renew itself in times of economic uncertainty Main Issue We have developed three alternatives to solve this company's problem Alternatives Focus their efforts on marketing Alternative One Recommendations Continue to use the same business model or develop a new strategy? Continue to use the same business model Alternative Two Use the current business model but continually update based on the economic activity Alternative Three Why focus marketing efforts? Advances in technology have decreased need for office furniture Increase in the need for ergonomically correct furniture due to increased time in front of a computer Why use the same business model? Current business model has proven effective in past recessions Why update the current business model? Current model has many effective policies currently in place We cannot effectively predict how the economy will change Most effective strategy to combat an uncertain economy is to stay with what has worked well and update it as change occurs Current business model is still fitting with company values and goals Office furniture industry is constantly in a state of flux 2002 March (cc) image by jantik on Flickr Equa Chair...
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...Entrance (easy entrance and exit from the restaurant) | | | | 4 | 4. Ease of Parking (whether it be self park or Valet) | | | | 4 | 5. Windows and Doors clean and free of streaks and spots | | | | 4 | Hostess | 1 | 2 | 3 | 4 | 1. Hostess Station easy to find | | | 3 | | 2. Greeting from hostess in a timely manner | | | | 4 | 3. Hostess made eye contact and used polite phrases such as “Please”,“Thank you”, and “Your Welcome” | | 2 | | | 4. If there was a wait, hostess quoted an accurate wait time | | | | 4 | 5. Hostess offered options for waiting (e.g. Recommend a drink, pointed out the bar, or outside waiting) | | | 3 | | 6. Hostess attitude and appearance | | | 3 | | 7. Hostess escorted guests to table at a comfortable pace | | | | 4 | 8. Hostess sat guest in a desirable location or the most desirable location that was available | | | | 4 | 9. Acknowledgment from Hostess on your way out | | 2 | | | Person(s) on Duty: | | Main Entrance and Hostess Summary: The Main entrance was a tad weird in the placement category but as I walked in it was very clean and the hostess was prompt to sit us down. She was very efficient asking us what We wanted to order. She was very polite as well as presentable. She sat us at the last booth that was open which was optimal. She acknowledged us politely on the the way out and told us to have a great night. Dining Room and Patio | 1 | 2 | 3 | 4 | 1-Poor 2-Below Average...
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...1) List the events in this case that lead up to and include the accident. 1) Employee at Canadian Linen and Uniform Service Co. went into work On February 7, 2006. 2) A part of the workers duties for that day was to empty a bag of soiled garments and count how much there were so they could be transported to another plant. 3) The soiled garments were hanging n an overhead railed conveyer system 4) In order to reach these garments the worker stood on a stainless steel table at the workplace to take down a bag 5) After getting a hold of the bag, the worker tried to climb down from the table 6) The worker lost balance and fell to the floor. 2) Describe the injury sustained and the direct cause. The injury that was sustained by the worker was a broken right lower leg. After falling off the table that was 79 centimeters off the ground, the impact that the workers body had with the floor caused for their right lower leg to get injured. The awkward impact of the fall resulted in the direct cause of the injury as the worker suffered a broken right lower leg. 3 a) what section(s) of the Act (and what Regulation(s) if cited in your case) were violated? Please write out verbatim those section(s) of the Act and regulation(s). Act Part 3 – DUTIES OF EMPLOYERS AND OTHER PERSONS Section 25 (1)(c) – an employer shall ensure that, the measures and procedures prescribed are carried out in the workplace; Regulation Material Handling Section...
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...CHAPTER I Technical Aspect This chapter describes the activities to be done before the business will operate as a business. -Target Opening Date: July 1, 2009 Table 1 Pre-Operational Activities |Business Plan |Target Dates | |Renovation of the Business Space |June 8- 15, 2009 | |Application of Permits and Licenses |June 11-25, 2009 | |Selection and Buying of Equipment and Office Furniture |June 16-25, 2009 | |Arranging and Positioning of Equipment and Furniture |June 26-27, 2009 | |Trial Operation |June 28, 2009 | |Normal Operation |July I, 2009 | | | | Table I shows the different activities that “YOUR CHOICE FOOD SERVICE” will have to accomplish from the month of June 2009 until the business will start on July 1, 2009. It reflects the planned activities before the...
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