Intuitive: relationships, innovation, dislike repetition
Sensing: facts, established methods
Reflective: think quietly
Inductive: novices
Deductive: experts
Data formatting
Short: 5 digits
Long: 15 for double, 7 for single
Short e: 3.1415e+000
Long e: Short g: 5
Long g: 15
Short eng: 5 and power of mult 3
Long eng: 15 and power of mult 3
Bank: 3.14
Euler’s method: new = old + slope step
Use clear to clear the variables in storage Use clc to clear the command window
If A = [1 2 3; 4 5 6; 7 8 9], then the value for A(2,3) is 6 b(4) will access the fourth element of the column vector b
>> A(2,:) if A[1 2 3; 4 5 6; 7 8 9] ans = 4 5 6
Linspace function generates a row vector of equally spaced points linspace(x1, x2, n)
>> linspace (0,1,6) ans = 0 0.2000 0.4000 0.6000 0.8000 1.000
Sqrtm is a matrix version of the square root. round (rounds to the nearest integer) E =[ -1.6 -1.5] round(E) = -2 -2 ceil rounds to the nearest integer towards infinity floor rounds to negative infinity
M-files put commands in text files (script[commands that are saved on a file - when MATLAB runs a script file] and function files[can accept input arguments from the command window return outputs to the command window but variables created and manipulated within the function do not impact the command window]) outvar = the name of the output variable; arglist = function’s argument list formatted output, or for output generated by combining variable values with literal text, use the fprintf command
A for loop ends after a specified number of repetitions established by the number of columns given to an index variable.--> for index = start:step:finish statements end
A while loop ends on the basis of a logical condition while condition statements end
True value = approximation + error
True numerical error (ET ) = true value-approximation
Absolute error = absolute value (ET ) True fractional relative error = (true value-approximation)/(true value)
True percent relative error: εT = ((true value-approximation)/(true value)) x 100% εa = (approximation error/approximation) *100%
Percent relative error (good for iteration) εa = (present approximation-previous approximation/present approximation) *100%
Decision loops (if or while) preferable for iterative solutions in the previous problem if you are using a stopping criterion
Roundoff errors arise because digital computers cannot represent some quantities exactly.
1.decimal (base-10) = 10 digits (0-9) 42.9 = (4x101 )+(2x100 )+(9x10-1 ) 2. binary (base – 2) = 0 and 1 digits
0 – positive 1 – negative
Fractional quantities are represented in floating-point format +/- s x be s= significand (mantissa), b = base number system, e=exponent; S1d1 .d2 x10s0d0 realmax – displays the largest positive real number realmin - displays the smallest positive real number
The Taylor series provides a means to express this idea mathematically: The more terms are used, the smaller the error, and The smaller the spacing, the smaller the error for a given number of terms.
Maclauren Series: