Lab Assignment Coversheet This sheet must be included with your work submission Required Academic Integrity Statement Texas A M University Policy Statement Academic Integrity Statement All syllabi shall contain a section that states the Aggie Honor Code and refers the student to the Honor Council Rules and Procedures 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 preprinted and 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 received unauthorized 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 Points Adherence to the SPE Style Guide Petroleum Engineering Handbook 10 Grammar Professionalism 5 Completeness of Literature Review 15 Completeness of Introduction 10 Completeness of Methodology 15 Completeness of Discussion 15 Completeness of Conclusions 10 Completeness of References 10 Completeness of Nomenclature 10 Final Grade 100 During this lab the concepts of Taylor s Series and error were used Taylor s Series is a formula that can be effectively utilized to make an approximation by predicting the function value at one point in terms of the function value and its derivative at another point Below this paragraph Eq 1 represents the Taylor s Series Approximation Equation As one makes imperative approximations with Taylor s Series numerical errors during such mathematical operations or procedure can arise Such numerical error that can occur during the arithmetic operations is truncation error Truncation error is a type of error that occurs when approximations are used to represent mathematical procedures This kind of error can be calculated by using Eq 2 f x i h2 f 3 x i h 3 f n x i hn f x i 1 f x i f x i h Rn Eq 1 2 3 n Et actual solution approximate solution Eq 2 Introduction The objective of this lab was to successfully create Taylor s Series Approximation of Cos X VBA functions that can accept the two arguments the value of x in radians and n the number of terms to include in the Taylor Series approximation upper limit of truncated summation After fulfilling this significant objective another goal of this experiment was to generate more accurate results that have errors less than the maximum absolute true error Methodology Option Explicit Determine sign of terms for Cosine Maclaurin Series Expansion Function cos sign i As Long As Long If i Mod 4 0 Or i Mod 4 3 Then cos sign 1 Else cos sign 1 End If End Function Function cos a0 x As Double n As Integer As Double Dim i As Long Const a As Integer 0 cos a0 1 For i 2 To n Step 2 cos a0 cos a0 cos sign i x a i Application WorksheetFunction Fact i Next i End Function Function cos a1 x As Double n As Integer As Double Dim i As Long Dim pi As Double temp As Double pi Application WorksheetFunction pi temp 1 Sqr 2 cos a1 temp For i 1 To n cos a1 cos a1 cos sign i temp x pi 4 i Application WorksheetFunction Fact i Next i End Function Function choose1 x As Double n As Integer As Double Dim pi As Double pi Application WorksheetFunction pi If x pi 8 Then choose1 cos a0 x n Else choose1 cos a1 x n End If End Function Discussion Figure 1 Actual Solutions of Cos X Figure 1 Cos X Taylor Approximation Series in VBA with N Terms About A 0 Figure 2 Error Calculation of Cos X Taylor Approximation Series with N Terms About A 0 Figure 3 Cos X Taylor Approximation Series in VBA with N Terms About A Pi 4 Figure 4 Error Calculation of Cos X Taylor Approximation Series with N Terms About A Pi 4 Figure 5 Cos X Taylor Approximation Series With N Terms About A Pi 8 Figure 6 Error Calculation of Cos X Taylor Approximation Series With N Terms About A Pi 8 Conclusions Taylor s Series of Cos X about a pi 8 provides better approximations overall than both the Taylor s Series of Cos X about a 0 and the Taylor s Series of Cos X about a pi 4 Taylor s Series of Cos X about a pi 8 generated the most accurate results The Taylor s Series of Cos X about a pi 4 generated the least accurate results Adding more terms in Taylor s Series equation can significantly reduce the error of the approximations References Canale P Raymond and Chapra C Steven 2015 Numerical Methods for Engineers 7th Edition New Delhi India McGraw Hill Education Nomenclature cos sign Sign of a subsequent term in a Taylor Series equation x Value Integer in Radians n Number of Terms in a Taylor Series equation cos a0 Cos X Taylor Series Approximation About a 0 cos a1 Cos X Taylor Series Approximation About a pi 4 choose1 Cos X Taylor
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