TAILIEUCHUNG - Ebook Basic engineering mathematics (4th edition): Part 2

(BQ) Part 2 book "Basic engineering mathematics" has contents: Reduction of non-linear laws to linear-form, geometry and triangles, introduction to trigonometry, trigonometric waveforms, areas of plane figures, volumes of common solids, adding of waveforms,. and other contents. | 16 Reduction of non-linear laws to linear form Determination of law Frequently, the relationship between two variables, say x and y, is not a linear one, . when x is plotted against y a curve results. In such cases the non-linear equation may be modified to the linear form, y = mx + c, so that the constants, and thus the law relating the variables can be determined. This technique is called ‘determination of law’. Some examples of the reduction of equations to linear form include: (i) y = ax2 + b compares with Y = mX + c, where m = a, c = b and X = x2 . Hence y is plotted vertically against x2 horizontally to produce a straight line graph of gradient ‘a’ and y-axis intercept ‘b’ a (ii) y = + b x 1 y is plotted vertically against horizontally to produce a x straight line graph of gradient ‘a’ and y-axis intercept ‘b’ (iii) y = ax2 + bx y = ax + b. x y Comparing with Y = mX + c shows that is plotted vertix cally against x horizontally to produce a straight line graph y of gradient ‘a’ and axis intercept ‘b’ x If y is plotted against x a curve results and it is not possible to determine the values of constants a and b from the curve. Comparing y = ax2 + b with Y = mX + c shows that y is to be plotted vertically against x2 horizontally. A table of values is drawn up as shown below. x x2 y 1 1 2 4 3 9 4 16 5 25 A graph of y against x2 is shown in Fig. , with the best straight line drawn through the points. Since a straight line graph results, the law is verified. y 53 50 A 40 30 Dividing both sides by x gives Problem 1. Experimental values of x and y, shown below, are believed to be related by the law y = ax2 + b. By plotting a suitable graph verify this law and determine approximate values of a and b. 20 17 B C 10 8 0 5 10 15 20 25 Fig. x y 1 2 3 4 5 From the graph, gradient a = AB 53 − 17 36 = = = BC 25 − 5 20 x2 118 Basic Engineering Mathematics and the y-axis .

• Toán học
• Basic engineering mathematics
• Introduction to trigonometry
• Trigonometric waveforms
• Areas of plane figures
• Volumes of common solids
• Adding of waveforms
• Basic arithmetic
• Engineering notation
• Computer numbering systems
• Simple equations
• Quadratic equations