Numerical Analysis Lecture 1 PDF

Numerical Analysis Lecture 1 Numerical Computation Numerical Methods Numerical Analysis Rs. 2.1234567 2.12 Rs 2.1234567 Th 2,123.45 Rs 2.1234567 M 2,123,456.70 Millennium Bug 2000 September 24, 1978 092478 092498 092499 123199 123199 010110 010120 010100 12311999 01012000 ...

Numerical Analysis Lecture 1 Numerical Computation Numerical Methods Numerical Analysis Rs. 2.1234567 2.12 Rs 2.1234567 Th 2,123.45 Rs 2.1234567 M 2,123,456.70 Millennium Bug 2000 September 24, 1978 092478 092498 092499 123199 123199 010110 010120 010100 12311999 01012000 Bank Account Profit as %age 602.55565 Rupees 0.00565 x 100 0.565 x 1,000 5.65 x 1,000,000 5,650.00  Course Contents Introduction Solution of Non Linear Equations Solution of Linear System of Equations Approximation of Eigen Values Interpolation and Polynomial Approximation Numerical Differentiation Numerical Integration Numerical Solution of Ordinary Differential Equations  Chapter 1 Introduction Number (s) System (s) In our daily life, we use numbers based on the decimal system. In this system, we use ten symbols 0, 1,…,9 and the number 10 is called the base of the system. Thus, when a base N is given, we need N different symbols 0, 1, 2, …,(N – 1) to represent an arbitrary number. The number systems commonly used in computers are Base, N Number 2 Binary 8 Octal 10 Decimal 16 Hexadecimal An arbitrary real number, a can be written as m m 1 a am N  am 1N   1 1 a1N  a0  a 1N m   a m N In binary system, it has the form, m 1 a am 2  am  1 2 m   1 1 a1 2  a0  a 1 2    a m 2 m The decimal number 1729 is represented and calculated 3 2 (1729)10 110  7 10  1 0 2 10  9 10 While the decimal equivalent of binary number 10011001 is 0 1 2 12  0 2  0 2 3 4 5 12  12  0 2 6 7 0 2  12 1 1 1 1    8 16 128 (1.1953125)10 Electronic computers use binary system whose base is 2. The two symbols used in this system are 0 and 1, which are called binary digits or simply bits. The internal representation of any data within a computer is in binary form. However, we prefer data input and output of numerical results in decimal system. Within the computer, the arithmetic is carried out in binary form. Conversion of decimal number 47 into its binary equivalent 2 47 Remainder 2 23 1 2 11 1 2 5 1 2 2 1 2 1 0 0 1 Most significant bit (47)10 (101111) 2 Binary equivalent of the decimal fraction 0.7625. Product Integer 0.7625 x2 1.5250 1 0.5250 x2 1.0500 1 0.05 x2 0.1 0 0.1 x2 0.2 0 0.2 x2 0.4 0 0.4 x2 0.8 0 0.8 x2 1.6 1 0.6 x2 1.2 1 0.2 x2 0.4 0 (0.7625)10 (0.11....11(0011)) 2 Conversion (59)10 into binary and then into octal. 2 59 2 29 1 2 14 1 2 7 0 2 3 1 2 1 1 0 1 (59)10 (11011) 2 (111011) 2 111011 (73)8 Numerical Analysis Lecture 1