Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Newton’s interpolating polynomial

This screenshot is topic for part 1 and 2 for Writing Goal, research , Curve Fitting and Literature Proposal.

Part1: Curve Fitting: Readings & Resources (Chapra & Canale, 2015) Read Chapters 19 & 20 Assignment: Research Proposal (25 points) Now that you have defined your problem draft 1 and 2, goal, and determined what’s already been done to address it, it’s time for you to propose what your next steps will be. Finalize your research proposal with an “Approach” section in which you respond to the following: • What will you build? Will you modify an existing model? Will you start from scratch? Provide details on how you will create the mathematical/computational model. What language(s) will you use? Flowcharts, class diagrams, and other diagrams may be useful to explain your intentions. • How will you evaluate and test your model? How will you know if you have achieved your goal? Support your new section with at least four (4) scholarly peer-reviewed sources in addition to those already used in the prior sections. Format your submission according to the APA style guide. Remember that all work should be your own original work and assistance received from any source and any references used must be authorized and properly documented. Recommended length: 12-15 pages double-spaced including prior sections, not including front and back matter.

Part 2: Readings & Resources (Chapra & Canale, 2015) Read Chapters 15 & 16 Assignment: Goal, Research Questions, & Literature Review (16 points) After you have defined the problem draft 1 and 2, you need to understand what has been done so far to try to solve it. Compose two new sections and add them to your problem paper where you respond to the following. Percentages are provided as a guide for the relative length of each section. • Goal (15%) What is the goal you are trying to achieve? Will it be to better understand the problem? Create a model that will inform a solution to the real-world problem? How will your model help address the real-world problem you have identified? CISC600 Scientific Computing I Page 8 of 10 • Research Questions (10%) What are 3-5 questions the answers to which will help you realize your goal? • Review of the Literature (75%) What has already been done by other researchers to try to address this problem? In other words, what is the starting point from where you will begin your research? Is there already an imperfect model that you could expand upon? Is there a similar model in another problem domain that could be adapted to your problem? This should be a comprehensive outline of the state of the art in addressing the problem so far. Support your new sections with at least eight (8) scholarly peer-reviewed sources in addition to those already used in the prior section. Format your submission according to the APA style guide. Remember that all work should be your own original work and assistance received from any source and any references used must be authorized and properly documented. Recommended length: 8-10 pages double-spaced including prior sections, not including front and back matter.

Part 3 Complete the following problems from the textbook. Show all your work. If you write code, include screenshots of your code and any test runs that you perform. Remember that all work should be your own original work and assistance received from any source and any references used must be authorized and properly documented.

17.23) 17.23 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement linear regression. Among other things: (a) include statements to document the code, and (b) determine the standard error and the coeffi cient of determination.

18.17) Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Newton’s interpolating polynomial based on Fig. 18.7

18.18) Test the program you developed in Prob. 18.17 by duplicating the computation from

18.21) 18.21 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Lagrange interpolation. Base it on the pseudocode from Fig. 18.11. Test it by duplicating Example 18.7.

18.23 Develop, debug, and test a program in either a high-level language or macro language of your choice to implement cubic spline interpolation based on Fig. 18.18. Test the program by duplicating Example 18.10 Use Newton’s interpolating polynomial to determine y at x 5 8 to the best possible accuracy. Compute the fi nite divided ifferences as in Fig. 18.5 and order your points to attain optimal accuracy and convergence.

19.10) Develop a user-friendly program for the DFT based on the algorithm from Fig. 19.12. Test it by duplicating Fig. 19.13.

19.12 Develop a user-friendly program for the FFT based on the algorithm from Fig. 19.18. Test it by duplicating Fig. 19.13.

20.23 Use multiple linear regression to derive a predictive equation for dissolved oxygen concentration as a function of temperature and chloride based on the data from Table P20.21. Use the equation to estimate the concentration of dissolved oxygen for a chloride concentration of 5 g/L at T 5 178C.

20.25 In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water fl ow in the river that is being impounded. For some rivers, long-term historical records of such fl ow data are diffi cult to obtain. In contrast, meteorological data on precipitation is often available for many years past. Therefore, it is often useful to determine a relationship between fl ow and precipitation. This relationship can then be used to estimate fl ows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed:

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