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  • Diagnostic Assessment 1

    Purpose:

    This assignment helps you practice diagnostic reasoning by applying DSM-5-TR criteria to real client presentations. You will watch pre-recorded interviews, identify a diagnosis, connect symptoms to each criterion, consider differentials, highlight client strengths, and propose treatment goals.

    Link to Diagnostic Assessment 1: https://youtu.be/d6E8CiApCzQ

    Instructions:

    You will be given access to four recorded client interviews. Each recording presents a different client scenario. For each case, write a diagnostic assessment paper (12 single-space pages) that includes the following sections:

    1. Identifying Information and Diagnosis
    • Situate the clients intersectional identity and summarize their history.
    • Identify the most accurate DSM-5-TR diagnosis for the client.
    • Clearly connect the clients reported symptoms to each diagnostic criterion.
    • Example: The client meets Criterion A because she reports a depressed mood nearly every day for four months and has experienced a loss of appetite and hypersomnia nearly every day. She meets Criterion B because she has missed the last week of work and canceled appointments with friends.
    1. Client Strengths
    • Identify at least five specific strengths (e.g., coping skills, supports, values, resilience factors).
    1. Differential Diagnosis
    • Identify at least one differential diagnosis.
    • Describe which criteria fit the clients presentation, which did not, and why you ruled this diagnosis out.
    1. Treatment Goals
    • Identify at least one broad treatment goal for the client.
    • Write at least two SMART objectives (Specific, Measurable, Achievable, Relevant, Time-bound).

    Format:

    • 1-2 pages, single-spaced.
    • Write in clear, professional prose (not bullet points only).
    • APA format is not required.
    • Use the Diagnostic Assessment Example provided as a model.
    • Please submit as a Word file (.doc or .docx). Other file types will not be accepted.

    Diagnostic Assessment Example

    Primary Psychiatric Disorder(s): F50.01 Anorexia nervosa, restricting type, severe

    Rationale (what did you see that supports the diagnosis?)

    Client is a 54 17-year-old heterosexual cisgender White female who reports that she weighed 115 pounds two years ago when she was on a competitive gymnastics team and was pressured by her coach to lose weight. She then decided to go on a diet that got a little out of control. She has steadily lost weight over the past two years, and now she is at her lowest weight at 87 lbs. She is currently not participating in sports and is on medical homeschooling due to her frailty and low body weight. She was hospitalized last month for medical re-feeding and gained eight pounds in the hospital, but has since lost six pounds. Although markedly underweight, she says that she feels fatter than ever and perceives herself to be obese. She confided during the interview that her parents give her high-calorie supplemental nutrition shakes when she does not eat at family meals, and she pretends to drink them but secretly pours them out whenever she can. She also reports that she exercises frantically by running around her room and doing jumping jacks. She reports that she must exercise secretly because her doctor forbade her to exercise.

    She meets criteria A for anorexia nervosa, restricting type, because she reports restrictive food intake and dangerously low body weight. She meets criteria B because she reports intense fear of gaining weight, being fat, and behavior that interferes with weight gain, such as pouring out her nutritional shakes. She meets criteria C because she lacks insight into her underweight condition, reporting herself to be fatter than ever despite her awareness of her current weight. She meets the criteria for restricting type because she denies any purging behavior. Her weight loss is accomplished through fasting and excessive exercise.

    Client Strengths:

    1. Client is a bright young woman who aspires to be a doctor.
    2. Client is fearful of gaining weight but reports a high degree of motivation for treatment.
    3. Clients parents are supportive, and the home/family environment is stable.
    4. Client has health insurance, so she has good access to care.
    5. Client reports having some strong friendships.
    6. Client denies any complicating legal history that might interfere with treatment.
    7. Although her physical condition is fragile, the client is alert and responsive and can engage in change-focused psychotherapy.
    8. Other than her eating disorder, cthe lient has no complicating psychiatric illnesses.
    9. Client is not suicidal or homicidal.

    Differential Diagnosis

    I considered a diagnosis of bulimia nervosa (BN) because she reported that she secretly binges at least twice a week. However, on further questioning, she reported that her typical binge includes exactly 25 Cheerios and an eighth of a cup of skim milk. Although this seems like binge behavior to her, given her distorted thoughts about food intake, this does not meet criteria for a BN binge, described in the DSM as an amount of food definitely larger than what most individuals would eat in a similar period of time.

    Treatment Goal:

    • Challenge and reduce distorted beliefs about food intake and body size to support healthier self-perceptions.

    SMART Objectives:

    1. Cognitive Reframing: Within the next 4 therapy sessions, client will identify at least 3 distorted thoughts related to body size or food (e.g., I am fat even though I am underweight) and practice reframing each thought into a more balanced statement, as documented in session notes.
    2. Behavioral Experiment: By the end of 6 weeks, client will participate in at least 2 therapist-guided exposure exercises (e.g., eating a forbidden food item in session or challenging mirror-checking behavior) and record her emotional response, demonstrating reduced distress over time.
  • Philosophy Question

    Format: 8.5″x11″ pages, 1″ margins, Times New Roman font, double spaced lines, indented the first line of each paragraph. Substantial errors in spelling or grammar will result in a reduction of grade. Student name and page number may be placed in a header within the margins, but this is not required (since Canvas will tell me who each paper was submitted by). Professor name, course name, date, etc. need not be included.

    File should be in .doc or .docx (Microsoft Word) format. Note that as students of Florida Tech you have access to Microsoft Office, including via a web browser, so this should not present any difficulty. Submit the final version here, via Canvas.

    Content: Your first paper should summarize the position, on a matter of philosophical import, of a philosopher who lived between about 1650 A.D. and today. This need not be a philosopher we have or will discuss in class. This should be done in approximately 600 words.

    Since your second paper will need to do the same thing with a philosopher who does not entirely agree with the position summarized in your first paper, you will want to choose carefully. A few hints: you should not try to summarize everything the philosopher claims–just one claim should be summarized in depth. It may be a metaphysical claim, a value claim, or an epistemological claim, but it should be one of those! If you can figure out how to navigate. . it may prove quite helpful to you. Just be wary of the dates, many philosophers on that list are not included in the appropriate time range! You may also find the useful. Your paper should cite few sources–obviously you should cite the original work of the philosopher you are summarizing, but beyond that you should not use more than one or two other sources. Your bibliography should not be included in your word count. I do not have a citation format preference beyond “consistent.”

    Your paper will be graded across five areas:

    • Did you identify a specific argument about metaphysics, values, or epistemology from a philosopher of the appropriate time period? (0-20 points)
    • Did you clearly and accurately summarize that argument? (0-40 points)
    • Did you cite the original text(s) in which that argument was made, along with no more than two other academically appropriate sources? (0-20 points)
    • Is your paper grammatically correct, proofread, formatted as instructed, and otherwise linguistically coherent? (0-20 points)

    Requirements: short paper follow instuctions given above

  • Film Research, Writing, and Discussion Preparation I

    Movie: Tootsie (Sydney Pollack, 1982) – Watch this movie for the assignment online

    Instructions: Research Materials

    You will find two critical reviews of the film, following these guidelines:

    • Both reviews must be by legitimate, professional critics or other kinds of writers (e.g., film scholars, film festival curators, etc.), and must have been published either in print or online.
    • At least one of the reviews must have been published at the time of the films original theatrical release.
    • The reviews should be noticeably different, either in their evaluation of the film (e.g., a positive and a negative review) or in the way they approach the film critically.
    • These should be critical reviews rather than scholarly or academic texts or historical accounts of the film. They will likely be relatively brief but should still be substantive.

    Do not simply select the first two reviews you find. Find multiple reviews, read them carefully, then select two that best meet the above criteria and that are substantive, interesting, and different from one another in meaningful ways.

    You will also find one additional reading about the film other than a critical review, following these guidelines:

    • This reading might include evaluative commentary about the film but should not just be another film review.
    • It might be an article about the film in a newspaper, magazine, film-related website, or a more scholarly account of the film.
    • Avoid texts that use confusing academic jargon or that are for a highly specialized, narrow readership.
    • The text may be a blog entry as long as the author is a noted critic, scholar, director, film curator, etc. This is easy to determine with a Google search.
    • Ideally, this text should be relatively short say, between 4 and 10 pages.

    You will download the two critical reviews and the additional text as PDFs and label them like so:

    • The critical reviews should be labeled: Film Title Review in Source by Author Last Name (e.g., No Country for Old Men – Review in Washington Post by Hunter.pdf)

    The additional reading should be labeled: Author Last Name Title of Text (e.g., Prose All Hell Breaks Loose: No Country for Old Men)

    Written Text

    Once you have completed the above research, you will write a short essay about the critical reviews and the additional reading. This is NOT simply a report of what each reading says, but a more synthetic account of the readings. Synthetic means that you are drawing together ideas from all three readings to produce your own original take on what they say about the film. What common ideas, criticisms, or references do the readings share? How do they differ? What bigger picture do they paint of the films status as great? Do they agree that the film is great or worthy of a place in the cinema canon? If they do, is it always for the same reasons? If they disagree about the quality of the film, what is the basis for the disagreement?

    This essay should be approximately 500 words, or about one full page of single-spaced text assuming standard 12-point font.

    At the bottom of the essay, write two questions about the film for us to discuss in class. These should be modeled on the questions I provide on the Screening Guides for each weeks film. These questions are not part of the above-mentioned word count for the essay.

    Turning it in

    Save your essay, with discussion questions, as a Word doc, labeled: Your Last Name Essay on Film Title (e.g., Walley Essay on The Thin Blue Line). Submit the essay and the three readings you have found in a folder on Google docs. The folder should be named: Your Last Name Film Title. Email me the link to the folder on Google docs; be sure that the Share settings will allow me to access the folder when I click on the link.

    The due dates for this assignment are staggered. Your folder should be completed and made available to me by 5:00pm on the Wednesday prior to the screening of your film. For example, if you choose Do the Right Thing, which screens on Wednesday, March 4, your folder will be due by 5:00pm on Wednesday, February 25.

    Evaluation

    When I evaluate your work on this assignment, I will consider the following:

    • That you have completed all portions of the assignment and followed all the instructions (including labelling and submission instructions) in the above prompt.
    • That the critical reviews you have submitted follow the guidelines listed above. Were they well chosen? Are they different from one another in meaningful ways? Are they substantive, addressing the film in at least some detail to illustrate and support the critical claims they make?
    • That the additional reading is also well chosen, aligns with at least some of the ideas in one or both critical reviews, and offers original and insightful information or ideas about the film.
    • That the short essay genuinely addresses all three texts you have found; that is does not merely summarize them but draws their ideas together, offering an original perspective on them (i.e., your own!).
    • That the essay has a central idea about the film and the responses to the film you are writing about. This makes for a cohesive piece of writing, and one that goes beyond merely summarizing the readings.
    • That the short essay was carefully written and proofread. Pay close attention to grammar, punctuation, and spelling.
  • CHAPTER APPLICATION PAPER

    OVERVIEW

    The purpose of this paper is to present your well-articulated perspective and thoughts from the

    chapters assigned from the reading. The integration of textbook and article sources is important

    in developing critical thinking skills in the abstract content that is in this course and in courses to

    come. This assignment should not be taken lightly nor should it be rushed. Articulating and

    developing critical thinking requires time thinking about the material.

    INSTRUCTIONS

    Select one chapter from chapters 11-13 in Snipes: Volds Theoretical Criminology and write

    an 8-10 page paper that summarizes, synthesizes, and then applies the information from the

    Chapter to issues/policies relevant to the topic. Your paper must be well-organized and be

    reflective of your thinking and struggles in these very complex areas of dealing with criminal

    offending. This paper must use 4-5 citations in proper APA format.

    Each paper must identify the premise and supporting points of the chapter, a synthesis of the

    information from the chapter, and a critical application of the premise(s) and supporting points

    from the chapter to an issue of criminal offending. The paper should address:

    Key points, patterns, and trends from the information in the chapter with citations for the

    textbook

    How the chapter information applies to issues of criminal offending supported by sources

    outside the textbook

    Analysis of the chapter information from a Christ-centered perspective with citations

    from Scripture

    The organization of your paper is very important. Please follow APA and make sure to use

    section headings in your paper. Make sure to include a cover page, a references page, and

    develop a well-formatted, grammatically correct paper. The cover page and reference page do

    not count toward the minimum number of pages for the assignment.

  • Discussion

    1. First, watch the required videos, review power points, and complete the assigned readings for the week.
    2. Reflect on how we now know that race is a social construct meaning that while we may have differences in appearance and heritage, human beings are genetically the same species. Historically, however, for many centuries people used the idea of biological racial difference rooted in scientific racism to justify laws, policies, economic structures (like slavery), and different treatment of individuals based on their racial identity.
    3. In a 400-word minimum post, describe how ideas of race, racial differences, and the history of scientific racism impacted how the United States and European countries viewed independent nations in Latin America, like Panama and Haiti. Also, please address how the notion of “Western Civilization” continued to perpetuate these ideas?

    **READINGS

    -ERASED chapter 1

    -HISTORY OF LATIN AMERICA chapter 3

    Attached Files (PDF/DOCX): Erased.pdf, Haitian Revolution_revised_2024.pdf, Slave-Letters-Martinique-1789.pdf

    Note: Content extraction from these files is restricted, please review them manually.

  • Discussion

    1. First, watch the required videos, review power points, and complete the assigned readings for the week.
    2. Reflect on how we now know that race is a social construct meaning that while we may have differences in appearance and heritage, human beings are genetically the same species. Historically, however, for many centuries people used the idea of biological racial difference rooted in scientific racism to justify laws, policies, economic structures (like slavery), and different treatment of individuals based on their racial identity.
    3. In a 400-word minimum post, describe how ideas of race, racial differences, and the history of scientific racism impacted how the United States and European countries viewed independent nations in Latin America, like Panama and Haiti. Also, please address how the notion of “Western Civilization” continued to perpetuate these ideas?

    **READINGS

    -ERASED chapter 1

    -HISTORY OF LATIN AMERICA chapter 3

    Attached Files (PDF/DOCX): Erased.pdf, Haitian Revolution_revised_2024.pdf, Slave-Letters-Martinique-1789.pdf

    Note: Content extraction from these files is restricted, please review them manually.

  • Organization Analysis

    PROJECT DESCRIPTION

    You are charged with creating a strategic marketing plan for Fabletics. Your first tasks will be to do some research

    (A) to understand the strengths and weaknesses of your company/department, (B) to

    understand the competitive landscape, and (C) to more narrowly define your target market

    so that you can create a marketing plan to meet the needs of those consumers. You are also

    encouraged to consider upcoming and current sport trends for this assignment.

    SECTION 1: BRAND OVERVIEW

    This brief section (up to 500 words in length) should provide an overview of the brand,

    including history/background of the brand, relevant product category(ies), vision/mission

    statement. (Note: utilize brand website as primary-but not only-source)

    SECTION 2: SWOT ANALYSIS

    In order to determine your marketing objectives, strategies, and tactics, you must first do a

    detailed SWOT analysis. To populate your SWOT, you must do some research. Be sure to

    look through a variety of sources such as SportsBusiness Journal, academic research through

    the library, library databases (SportDiscus, etc.), secondary data sources (census data,

    published reports on companies and industries, etc.), financial data, public records, reputable

    news sources, etc… You may also consider collecting your own data, such as conducting

    interviews or focus groups or observing social media conversations or organizational websites

    for information about product offerings and reviews. Focus on information that will

    ultimately inform your overall marketing plan. Again, be specific and make your statements

    based on research and not on assumptions.

    Focus on information that will ultimately inform your marketing plan. For example, if

    you are creating a new Nike product, you dont need to cover everything about Nikes history.

    You should focus on your particular product category and the strengths and weaknesses of

    Nike that will impact your ability to sell your product. Be specific and make your statements

    based on research and not on assumptions.

    SECTION 3: PRODUCT DESCRIPTION

    After presenting sufficient information for the reader to understand the organization under

    question as well as the situational landscape in which they exist, it is time to identify the

    product

    you will be focusing on for your marketing plan. You will create a new product (good or

    service). Based on your understanding of the existing landscape, you might have noticed an

    area that needs to be filled. For example, perhaps your company does not offer X product

    or service, while your competitors do. In this case, you may want to develop a new product /

    service for your company. Here you must describe the basic concept of your product /

    service and what hole it is filling (i.e., why it must be invented, offered, and marketed by

    your organization).

    SECTION 4: TARGET MARKETS

    For this part of the assignment, you are to identify at least two (2) different market segments

    who are likely to buy or use the product/service that you have created. You want to be

    specific about what defines each group of users without limiting the number of people in each

    segment.

    Remember that traditional marketing strategies segment consumers based on simple

    demographic profiles (location, age, gender, etc…); however, new marketing is different. It

    is critical that you consider attitudinal and behavioral characteristics as well in your

    segmentation strategy. Finally, remember that some of your target segments may be

    businesses instead of individual consumers. Please give each market segment a creative

    and descriptive name.

    The correctness of your answer is determined largely by your ability to find credible

    information to support your ideas. Do not make any assumptions about people, their

    attitudes, or their behaviors. Define your market segments based on data (see the example

    below). If you have any questions about what sources are credible, please let me know.

    Bad example:

    We have an opportunity to market to young kids because most kids like shoes.

    Good example:

    According to census data, our target market has a large percentage of families with

    children living at home (Denver Community Planning and Development, 2006).

    Further, our market is also highly active (56% engage in outdoor activities such as

    tennis, hiking, running, and basketball). Therefore, we have an opportunity to expand

    our market to include these highly active families, both children and adults.

    SECTION 5: PERSONA DESCRIPTIONS

    Consistent with the corporate structure presented in the Rethinking Marketing reading (see

    Assignment Instructions on Canvas), your role will be of Customer Segment Manager

    where youll be asked to develop the marketing plan for one specific market segment. In

    this section write a brief biography for one (1) potential consumer in EACH of your

    selected market segments 2 personas total. You may find it useful to do additional

    research as well. Each biography should be about 250 words.

    Example: Ashley, 34, wakes up early to go running since she knows she wont have time

    later. A former high school tennis player, Ashley is now of mother of two who lives in a

    small suburban community just outside the city of Denver. She enjoys hiking with her

    family and prides herself on keeping fit. This core value carries over into her parenting style

    as she pushes her children to participate in as many extracurricular activities as possible.

    While she works hard to maintain her active lifestyle, time and budget restrictions limit her

    ability to be as active as she would like. This year, her fitness goals are less about actual

    fitness and more about participating in as many activities as possible with her husband and

    kids. She hopes that by eating right and staying active, she will maintain her current fitness

    level even if she isnt able to improve it. (150 words)

    ** Other information that would be relevant in this example include, but are not restricted to,

    the kind of job she has, other parts of her past, her perception of fashion, her favorite

    products/brands, political affiliation, her social networks, etc…

    SECTION 6: MARKETING OBJECTIVES

    The purpose of the above situational analysis is to provide direction on how to capitalize on

    your opportunities and identify/minimize your threats. For this part of the assignment,

    connect specific pieces of information from your analysis and develop three

    S.M.A.R.T. objectives. Consider as marketers, you should be concerned with other

    aspects of your companys performance such as generating awareness for your product or

    creating/enhancing your brand image. Use these guidelines for creation of the three objectives:

    One of these objectives should be tied to sales or other financial outcomes (i.e.,

    involving Product and/or Price elements).

    One of your objectives should lead to a strategy of creating an ad/marketing

    campaign (Promotion element).

    One should utilize one (or a combination) of marketing mix elements not employed in the

    other two objectives.

  • Social Program Development Project (SPDP)

    This is a semester long project but this assignment is just the first part “Population and problem”

    The professor strongly encourages using the US census data, “https://www.census.gov/en.html” The population I chose is Veterans in the state of Arkansas and the problem is substance use disorders. If you have any questions please let me know.

    Attached Files (PDF/DOCX): SPDP-Part 1-rubric2026.docx, SPDP-Assignment overview-in-class final.docx

    Note: Content extraction from these files is restricted, please review them manually.

  • Social Science Question

    Person-focused pay programs are not really new. Various early forms of these programs appeared in the 1980s. Organizational adoption was slow partly because they can very quickly drive labor costs up. Why is this changing? Explain the reasons for this change. Consider Susan Jacksons situation. Susan is a young professional in her 8th year of her technological manufacturing career since graduating from college. She is frustrated by the lack of opportunity to showcase her talent and skillset. Susan feels like she has so much more to offer than is asked of her. Consequently, she is once again on the job market. If she succeeds in her search, Susan will join her third organization in 8 years. Explain why a job with a person-focused pay program might help alleviate her frustration. Finally, what are the potential advantages and disadvantages of these programs for the organization? For the employee?

    INSTRUCTIONS

    Respond to the discussion questions provided. Each assignment requires 3 4 full pages and at least 5 peer-reviewed resources within 5 years to substantiate your position in your answer. You must carefully read the requirements below, noting the expectations beforehand. These exercises are meant to foster your comprehensive research and writing skills.

    The specific requirements are as follows:

  • As a graduate student, the expectation is quite high for your required quality and effort.
  • Your work must be written near the standard and quality of journals and other published materials.

  • Cover page, abstract, and reference page do not count toward the minimum page length requirement.
  • Add biblical integration which contain 1) a quoted Bible verse that is correctly cited and
  • 2) integration that ties verse to topic by using a minimum of 3 sentences.
  • At least 5 peer-reviewed sources within the last 5 years are required.
  • Correctly cite your sources and quotations using current APA format.
  • The use of sources such as Wikipedia, Investopedia, blogs, personal, consulting or corporate websites are discouraged and will not count toward the required 5 references
  • Use of term papers or solutions-type websites is not allowed and will be treated according to the terms of academic honesty requirements.
  • Use of headings is required to differentiate distinct sections of the paper; however, students should not use the questions as a heading/subheading.
  • Note: Meeting the minimum specifications will result in the minimum passing grade. You are

    expected to provide an in-depth, analytical review of the topic. Assignments that do not meet

    the minimum criteria will not receive a passing grade.

    Requirements: 14

  • Applied Mathematics Question


    Term Paper Segmentation Guide

    Main Research Question

    How do truncation errors, rounding errors, and conditioning collectively influence the stability of numerical algorithms, and under what theoretical conditions can an unstable algorithm still produce acceptable results?


    SECTION I: Foundations of Error Theory (Conceptual + Theoretical Demonstration)

    1. Truncation Error

    Students should:

    a) Define truncation error formally.
    b) Derive truncation error for at least one example:

    • Taylor series approximation
    • Finite difference derivative
    • Numerical integration formula

    c) Show how truncation error depends on step size hh.
    d) Prove the order of accuracy for the chosen method.

    Expected demonstration:
    Mathematical derivation using Taylor expansion and Big-O notation.


    2. Rounding Error

    Students should:

    a) Define floating-point representation and machine epsilon.
    b) Explain how rounding errors accumulate in iterative algorithms.
    c) Derive error bounds caused by floating-point arithmetic.
    d) Provide an example (e.g., subtraction of nearly equal numbers).

    Expected demonstration:
    Model floating-point arithmetic as:

    fl(x)=x(1+),??machinefl(x)=x(1+),??machine

    and propagate this through an algorithm.


    3. Conditioning of a Problem

    Students should:

    a) Define well-conditioned vs ill-conditioned problems.
    b) Define the condition number of a function and of a matrix.
    c) Derive the condition number for:

    • Scalar function f(x)f(x)
    • Linear system Ax=bAx=b

    d) Interpret geometrically what a large condition number implies.

    Expected demonstration:

    (A)=AA1(A)=AA1

    Show sensitivity of solution to perturbations.


    SECTION II: Stability of Algorithms

    4. Distinguish Conditioning vs Stability

    Students must:

    a) Explain why conditioning is a property of the problem.
    b) Explain why stability is a property of the algorithm.
    c) Provide examples where:

    • Well-conditioned problem + unstable algorithm
    • Ill-conditioned problem + stable algorithm

    Expected demonstration:
    Formal reasoning, possibly using linear systems.


    5. Forward and Backward Error Analysis

    Students should:

    a) Define forward error.
    b) Define backward error.
    c) Show how backward stability is used to assess algorithms.
    d) Demonstrate backward error analysis for:

    • Gaussian elimination
      OR
    • Newtons method

    Expected demonstration:
    Prove that computed solution solves a slightly perturbed problem.


    SECTION III: Interaction Between the Three Concepts

    6. Combined Error Model

    Students must:

    a) Construct a total error model:

    Total Error=Truncation Error+Rounding ErrorTotal Error=Truncation Error+Rounding Error

    b) Show how decreasing step size reduces truncation error but increases rounding error.
    c) Derive an expression for optimal step size balancing both errors.

    Expected demonstration:
    Minimize error expression using calculus.


    7. Case Study Analysis

    Students should analyze one algorithm (choose one):

    • Numerical differentiation
    • Gaussian elimination
    • Eulers method
    • Iterative solvers

    They must:

    a) Identify all three error sources.
    b) Analyze how they interact.
    c) Discuss stability implications.


    SECTION IV: When Can an Unstable Algorithm Still Work?

    This is the deeper theoretical part.

    Students must investigate:

    8. Theoretical Conditions for Acceptable Results

    They should analyze and justify:

    1. If the problem is very well-conditioned.
    2. If perturbations remain small relative to solution scale.
    3. If instability grows slowly (e.g., sub-exponentially).
    4. If input data is low-noise.
    5. If error cancellation occurs.
    6. If instability is dominated by truncation error.

    They must:

    a) Provide at least one mathematical example.
    b) Use error bounds to justify conclusions.
    c) Provide a counterexample where instability destroys accuracy.


    SECTION V: Critical Reflection

    Students should conclude by addressing:

    • Can a stable algorithm solve an ill-conditioned problem accurately?
    • Is backward stability sufficient for reliability?
    • How does finite precision arithmetic limit theoretical guarantees?

    Optional Grading Structure

    Section Weight
    Error Theory 20%
    Conditioning 15%
    Stability Analysis 20%
    Combined Error Modeling 20%
    Case Study 15%
    Critical Reflection 10%

    Requirements: 2000