Lecture Notes for PAMC (07) - Ch4_L2

Lecture 7I’ve pre-drawn some molecules here. Let’s see if we can use what we know to name them. So what do we have? This first molecule right here, I have a bunch of rings. This is a one, two, three, four, five, six carbon ring. These are each four carbon rings: one, two, three, four, so the largest ring is essentially going to be our backbone. It’s going to be this six-carbon ring right here: one, two, three, four, five, six carbons. So that is a cyclohexane. All double bonds. That’s where we get the –ane. Six carbons hex-, it’s in a cycle, cyclo-, and then we have two of these four-carbon rings. So four carbons, we’re dealing with the prefix but-, but- for four. We’ve got two of them, so both of these are butyl groups. But they’re in a cycle, so they’re actually cyclobutyl groups. We have two things attached to this ring right there. If we only had one thing attached to it, you wouldn’t have to number it. But when you have two things, you start numbering at one of them. Let’s say we start numbering here, and you go in the direction so that the next group has the lowest number. So in this case, you want to go in the counterclockwise direction. If we went this way, it would be one, two, three, four, five. This guy would be a five. If we go in the counterclockwise, it would be one, two, three. This guy will only be a three. So this right here, we have two cyclobutyls, so it’s dicyclobutyl. We have two of them and they are at the one and three positions. So at the one and three position, I have two cyclobutyls on my cyclohexane main ring.Let’s try this one right here. I have a five-carbon ring, one, two, three, four, five right there, and then I have a one, two, three, four, five, six-carbon ring right there, so this is going to be the main ring. That is a cyclohexane. It has six carbons on them in a cycle, all single bonds. Attached to that, I have a cyclopentyl group, -yl for the group. This is a cyclopentyl group on it. We don’t have to number it because it’s only one group attached to the main ring. If there was another group, we would have to number it like we did up here. This is cyclopentyl. That’s this part right here. Cyclopentyl attached to cyclohexane: cyclopentylcyclohexane.Let’s try this one over here. The first thing we want to do, there’s no cycles here, but we have to identify the longest chain. To do that, let’s just count it out. It could be one, two, three, four, five, six, seven. That’s not the longest chain. Maybe it’s one, two, three, four, five, six, seven, eight. That looks like the longest chain, so let’s make that the longest chain. Let’s make that the longest chain right over there. We want to start numbering in the direction so we encounter the first attached groups first. We do want to start numbering down here, because we have groups attached right on the two carbon. If we started over here, we’d have to to pretty far until something’s attached. So we go one, two, three, four, five, six, seven, eight. We know we’re dealing with an octane, all single bonds. It’s not a cyclooctane. It’s not in a cycle, so we know we’re dealing with an octane. Now we just have to add the groups to it. So what do we have here? This right here is just one carbon attached to the main chain. This is another carbon attached to the main chain. Both of these right here are methyl groups. Meth- is for one carbon. Those are methyl groups. If you look at all of them, these are the only methyl groups. These two up here aren’t methyl groups, so we have two methyl groups on our entire chain, so it’s going to be dimethyl. Both of the methyl groups our at our two position, so this is going to be 2,2-dimethyl. This part right here is 2,2. That right there is 2,2-dimethyl. We’re going to decide what order to write it after we figure out what these are called because it has to be in alphabetical order. This is 2,2-dimethyl. The whole chain is an octane. What are these over here? How many carbons do we have here? One, two, three. They actually look the same. We have one, two, three here. We have one, two, three there, so these areboth propyl groups. If we deal with common names, this is kind of that Y shape. You could call it sec-propyl because this carbon right here that’s attached to the main chain is attached to two other carbons. But the more common one, because it forms this Y shape, is isopropyl. We have two isopropyl groups. These are both isopropyl. We could have disopropyl. They ‘re occurring at the four and five positions, two isopropyls at four and five. This is 4,5-disopropyl. That’s that group and that group right there are accounted for with this. Now we have to just figure out the order that we write it in. You ignore the di- or the tri- out front and you just look at them in alphabetical order. We have an I for isopropyl. We have an M for methyl. Let’s write the isopropyl first. I’ve actually seen some people want to go for the p, but the main thing I ignore is just the di- or the tri- in front of the isopropyl. You shouldn’t involve that. But everything after that, you do involve. So I’ll write the isopropyl first. I comes before M, so this is going to be—if we were going to write the whole thing, this is going to be 4,5-disopropyl, 2,2-dimethyl. Actually, this should be a comma here, 4,5-disopropyl-2,2-dimethyloctane. And we’re done. But this was just the common name. you might remember that when we deal with iso- or sec- or tert- butyl or propyl, that’s the common name. if we want the systematic name, we can start at where we are attached to the main chain and view that as one and then make the longest chain with that so one. And so you could say that we have a chain there and this would be both of these cases. So this is one, two carbons. two carbons, we’re dealing with an ethyl. And on the first carbon, you have a methyl attached to it. So you could also call each of these groups a 1-methylethyl instead of an isopropyl. So you can either say isopropyl for each of these groups or you could call each of them a methylethyl if you do systematic naming. We have two of these 1-methylethyl groups, just like we had two isopropyl groups. If you’re using common naming, you can say disopropyl to say you have two of these groups. When you’re using systematic naming, you don’t say di-1-methylethyl, although that would probably get the point across. You use bis-. Since we have two of them, instead of writing di-, you write bis-. That means you have two of these things right there, and it’s still in the four and the five position. If you look at it in alphabetical order now, methylethyl comes after methyl, right? So the order will now change. So now if you want to write it with systematic naming, it would be written as 2,2-dimethyl. That’s these two guys, 2,2-dimethylethyl. And then you would write this guy, so the order changed for the two groups just based on how they’re named. Bis-, and then over here you have two 1-methyl ethyl groups. I know it’s confusing, but when you just break it down, it actually makes a reasonable amount of sense. You have two of these methyl ethyl groups. Oh, sorry, I forgot where they’re located. So we have them at the four and five position, so in the four and five position, we have two, so bis-(1-methylethyl) groups. I know it’s a little daunting now, but it all makes sense when you break it down. Methylethyl groups. And then we can just add the octane at the end. Let me scroll over to the right a little bit. Octane. Now this might seem more confusing, but when you break it down, it makes sense. We have octane as be backbone. We have two methyls. They’re both sitting on the two position. So you have two methyls sitting on the two position, and then you have two 1-methylethyl groups sitting at the four and five positions. So in the four and five position, 1-methylethyl. You have an ethyl, and in the one position you have a methyl, so that’s all it’s saying. Or another way to think about it, just in case this doesn’t confuse you enough, you could call it that, or you could say 4,5-disopropyl. These two things are the same thing: common naming, systematic. Hopefully, you found that useful.。

Linear Algebra and Its Applications, Fourth EditionCourse DesignCourse BackgroundLinear algebra is one of the fundamental branches of mathematicswith a wide range of applications in many fields. With the increasing importance of data analysis and machine learning, the study of linear algebra has become increasingly relevant.This course is designed for undergraduate students majoring in mathematics, statistics, engineering, and other related fields. The mn goal of the course is to provide students with a solid understanding of the fundamental concepts of linear algebra and its applications.Course Objectives1.To enable students to understand and apply matrix algebraand linear systems of equations.2.To introduce students to vector spaces, lineartransformations, and determinants.3.To teach students the basics of eigenvalues and eigenvectorsand their applications in solving linear differential equationsand constructing orthogonal bases.4.To apply the concepts of linear algebra in solving problemsin various fields, including physics, engineering, and economics.Course OutlineWeek 1-2: Introduction to Matrix Algebra and Linear Systems of Equations•Introduction to matrices and their operations•Gaussian elimination and matrix inversion•Linear systems, solutions, and consistency•Applications in engineering and economicsWeek 3-4: Vector Spaces, Linear Transformations, and Determinants •Vector spaces and subspaces•Linear transformations and matrix representations•Determinants and properties•Applications in cryptography and signal processing Week 5-6: Eigenvalues and Eigenvectors•Definitions of eigenvalues and eigenvectors•Eigenvalues and eigenvectors of symmetric matrices•Diagonalization and similarity•Applications in differential equations and quadratic forms Week 7-8: Orthogonality and Inner Product Spaces•Inner products and orthogonality•Gram-Schmidt orthogonalization•Orthogonal projection and least squares•Applications in signal processing and Fourier analysis Week 9-10: Additional Topics and Applications•Singular value decomposition•Multivariate statistics and principal component analysis•Markov chns and transition matrices•Applications in network analysis and data science Assignments and AssessmentsThe course will include weekly problem sets, which will be graded, and a final exam. The problem sets will consist of theoretical questions and computational problems, including applications of linear algebra concepts in various fields.Textbook and ResourcesThe textbook for the course will be。

Course Design of Introduction to MathematicalStatistics (7th Edition) in English Version Course OverviewIntroduction to Mathematical Statistics is a basic course for undergraduate students majoring in mathematics, statistics, physics, and engineering. This course is designed to give students a basic understanding of statistical methods and principles, and to developtheir ability to use statistical methods to solve problems in real-world situations. The course covers a variety of topics including probability theory, random variables, probability distributions, estimation, hypothesis testing, and regression analysis.Course Objectives•To understand fundamental concepts and principles of probability theory, random variables, and probabilitydistributions•To acquire the basic knowledge of statistical inference•To be able to apply statistical methodologies to solve real-world problems•To develop the statistical literacy and critical thinking•To prepare for further studies in advanced statistics and related fieldsCourse ContentUnit 1: Introduction to Statistics•The use of statistics in making decisions•Types of data and data collection methods•Descriptive statistics and graphical presentationsUnit 2: Probability•Basic probability concepts and definitions•Rules of probability (addition, multiplication, and conditional probability)•Probability distributions and their propertiesUnit 3: Random Variables•Definition and properties of random variables•Continuous and discrete random variables•Probability density functions and probability mass functions Unit 4: Sampling and Estimation•Random samples and sampling distributions•Point estimation and interval estimation•Properties of estimatorsUnit 5: Hypothesis Testing•Basic concepts of hypothesis testing•Test statistics and p-values•Type I and Type II errors and power of testsUnit 6: Regression Analysis•Linear regression model and its assumptions•Estimation and hypothesis testing for regression parameters•Goodness-of-fit and predictionTeaching MethodologyThis course will be taught through a combination of lectures, class discussion, and problem-solving sessions. The lectures will cover the mn topics and concepts, while the problem-solving sessions will provide students with an opportunity to practice applying the concepts to real-world problems. Students will also be required to read the textbook and complete homework assignments independently.EvaluationThe evaluation of this course will be based on the following components: - Homework assignments: 20% - Mid-term exam: 30% - Final exam: 50%References•Hogg, R. V. (2019). Introduction to Mathematical Statistics (7th ed.). Pearson.•Larsen, R. J., & Marx, M. L. (2019). An Introduction to Mathematical Statistics and Its Applications (7th ed.). Pearson.•Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (9th ed.). Brooks/Cole.ConclusionIntroduction to Mathematical Statistics is an essential course for students interested in statistics, mathematics, physics, engineering, and related fields. This course covers a wide range of topics andprovides students with a solid foundation in statistical concepts and methods. Students who successfully complete this course will be well-prepared for further studies in advanced statistics and related fields.。

I. J. Mathematical Sciences and Computing, 2021, 4, 21-26Published Online December 2021 in MECS (/)DOI: 10.5815/ijmsc.2021.04.02Determination of Optimal Smoothing Constants for Foreign Remittances in BangladeshMd. Nayan Dhali a, Md. Biddut Rana, Nazrul Islam, Deepa Roy, Mst. Sharmin BanuJashore University of Science and Technology, Jashore-7408, BangladeshEmail: mndhali_math@.bd, justbiddut33@, nazrulislamdu.082@, deeparoy707@, surovyru@Received: 18 March 2021; Accepted: 25 May 2021; Published: 08 December 2021Abstract: Remittance is the tie that is sent to the country by earning money from abroad. In present Bangladesh, remittance is playing an important role in increasing reserves and revenue. For about two decades remittance has been contributing a huge portion of export earnings. Remittances have a significant impact on the budget of Bangladesh and also the budget depends a lot on remittances. So it is very crucial to know the future remittance to make an annual budget for upcoming year. This paper concentrates on choosing the appropriate smoothing constants for foreign remittances forecasting by Holt’s method. This method is very popular quantitative skilled in forecasting. The forecasting of this deftness depends on optimal smoothing constants. So, choosing an optimal smoothing constant is very important to minimize the error of forecasting. We have demonstrated the techniques by presenting actual remittances and also presented graphical comparisons between actual and forecasting remittances for the optimal smoothing constants.Index Terms: Foreign Remittance, Holt’s Method, and Smoothing Constants.1.IntroductionForecasting means predict about something basis on some past experience about that event. This is a process that has not yet been observed. With a good example something can be expected to change at certain times in the future. Guessing is an important issue, considering its general existence. Holt’s method is simple and can give precise forecasting results comparable to the results of more complex techniques. This method is prevalent, simple to utilize and generally works well in practical applications. In this method, two smoothing constants have been used to evaluate the forecast value and these constants smooth the forecast value. So finding the optimal value of smoothing constants is very essential to make better forecast.In Bangladesh, remittance is one of the most important economic variables in recent times as it helps in balancing balance of payments, increasing foreign exchange reserves, enhancing national savings and increasing velocity of money. The importance of foreign remittances in the economy of Bangladesh is widely recognized and requires little reiteration. Revenues from remittances now exceed various types of foreign exchange inflows, particularly official development assistance and net earnings from exports. Moreover, it is greater than foreign aid and thus helps in lessening dependence on foreign aid remittance gets momentum in recent time in Bangladesh. It also occupies an important part to make our national budget. So it is very important to know the forecast remittance to make an annual budget for next year. The aim of our project is to make a forecast for foreign remittance by using Holt’s method for optimal smoothing constants.A comprehensive procedures was used to evaluate optimal value of smoothing constants for Exponential smoothing method, Holt’s method and Holt-Winter’s seasonal multiplicative method[4, 5]. An appropriate forecasting technique is obtained for the newly launched biscuit company in Bangladesh [2]. For a given problem MAD & MSE are calculated with different values of smoothing constants and the optimal smoothing constants is determined by selecting the minimum values of MAD & MSE. Solver is used to determine the optimal value of smoothing constant for Exponential smoothing method [6, 7].Single smoothing forecasting techniques are attempted to evaluate the forecasts for solar irradiance and load demand [8]. Non-linear programming software is used to improve the demand forecast accuracy [11]. An appropriate quantitative forecasting method for demand forecasting of private car in Dhaka city is examined for optimal smoothing constants [13].2. Holt’s MethodHolt’s Method is a popular smoothing method for forecasting data with trend. Holt's method uses two parameters, one for the overall smoothing and the other for the trend smoothing equation. In that case, many techniques have been developed to resolve the complexities of forecasting errors and are generally referred to as the “Holt’s method”.It should be noted that Holt’s method performs well where only trend but no seasonality exists.The time series exhibits a trend here; the trend (slope) has to be calculated in addition to the level variable. The forecast for t+k period at the end of time t, is provided by*t k t tF L k T +=+Here, t L is the estimate of level made at the end of period and is given by(1)t t tL A F αα=+-t T is the estimate of trend at the end of period and is given by11()(1)t t t t T L L T ββ--=-+-βis also a smoothing constant between 0 and 1 and plays a role similar to that of αAgain, small values of α and βsuggest that consecutive level and trend variable estimates do not vary much from each other. In the sense of the new demand, any revision is minimal. This method requires estimation of the initial level component t L and the initial trend component t T to start off the series of forecasts. Initialization:The initial estimated base label 0L is assumed from the last period observation and initial trend 0T is the average monthly or weekly change.0L =Last period’s observation0T =Average monthly or weekly increase3. Foreign Remittance InvestigationForeign remittances data are given for some previous years. We have to forecast remittances for next ten years [The daily New Age].Table 1. Foreign remittance of Bangladesh in different yearsTable-1 describes the foreign remittance of Bangladesh in different year. To evaluate the forecast value by Holt’s method, first of all we have to initialize the estimated base label and trend. Initialization:Let the initial estimated base be 0L And the initial estimated trend be 0T0L =Last year’s observation0T =Average yearly increase( ) ( ) ( ) ( )Now, firstly we fixed a particular value of then calculate MAD, MSE & MAPE for the different values ofβ. After that, we fixed another value of αthen for different values ofβ, we compute MAD, MSE & MAPE. Continuing this process by fixing a particular value of αand changing the values ofβ, we get MAD, MSE & MAPE and find out whether MAD, MSE & MAPE give minimum value.The process is shown by the following Table 2:Table 2. MAD, MSE & MAPE for different values of &Table-2 shows that, MAD gives minimum value for smoothing constants & , MSE gives minimum value for smoothing constants & and MAPE gives minimum value for smoothing constants &Now, this time we fixed a particular value of then calculate MAD, MSE & MAPE for the different values of . After that we fixed another value of then for different values of , we compute MAD, MSE & MAPE. Continuing this process by fixing a particular value of and changing the values of , we get MAD, MSE & MAPE and find out whether MAD, MSE & MAPE give minimum value. The process is shown by the following table:Table 3. MAD, MSE & MAPE for different values of &Table-3 shows that, MAD gives minimum value for smoothing constants &, MSE gives minimum value for smoothing constants & and MAPE gives minimum value for smoothing constants &Lower values of MAD, MSE & MAPE and corresponding value of smoothing constants are shown in the following Table 4:Table 4. Optimal values of smoothing constants &From Table-4, we see that, MAD & MAPE both give the minimum value for the value of smoothing constants & ; therefore, & are the optimal value of smoothing constants.Now, we calculate forecast values for the optimal smoothing constants.The forecast of next ten years foreign remittances are in below:Table 5. Forecast values for optimal smoothing constants &From Table-5, we get the forecast value for the next ten years. Using Holt’s method the forecast value for the optimal smoothing constants & at the 2030th year is 24.6424The following Figure represents the comparison between actual remittances and corresponding forecast values for optimal smoothing constants.Fig.1. Comparison of actual remittances and forecast value (Holt’s Method)Figure-1 compares the actual remittances and forecast remittances and also describes the forecast remittances for the next ten years. From this figure we also conclude that the next ten years remittances will increase continuously.To solve the given problem, we use Holt’s method and we get the optimal smoothing constants &and the corresponding forecast value for the 2030th year is 24.64244.ConclusionBangladesh’s remittances have contributed to employment, poverty alleviation and foreign exchange reserves. As a result, a country is developed as a country with potential for the future. The resolution of the lesson shows that in recent year’s remittance growth increased thoug h migration decreased slowly. The role of remittances in the economies of labour sending countries such as Bangladesh is assuming increasing importance. The better a country forecasts is more ready to utilize potential prospects and decrease prospective risks. Thus, forecasts accuracy should be very crucial to maintain their information sources. Holt’s Method is widely used to forecast the future events and it has two smoothing constants. The aim of this project was to determine the optimal smoothing constants to calculate the forecast value for foreign remittances in Bangladesh. Mean Absolute deviation (MAD), Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) are applied to get optimal values of the smoothing constants. We have also computed corresponding forecast values for the next ten years foreign remittances.References[1]Taylor, J. W., 2003. Exponential smoothing with a damped multiplicative trend. International Journal of Forecasting, 19, 715-725.[2]Barman, N., Hasan, M. B., & Dhali, M. N., 2018. Advising an Appropriate Forecasting Method for a Snacks Item (Biscuit)Manufacture Company in Bangladesh. The Dhaka University Journal of Science, 66(1), 55-58.[3]Taylor, J. W., 2004. Smooth Transition Exponential smoothing. International Journal of Forecasting, 23, 385-394.[4]Dhali, M. N., Barman, N., & Hasan, M. B., 2019. Determination of Optimal Smoothing Constants for Holt-Winter’sMultiplicative Method. The Dhaka University Journal of Science, 67(2), 99-104.[5]Hasan, M. B., and M. N. Dhali, 2017. Determination of Optimal Smoothing Constant for Exponential Smoothing method &Holt’s method. Dhaka Univ. J. Sci. 65(1), 55-59.[6]Paul, S.K., 2011. Determination of Exponential Smoothing Constant to Minimize Mean Square Error and Mean AbsoluteDeviation. Global Journal of Research in Engineering, 11, Issue 3, Version 1.0.[7]Ravinder, H. V., 2013. Determining the Optimal Values of Exponential Smoothing Constants –Does Solver Really Work?American Journal of Business Education, 6, May/June.[8]Lim, P. Y., and C. V. Nayar, 2012. Solar Irradiance and Load Demand Forecasting based on Single Exponential SmoothingMethod. International Journal of Engineering and Technology, 4, 4.[9]Ravinder, H. V., 2013. Forecasting With Exponential Smoothing –What’s The Right Smoothing Constant? Review of BusinessInformation System –Third Quarter, 17, No.3[10]Singh, V. P., and V. Vijay, 2015. Impact of trend and seasonality on 5-MW PV plant generation forecasting using SingleExponential smoothing method. International Journal of Computer Applications, 130, 0975-8887.[11]Bermudez, J. D., J. V. Segura, and E. Velcher, 2006. Improving Demand Forecasting Accuracy Using Nonlinear ProgrammingSoftware. Journal of the Operational Research Society, 57, 94-100.[12]Gardner, E. S., 1985. Exponential Smoothing: The State of the Art, part-I. Journal of Forecasting, 4, 1-28.[13]Barman, N., Dhali, M. N., Hasan, M. B., 2021. Finding Appropriate Smoothing Constant for Demand Forecasting of PrivateCars in Dhaka City, International Journal of Mathematics and Computation, 32(1).[14]Gardner, E. S., 2006. Exponential Smoothing: The State of the Art, Part-II. International Journal of Forecasting, 22, 637-666.[15]Hyndman, R. J., A. B. Koehler, R. D. Snyder, and S. Grose, 2002. A state space framework for automatic forecasting usingexponential smoothing methods. International Journal of Forecasting, 18, 439-454.[16]Mohammed, U., Suleiman U. H., Usman, M., Sadiq T., 2020. Design of an Optimal Linear Quadratic Regulator (LQR)Controller for the Ball-On-Sphere System, International Journal of Engineering and Manufacturing (IJEM), Vol.10, No.3, pp.56-70. DOI: 10.5815/ijem.2020.03.05[17]Qasem, A. H. 2020. A Methodical Study for Time-Frequency Analysis Model with Experimental Case Study on Chirp Signal,International Journal of Engineering and Manufacturing (IJEM), Vol.10, No.3, pp.1-11. DOI: 10.5815/ijem.2020.03.01 Authors’ ProfilesMd. Nayan Dhali was born in Bangladesh. He has completed B.S. (Honor’s) and M.S. in Mathematics fromUniversity of Dhaka. Now he is performing as an Assistant Professor of Mathematics at Department ofMathematics in Jashore University of Science and Technology, Bangladesh. Email:mndhali_math@.bdMd. Biddut Rana was born in Bangladesh. H e has completed BSc (Honor’s) and MSc in Mathematics fromJashore University of Science and Technology, Bangladesh. Now he is doing research on optimizationproblems. Email: justbiddut33@Nazrul Islam was born in Bangladesh. He has completed B.S. (Honor’s) and M.S. in Mathematics fromUniversity of Dhaka. Now he is performing as a Lecturer of Mathematics at Department of Mathematics inJashore University of Science and Technology, Bangladesh. Email: nazrulislamdu.082@Deepa Roy was born in Bangladesh. Sh e has completed B.S. (Honor’s) and M.S. in Mathematics fromUniversity of Dhaka. Now she is performing as an Assistant Professor of Mathematics at Department ofMathematics in Jashore University of Science and Technology, Bangladesh. Email:deeparoy707@Mst. Sharmin Banu was born in Bangladesh. Sh e has completed B.Sc. (Honor’s) and M.Sc. in Mathematicsfrom University of Rajshahi. Now she is performing as a Lecturer of Mathematics at Department ofMathematics in Jashore University of Science and Technology, Bangladesh. Email: surovyru@ How to cite this paper: Md. Nayan Dhalia, Md. Biddut Rana, Nazrul Islam, Deepa Roy, Mst. Sharmin Banu," Determination of Optimal Smoothing Constants for Foreign Remittances in Bangladesh ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.7, No.4, pp.21-26, 2021. DOI: 10.5815/ijmsc.2021.04.02。

ADMINISTRIVIALecturer: Prof. Anant AgarwalTextbook: Agarwal and Lang (A&L) Readings are important!Handout no. 3Web site —/6.002/www/fall00 Assignments —Homework exercisesLabsQuizzesFinal examTwo homework assignments can be missed (except HW11).Collaboration policyHomeworkYou may collaborate withothers, but do your ownwrite-up.LabYou may work in a team oftwo, but do you own write-up. Info handoutReading for today —Chapter 1 of the bookPurposeful use of scienceWhat is 6.002 about?Gainful employment of Maxwell’s equationsFrom electrons to digital gates and op-ampsV?Lumped Circuit AbstractionFaraday’s Continuity OtherstBE∂∂−=×∇tJ∂∂−=⋅∇ρEερ=⋅∇tdlE B∂∂−=⋅∫φtqdSJ∂∂−=⋅∫εqdSE=⋅∫I ask you: What is the acceleration?You quickly ask me: What is the mass?I tell you:m You respond:mF a =Done !!!Fa ?In doing so, you ignoredthe object’s shapeits temperatureits colorpoint of force application Point-mass discretizationFa ?First, let us build some insight:Consider the filament of the light bulb.BWe do not care abouthow current flows inside the filament its temperature, shape, orientation, etc. Then, we can replace the bulb with adiscrete resistorfor the purpose of calculating the current.BReplace the bulb with adiscrete resistorfor the purpose of calculating the current.R represents the only property of interest!Like with point-mass: replace objectswith their mass m to find mF =and R =R IR represents the only property of interest!andRV I =RIRV I =relates element v and iR called element v-i relationshipR is a lumped element abstraction for the bulb.R is a lumped element abstractionfor the bulb.are definedfor the elementV IABAlthough we will take the easy way using lumped abstractions for the rest of this course, we must make sure (at least the first time) that ourabstraction is reasonable. In this case,ensuring thatA Array IBI into =I out of in the filament!True only when 0=∂∂tqAS B S B=∂t qdS J dS J A BS S ∂∂=A∫⋅AS dSJ ∫⋅BS dSJ must be defined.True when So let’s assume thisdefined when ABV 0=∂∂tBφoutside elementsdl E V AB AB⋅=∫s e eA& L Must also be defined .So let’s assume this tooSoDemoLumped element exampleswhose behavior is completelycaptured by their V–IDemoExploding resistor democan’t predict that!Pickle democan’t predict light, smell4R 5R VSo, what does this buy us?4R 5R V under DMD 0∫∫∫=⋅+⋅+⋅bc ab ca dl E dl E dl E 0=+++bc ab ca V V V 0SSunder LMD 00=++ba da ca I I I simply conservation of chargeKVL:loopKCL:node=∑j j ν0=∑j j i KVL and KCL Summary。