By Cleve B. Moler
Numerical Computing with MATLAB is a full of life textbook for an introductory path in numerical equipment, MATLAB, and technical computing. The emphasis is at the educated use of mathematical software program; particularly, the presentation is helping readers examine sufficient in regards to the mathematical capabilities in MATLAB to take advantage of them thoroughly, get pleasure from their obstacles, and adjust them accurately. The booklet makes vast use of special effects, together with interactive graphical expositions of numerical algorithms. It presents greater than 70 M-files, that are downloaded from the internet. a few of the greater than 2 hundred workouts contain enhancing and increasing those courses.
the themes lined comprise an advent to MATLAB; linear equations; interpolation; zeros and roots; least squares; quadrature; traditional differential equations; Fourier research; random numbers; eigenvalues and singular values; and partial differential equations. Motivating functions contain sleek difficulties from cryptography, touch-tone dialing, Google page-ranking, atmospheric technological know-how, and snapshot processing, in addition to classical difficulties from physics and engineering.
This revised version comprises alterations and corrections made because the unique variation used to be released in 2004.
Audience: Numerical Computing with MATLAB is designed for a one-quarter or one-semester path essentially for college students in technological know-how and engineering, on the complicated undergraduate or starting graduate point. must haves are calculus, a few familiarity with traditional differential equations and matrices, and a few laptop programming experience.
Contents: Preface; bankruptcy 1: creation to MATLAB; bankruptcy 2: Linear Equations; bankruptcy three: Interpolation; bankruptcy four: Zeros and Roots; bankruptcy five: Least Squares; bankruptcy 6: Quadrature; bankruptcy 7: traditional Differential Equations; bankruptcy eight: Fourier research; bankruptcy nine: Random Numbers; bankruptcy 10: Eigenvalues and Singular Values; bankruptcy eleven: Partial Differential Equations; Bibliography; Index.
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The functions rem(x,y) and mod(x,y) both compute the remainder if x is divided by y. They produce the same result if x and y have the same sign; the result also has that sign. But if x and y have opposite signs, then rem(x,y) has the same sign as x, while mod(x,y) has the same sign as y. Here is a table. x = [37 -37 37 -37]’; y = [10 10 -10 -10]’; r = [ x y rem(x,y) mod(x,y)] produces 37 -37 37 -37 10 10 -10 -10 7 -7 7 -7 7 3 -3 -7 We have chosen to encrypt text that uses the entire ASCII character set, not just the letters.
Matlab uses the floating-point system to handle integers. 0 are the same, but many programming languages would use different representations for the two. Matlab does not distinguish between them. We sometimes use the term flint to describe a floating-point number whose value is an integer. Floating-point operations on flints do not introduce any roundoff error, as long as the results are not too large. Addition, subtraction, and multiplication of flints produce the exact flint result, if it is not larger than 253 .
M can be used to produce printed output of the fern. m. 11. Flip the fern by interchanging its x- and y-coordinates. 12. What happens to the fern if you change the only nonzero element in the matrix A4? 13. What are the coordinates of the lower end of the fern’s stem? 14. The coordinates of the point at the upper tip end of the fern can be computed by solving a certain 2-by-2 system of simultaneous linear equations. What is that system and what are the coordinates of the tip? 15. The fern algorithm involves repeated random choices from four different formulas for advancing the point.