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L1_Rootfinding - MA2213 Lecture 1 Rootfinding Class...

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MA2213 Lecture 1 Rootfinding
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Class Schedule Lectures: Tuesday 2-4 in LT31 (building S16) Groups: Class will be divided into 5 groups Each group (of about 25 students) will: Tutorials: will meet in weeks 3,5,7,9,11 Labs: will meet in weeks 4,6,8,10,12 do tutorials and labs together Friday 2-4 in LT31 (building S16) be assigned a person who will supervise both tutorials and labs, and grade written homework (more information will be announced soon)
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Suggestions Do: Attend lectures, tutorials, and labs Complete assigned homework and give to your grader during tutorials and labs Do Not: Send or give me assigned homework Study the textbook and work problems Use the Module IVLE Website Email me questions whose answers are on the Module IVLE Website Purchase the required textbook
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Objectives and Prerequisites Learn Numerical Methods Accuracy and Errors Computer Algorithms (MATLAB) Calculus Real Numbers and Complex Numbers Fundamental Theorem of Algebra Fundamental Theorems of Calculus Linear Equations: Geometry and Matrix Algebra Vector Spaces and Linear Transformations Linear Algebra Prerequisites
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Required Textbook Elementary Numerical Methods by Atkinson and Han About 20 books are now in the Science COOP (due to limited shelve space) but more books will be transferred from the warehouse) Homework (Tutorial and Lab) may be assigned from this textbook Suggested Reading from this textbook Appendix A&B Math Rev, D MATLAB
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Lecture Schedule 1 Rootfinding 14, 17 Aug 2 Interpolation 21, 24 Aug 3 Approximation 28, 31 Aug 4 Numerical Integration 4, 7 Sept 5 Linear Equations (Direct) 11, 14 Sept 6 Linear Equations (Iterative) 18, 21 Sept Recess Week 24-28 Sept Review and Midterm Test 2, 5 Oct Lecture # Topic Dates
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Lecture Schedule 7 Eigenvalues 9, 12 Oct 8 Nonlinear Systems 16, 19 Oct 9 ODE (Explicit) 23, 26 Oct 10 ODE (Implicit) 30 Oct, 2 Nov 11 PDE 6, 9 Nov 12 Review 13, 16 Nov Lecture # Topic Dates EXAM : Friday, 30 Nov 200 (MORNING)
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Retirement Planning (pages 71-72) in P deposited at beginning of each of Amount r in N time periods. Interest is paid per period. End of Period Amount of Money in the Account 1 in P r A ) 1 ( ) 1 ( + = in P r A r A ) 1 ( ) 1 ( ) 1 ( ) 2 ( + + + = 2 in in P r P r ) 1 ( ) 1 ( 2 + + + = 1 + k in P r k A r k A ) 1 ( ) ( ) 1 ( ) 1 ( + + + = +
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Retirement Planning (pages 71-72) Specifying and the value of in terms of the value of suffices to write a computer program to compute ) 1 ( A A ) 1 ( + k A ) ( k A The figure shows that if you deposited $1000 monthy at r = 0.0025 you would have $584,194 after 30 years
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Retirement Planning (pages 71-72) Here is the smallest MATLAB code required function A = amount(Pin,Nin,r) A(1) = (1+r)*Pin; for k = 1:Nin-1 A(k+1) = (1+r)*A(k) + (1+r)*Pin; end you would write and store it in a m-file amount.m and then run it interactively using the commands: A = amount(1000,360,0.0025) plot(A); grid; xlabel(‘End of Period (Month)’) ylabel(‘Amount at end of Period’)
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