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# AMME2000/BMET2960 - Assignment 1 Due: Marks will be deducted for handwritten answers and screenshots of equations and/or gures.

Need handwritten solutions to all questions. Esp. Section 2.

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AMME2000/BMET2960 - Assignment 1 Due: Midnight Friday 22“Cl March 2019 Assignment Information This assignment is split into two sections. Your assignment is to be presented as a concise reportin a Word document or PDF. 10% of the assignment marks are allocated for overall clarity andpresentation of the report. Marks will be deducted for handwritten answers and screenshots ofequations and/or ﬁgures. The report should not exceed 1000 words (this limit excludes ﬁgurecaptions and your Matlab code in the appendix); additional words will not be marked. Any ﬁguresand tables you include in your report must be numbered and must be referred to and discussed.An electronic copy of the report should be submitted to Turnitin by the due date.Late submissions will incur a penalty of 5% per day late. In your report, be sure to clearly identify the start of each section and question, and to providea sub-heading (eg. Section 1 Question 1 “1.1 First Derivative of f(:r)”) Each question will bemarked separately, so make sure all relevant working and ﬁnal answers are in that section. Section 1: Taylor Series Approximations Consider the function;f(:r) = cos(2:c) (sin(cc) 7 \$33) (1) In this section you are required to compare the exact solution of the ﬁrst derivative of this function,f’(:c), to the four-point forward, backward and central ﬁnite difference stencils given respectively fjfmi) g —f£+2 + ﬁfigg; 3ft — 20—1 (2)f;(\$i) g 2ﬁ+1+3fi6—A:ﬁ—i+fi—2 (3)fxfiri) m —fi+2 + SfiEA—xSﬁ—l + fi—2 (4) where Act is the grid spacing, f; = f(:r,;). For the written report: 1. Show that the analytic expression for the ﬁrst derivative of f(1') is;f’(9:) = cos(2:r) (cos(:r) — 9:) — 2 sin(2:r) (sin(:r) — 0.5332) (5) (5%)