# Can you summarize the construction of the Laplace transform?

Learning Goal: I’m working on a differential equations question and need guidance to help me learn.discussion 10:https://foothillcollege.instructure.com/courses/19818/discussion_topics/571894ObjectivesDerive Laplace transform formulas using the definitionFind the Laplace transform of various elementary functionsFind the inverse Laplace transform of various functionsSolve IVP’s using Laplace TransformsInstructionsRead this essay on the motivation and derivation of the Laplace Transform (Links to an external site.)Reply to this discussion with your thoughts on this paper. Here are some guidelines and suggestions:Your reply should aim to help you and other students gain deeper understanding of the points in the videosCan you summarize the construction of the Laplace transform?Why do we require s to be positive?Does every function have a Laplace transform? Can you provide a counterexample?There’s also a relationship between power series and the Laplace transform. Can you explain it?If you are familiar with inner products of functions, is there anything to be said about the Laplace transform and the standard inner product of function spaces?Make sure to add something to this discussion. In other words, try not to just reiterate what the video states.Keep in mind our Netiquette guidelinesReply to at least one classmate. Here are some guidelines for your reply:Again, try to add a new thought to this discussion rather than just re-phrasing what someone else stated. If you think someone made a good point, let them know! Just make sure to also reply with your thoughts in addition to this compliment.Infographic for the Application Project: https://foothillcollege.instructure.com/courses/19818/discussion_topics/5718851. Topic: Global Temperature Modeling using Differential Equations2. Member: I am alone3. Source: https://www2.oberlin.edu/math/faculty/walsh/UMAPclimate.pdfInstructionsPart One: Initial Post Your group will create an infographic to share your project with the class. One student representative from your group must share the infographic (embed the image directly into the post, do not just share a link to it. Use the tutorial at the bottom of this page if you don’t know how to do this) with the following information on the discussion board (Note: All the following elements must be on the infographic, not in the text of the post):Project titleGroup member namesSummary of your group’s projectOne example from your project demonstrating how your group used techniques from this course to solve an application problem. Include enough detail so students can follow your example but do not include lengthy computations. Keep in mind that students in this class may not have taken a physics course, engineering, etc, so you will need to define any terms you use from another field.Include at least one photo/diagram/image that will assist other students in understanding your project.(OPTIONAL) Share your work with future iterations of this course by adding your research paper to this folder. (Links to an external site.) Make sure to remove your name if you prefer to share anonymously. Title the file with the title of your project. Make sure to follow Netiquette guidelines for all posts. Note that there is no required size for the infographic.Part Two: Question/AnswerThis is an individual component of the project. In other words, each member of the group must post one question and one answer. AnswerI will reply to each project shared on the application project forum with the same number of questions as group members for that project. I will be going over the projects in the order that they are posted on Tuesday, March 15th.The questions I ask will be related to your project or techniques from this course. You may use your notes or textbook to answer one of the questions for your group. Make sure to answer a question that has not already been answered by another group member. If you reference a source, make sure to cite it.QuestionReply to one other group’s initial post on this discussion board with a question regarding their project. Below are some guidelines for your question.do not ask a question that is already answered in the group’s postthe question should help you understand the group’s project betterthe question must be relevant to the group’s projectdo no repeat a question that another student or I have already askedmake sure your question is clear and makes sense. If the group you’re asking is confused, you might want to re-think how you pose your question (and edit your reply).GradingMake sure to view the rubric by clicking on the three vertical dots above and then “Show Rubric” before making your initial post. To receive full credit, your initial post must be made before midnight on Monday, March 14th. Your question must be posted by midnight on Tuesday, March 15th for full credit. All mathematical expressions must be formatted correctly. Use the Canvas equation editor when typing mathematical expressions in a post.Research paper: https://foothillcollege.instructure.com/courses/19818/assignments/5900261. Topic: Global Temperature Modeling using Differential Equations2. Member: I am alone3. Source: https://www2.oberlin.edu/math/faculty/walsh/UMAPclimate.pdfInstructionsThis is an individual component of the group project. You may consult with your group members regarding your answers, but this assignment must represent your own work. All computations must be done by you and in your own words. If group members submit papers or presentations that are identical or if portions are identical, no credit will be given.You may write a paper, create a video (I recommend Studio for this), or create a presentation (such as a PowerPoint or using Microsoft Sway) to share your work.Make sure you only present your own work and cite all sources. Read about academic honesty policies here.I suggest that use any feedback you received on the Application Project discussion board before submitting this assignment.If writing a paper, follow these instructions.Include a title page with the following information: the title of your projectyour full nameyour group members’ full namesInclude an introduction to your project. Make sure to include the following information:an abstract (at least 50 words) – Note that the abstract should be the first paragraph of the paper and includes the subtitle “abstract” above it. The abstract must be distinguished from the rest of the paper for full credit.a brief history of the problem (at least 50 words)When did researchers become interested in this type of problem?What strategies were first used to solve this type of problem?How was the strategy that you are using developed?the field in which you are applying linear algebra methods toan explanation of the importance of the problem and why you are particularly interested in it (at least 50 words)Summary of how you used linear algebra to solve your chosen problem (at least 50 words)Include the names of all methods and theorems used. These names should be consistent with the terminology used in this coursePresent the solution to your problem (approximately 2 handwritten pages). Make sure to include:A statement preceding each computation explaining why the computation is necessary and where each piece of the computation comes from. Students should be able to read this statement and then understand how to replicate this computation for a similar exercise.A concluding statement following each computation that interprets the result in contextAll steps for solving equations. Do not use software to solve equations.All steps necessary for graphing by handGraphs and diagrams, if relevantInclude a conclusion (at least 50 words). Include the following informationSummarize the answer of your problemAny insights you may have had while working on the projectAn unanswered question (or questions) related to your problem that you leave for the reader to explore. Your unanswered question should be related to the content to this course and an acceptable topic for a future student to attempt to answer (revisit the Topic assignment to determine if this question leads to an acceptable future student’s project topic).Works Cited(OPTIONAL) Share your work with future iterations of this course by adding your research paper to this folder. (Links to an external site.) Make sure to remove your name if you prefer to share anonymously. Title the file with the title of your project. If you are using an alternative format such as a video or PowerPoint, you must include the same required information. If you are uncertain on how to satisfy any of the steps listed above, please schedule an appointment with me.FormattingFor full credit, make sure you either write mathematical expressions by hand and submit photos of your work or use a math-typesetting program (such as LaTex). Points will be taken away if mathematical expressions not clearly represented. For example, your paper should not include “x^2” but rather . For this reason, you may hand-write your work for item 4. Type your work for items 1-3 and 5-6. You do not need to follow any particular formatting, such as MLA or APA.

Requirements: As above