Numerical Methods - Berlin Chen

Numerical MethodsBerlin Chen ( 陳 柏 琳 )Department of Computer Science & Information EngineeringNational Taiwan Normal University

What are Numerical Methods? (3/3)NM – Berlin Chen 4

Why Studying Numerical Methods? (1/2)• Numerical methods greatly expand the types ofproblems you can address– E.g., handling large systems of equations, nonlinearities, andcomplicated geometries– As such, greatly enhance your problem-solving sills• Numerical methods allow you to use “canned” softwarepackages with insight rather than treating them as “blackboxes”– Enable intelligent use of these packages by an understandingthe basic theory underlying the methods• Many problems cannot be approached using cannedprograms– With the help of numerical methods, you can design yourprograms to solve problemsNM – Berlin Chen 5

Why Studying Numerical Methods? (2/2)• Numerical methods are an efficient vehicle for learning touse computers and can also illustrate the power andlimitations of computers– We should learn to acknowledge and control the errors ofapproximation that are part and parcel of large-scale numericalmethods• Numerical methods provide a vehicle for you to reinforceyour understanding of mathematics– One function of numerical methods is to reduce highermathematics to basic arithmetic operations. In so doing, we canenhance our understanding and insight of complicated problemsNM – Berlin Chen 6

Objectives of this Course• This course sets out to introduce the fundamentalsunderpinning numerical methods• Learn to decide how and when to choose a numericalmethod, and how to implement and apply it to solvepractical problems in science and engineering• Understand how numerical methods and computerswork in tandem to generate reliable solutions tomathematical problems• Have a solid appreciation of the capabilities andlimitations of various numerical methodsNM – Berlin Chen 7

Textbooks• Steven C. Chapra, Applied NumericalMethods with MATLAB for Engineersand Scientists, McGraw-Hill, 2012• Steven C. Chapra and Raymond P.Canale, Numerical Methods forEngineers, McGraw-Hill, 2010NM – Berlin Chen 8

Some Numerical Methods (1/2)NM – Berlin Chen 9

Some Numerical Methods (2/2)NM – Berlin Chen 10

Outline of Course ContentNM – Berlin Chen 11

Grading (Tentative)• Midterm and Final: 45%• Homework/Projects: 40%• Attendance/Other: 15%NM – Berlin Chen 12