ECE257ECE257 NumericalNumerical Methods Methods andandScientificScientific ComputingComputingJohn A. ChandyJohn A. ChandyECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutTodayToday’’s class:s class:••Introduction to numerical methodsIntroduction to numerical methods••Basic content of course and classBasic content of course and classexpectationsexpectations••Mathematical modelingMathematical modelingECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutIntroductionIntroduction••What are numerical methods?What are numerical methods?––““…… techniques by which mathematical problems are techniques by which mathematical problems areformulated so that they can be solved with arithmeticformulated so that they can be solved with arithmeticoperations.operations.”” (Chopra and Canale) (Chopra and Canale)••What type of mathematical problems?What type of mathematical problems?––RootsRoots––IntegrationIntegration––OptimizationOptimization––Curve FittingCurve Fitting––Differential EquationsDifferential Equations––Linear SystemsLinear SystemsECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutIntroductionIntroduction••How do you solve these difficult mathematicalHow do you solve these difficult mathematicalproblems?problems?••Example: What are the roots of xExample: What are the roots of x22-7x+12?-7x+12?••Three general non-computer methodsThree general non-computer methods––AnalyticalAnalytical––GraphicalGraphical––ManualManualECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutAnalytical solutionsAnalytical solutions••This is what you learned in math classThis is what you learned in math class••Gives exact solutionsGives exact solutions••Not always possible for all problems and usuallyNot always possible for all problems and usuallyrestricted to simple problems with few variables orrestricted to simple problems with few variables oraxesaxes••The real world is more complex than the simpleThe real world is more complex than the simpleproblems in math classproblems in math class••Example:Example:––Roots at 3 and 4Roots at 3 and 4€ x2− 7x + 12 = (x − 3)(x − 4)ECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutGraphical SolutionGraphical Solution-1001020304050607080-6 -4 -2 0 2 4 6ECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutManual SolutionManual Solution••Using pen and paper, calculators, slideUsing pen and paper, calculators, sliderules, etc. to solve an engineering problemrules, etc. to solve an engineering problem••Very time consumingVery time consuming••Error-proneError-proneECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutIntroductionIntroduction••What are numerical methods?What are numerical methods?––““…… techniques by which mathematical problems are techniques by which mathematical problems areformulated so that they can be solved with arithmeticformulated so that they can be solved with arithmeticoperations.operations.”” (Chopra and Canale) (Chopra and Canale)••Arithmetic operations map into computer arithmeticArithmetic operations map into computer arithmeticinstructionsinstructions••Numerical methods allow us to formulateNumerical methods allow us to formulatemathematical problems so they can be solved bymathematical problems so they can be solved bycomputercomputerECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutCourse OverviewCourse Overview••What is this course about?What is this course about?––Using computers and numerical methods toUsing computers and numerical methods tosolve mathematical problems that arise insolve mathematical problems that arise inengineeringengineering––Most of the focus will be on electricalMost of the focus will be on electricalengineering problemsengineering problemsECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutClass meetings:Class meetings:••Lectures are Lectures are Tuesday and Thursday,Tuesday and Thursday,1111––12:1512:15••No specific lab time, but significantNo specific lab time, but significantcomputer time expected.computer time expected.••Computers are available in C25 and C27.Computers are available in C25 and C27.ECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutClass Class assignmentsassignments••Homework will be Homework will be assignedassigned once every once every week or twoweek or twoand due usually the following week.and due usually the following week.••You may collaborate on the homework, but yourYou may collaborate on the homework, but yoursubmissions should be your own work.submissions should be your own work.••Grading:Grading:––HomeworksHomeworks40%40%––Exam 1 and 2Exam 1 and 240%40%––Final ExamFinal Exam20%20%ECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutMathematical BackgroundMathematical Background••MATH 210Q/211QMATH 210Q/211Q••Taylor seriesTaylor series••Differentiation/IntegrationDifferentiation/Integration••Linear AlgebraLinear AlgebraECE 257 Numerical Methods and Scientific ComputingFall 2004Lecture 1John A. ChandyDept. of Electrical and Computer EngineeringUniversity of ConnecticutComputer BackgroundComputer Background••Languages toLanguages to be covered: be covered:––C, C++, Fortran, C, C++, Fortran, MatlabMatlab••CSE 123/124 programming experienceCSE 123/124 programming