Introduction to Numerical Methods: A Comprehensive Overview
Numerical methods play a crucial role in solving mathematical problems efficiently through arithmetic operations. This lecture by Dr. Nur Uddin covers the fundamental concepts of numerical methods, emphasizing their importance in engineering problem-solving with the use of modern digital computers. The lecture outlines various mathematical areas within numerical methods, such as roots of equations, linear algebraic equations, optimization, curve fitting, integration, ordinary and partial differential equations. Practical aspects, grading criteria, course rules, and the motivation behind studying numerical methods are also covered in this comprehensive introduction.
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Numerical Method Lecture 1: Introduction By: Nur Uddin, Ph.D 1
Lecturer: Nur Uddin, PhD. ( Email: nur.uddin@upj.ac.id ) Reference: S.C. Chapra and R.P. Canale, Numerical Methods for Engineers 7th Edition, Mc Graw-Hill Education, 2015. Grading: UTS (30%) + UAS (30%) + Tugas (30%) + Keaktifan (10%) Software: Python 3.7 (Preferably install Anaconda 3) 2
Aturan kuliah 1. Toleransi keterlambatan: 30 menit (08.00) 2. PR & Quiz: Setiap minggu 3. Komputer: 3
Motivation Numerical methods are techniques where mathematical problems are formulated so that they can be solved with arithmetic operations. Although there are many kinds of numerical methods, they have one common characteristic: they invariably involve large numbers of tedious arithmetic calculations. It is little wonder that with the development of fast, efficient digital computers, the role of numerical methods in engineering problem solving has increased dramatically in recent years. 4
The most mathematical areas in numerical method 1. 2. 3. 4. 5. 6. 7. Roots of Equations Systems of Linear Algebraic Equations Optimization Curve Fitting Integration Ordinary Differential Equations Partial Differential Equations 5
Non-computer methods Solutions were derived for some problems using analytical, or exact, methods. Graphical solutions were used to characterize the behavior of systems. Calculators and slide rules were used to implement numerical methods manually. 13
Pre-computer era During the pre-computer era, significant amounts of energy were expended on the solution technique itself, rather than on problem definition and interpretation 14
Computer era Today, computers and numerical methods provide an alternative for such complicated calculations. Computer can be used to obtain solutions directly. Numerical methods represent alternatives that greatly enlarge your capabilities to confront and solve problems. As a result, more time is available for the use of your creative skills. More emphasis on problem formulation and solution interpretation and the incorporation of total system, or holistic, awareness 15
Numerical methods and engineering practice Since the late 1940s the widespread availability of digital computers has led to a veritable explosion in the use and development of numerical methods. At first, this growth was somewhat limited by the cost of access to large mainframe computers. The recent evolution of inexpensive personal computers has given us ready access to powerful computational capabilities. 16
Why should we study numerical methods? 1. Numerical methods are extremely powerful problem-solving tools. During your careers, you may often have occasion to use commercially available prepackaged, or canned, computer programs that involve numerical methods. Many problems cannot be approached using canned programs. You can design your own programs to solve problems without having to buy or commission expensive software. Numerical methods are an efficient vehicle for learning to use computers. Numerical methods provide a vehicle for you to reinforce your understanding of mathematics. 2. 3. 4. 5. 17
