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The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics (predicting the motions of planets, stars, and galaxies); numerical linear algebra is important for data analysis stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

Before the advent of modern computers, numerical methods often depended on hand interpolation formulas applied to data from large printed tables. Since the mid 20th century, computers calculate the required functions instead, but many of the same formulas nevertheless continue to be used as part of the software mathematics.

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**BOOK NAME** – NUMERICAL ANALYSIS HAND WRITTEN NOTE

**AUTHOR** – PI AIM INSTITUTE

**SIZE** – 37.7MB

**PAGES** – 78

The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Numerical analysis continues this long tradition: rather than exact symbolic answers, which can only be applied to real-world measurements by a translation into digits, it gives approximate solutions within specified error bounds.

Numerical analysis, area of mathematics and computer science that creates, analyzes, and implements algorithms for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of digital computers has led to the increasing use of realistic mathematical models in science and engineering, and numerical analysis of increasing sophistication is needed to solve these more detailed models of the world. The formal academic area of numerical analysis ranges from quite theoretical mathematical studies to computer science issues.

With the increasing availability of computers, the new discipline of scientific computing, or computational science, emerged during the 1980s and 1990s. The discipline combines numerical analysis, symbolic mathematical computations, computer graphics, and other areas of computer science to make it easier to set

Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of the square root of 2, the modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.

Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century also the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in celestial mechanics (planets, stars, and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.

**CSIR NET Exam Pattern 2020:**

NTA has released the CSIR NET Exam Pattern for all the five subjects. Candidates will have to pick any one subject and apply for the same. The CSIR UGC NET exam pattern and marking scheme are different for all the subjects.

- CSIR NET question paper for each subject is divided into three parts namely, Part A, Part B, Part C.
- All three sections are compulsory.
- There will be no break between the three sections.
- All 3 parts will have only Multiple Choice Questions (MCQs).
- The CSIR NET 2020 will be conducted for a total of 200 marks.
- The exam will be held for a duration of 3 hours.

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