(This sheet must be included with your work submission)Required Academic Integrity Statement: (Texas A&M University Policy Statement)Coursework Copyright Statement: (Texas A&M University Policy Statement)Lab Assignment Coversheet(This sheet must be included with your work submission)Required Academic Integrity Statement: (Texas A&M University Policy Statement)Academic Integrity StatementAll syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules andProcedures on the web.Aggie Honor Code"An Aggie does not lie, cheat, or steal or tolerate those who do."Upon accepting admission to Texas A&M University, a student immediately assumes a commitment to uphold the Honor Code, to accept responsibility for learning and to follow the philosophy and rules of the Honor System. Students will be required to state their commitment on examinations, research papers, and other academic work. Ignorance of the rules does not exclude any member of the Texas A&M University community from the requirements or the processes of the Honor System. For additional information please visit: www.tamu.edu/aggiehonor/On all course work, assignments, and examinations at Texas A&M University, the following Honor Pledge shall be preprintedand signed by the student:"On my honor, as an Aggie,I have neither given nor received unauthorized aid on this academic work."Aggie Code of Honor:An Aggie does not lie, cheat, or steal or tolerate those who do.Required Academic Integrity Statement:"On my honor, as an Aggie, I have neither given nor receivedunauthorized aid on this academic work." Evan Situ____________(Print your name) Evan Situ____________(Your signature)Coursework Copyright Statement: (Texas A&M University Policy Statement)The handouts used in this course are copyrighted. By "handouts," this means all materials generated for this class, which include but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and additional problem sets. Because these materials are copyrighted, you do not have the right to copy them, unless you are expressly granted permission.As commonly defined, plagiarism consists of passing off as one’s own the ideas, words, writings, etc., that belong to another. In accordance with this definition, you are committing plagiarism if you copy the work of another person and turn it in as your own, even if you should have the permission of that person. Plagiarism is one of the worst academic sins, for the plagiarist destroys the trust among colleagues without which research cannot be safely communicated.If you have any questions about plagiarism and/or copying, please consult the latest issue of the Texas A&M University Student Rules, under the section "Scholastic Dishonesty."Lab Assignment Grading Rubric(This sheet must be included with your work submission)Criteria PointsAdherence to the SPE Style Guide & Petroleum Engineering Handbook / 10Grammar/Professionalism / 5Completeness of Literature Review / 15Completeness of Introduction / 10Completeness of Methodology / 15Completeness of Discussion / 15Completeness of Conclusions / 10Completeness of References / 10Completeness of Nomenclature / 10Final Grade /100Literature ReviewThe concepts that were used during this lab is the utilization of Newton Raphson Method with the Jacobian Matrix for multivariable functions. A Jacobian matrix is a matrix comprised of first-order, partial derivatives of a multivariable function. Figure 1 shows an example of this particular type of matrix. Newton Raphson Method, which was used in the execution of Jacobian matrix, is a mathematical technique predicated on using the derivative of the function to estimate its intercept with the axis, or axes, of independent variable(s).Fig. 1 – Jacobian Matrix of First-Order Partial Derivatives of Multivariable FunctionsIntroductionA major goal of this lab was to find the accurate values of x, y, and z to make u(x, y, z), v(x, y, z), and w(x, y, z) zero by programming imperative functions in Visual Basis for Application in Excel and by using an integrated-Excel tool called a solver. Not only that, the Euclidean norm can be minimized by changing the values of x, y, and z. Before beginning the experiment, here were the equations were kept into mind. Initial values of x, y, and z that were used to start the experiment was 5, 5, and 5.u(x , y , z)=xz +2 y2z −3 zy −15…………………………………………...…………………………….Eq. 1v(x , y ,z)=x2y−12y3z+2 zx+20……………………………………….………………………………Eq. 2w(x , y , z)=−2 xy z2+3 y2x+zy+5………………………………………………..……………………Eq. 3MethodologyOption ExplicitFunction u(x As Double, y As Double, z As Double) As Double u = x * z + 2 * y ^ 2 * z - 3 * z * y - 15End FunctionFunction dudx(x As Double, y As Double, z As Double) As Double dudx = zEnd FunctionFunction dudy(x As Double, y As Double, z As Double) As Double dudy = 4 * y * z - 3 * zEnd FunctionFunction dudz(x As Double, y As Double, z As Double) As Double dudz = x + 2 * y ^ 2 - 3 * yEnd FunctionFunction v(x As Double, y As Double, z As Double) As Double v = x ^ 2 * y - 0.5 * y ^ 3 * z + 2 * z * x + 20End FunctionFunction dvdx(x As Double, y As Double, z As Double) As Double dvdx = 2 * x * y + 2 * zEnd FunctionFunction dvdy(x As Double, y As Double, z As Double) As Double dvdy = x ^ 2 - 1.5 * y ^ 2 * zEnd FunctionFunction dvdz(x As Double, y As Double, z As Double) As Double dvdz = -0.5 * y ^ 3 + 2 * xEnd FunctionFunction w(x As Double, y As Double, z As Double) As Double w = -2 * x * y * z ^ 2 + 3 * y ^ 2 * x + z * y + 5End FunctionFunction dwdx(x As Double, y As Double, z As Double) As Double dwdx = -2 * y * z ^ 2 + 3 * y ^ 2End FunctionFunction dwdy(x As Double, y As Double, z As Double) As Double dwdy = -2 * x * z ^ 2 + 6 * y * x + zEnd FunctionFunction dwdz(x As Double, y As Double, z As Double) As Double dwdz = -4 * x * y * z + yEnd FunctionAccording to the code from the Visual Basics for Application for Excel, u, v and w functions were concocted and the first-order partial derivatives of each respective multivariable function with respect to x, y and z separately were created as well. Then, a solver was utilized to solve for the x, y, and z values that make the u, v and w functions
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