# Advanced Engineering Math Solution 10th

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Proof We square both sides and compare them. Write z1 = x1 + iy1 and z2 = x2 + iy2. Then |z1 + z2|2 = (x1+x2)2 + (y1+y2)2 = x12 + x22 + 2x1x2 + y12 + y22 + 2y1y2. On the other hand, (|z1| + |z2|)2= |z1|2 + 2|z1||z2| + |z2|2 = x12 + x22 + y12 + y22 + 2|z1||z2|. Subtracting, (|z1| + |z2|)2 - |z1 + z2|2 = 2|z1||z2| - 2(x1x2 + y1y2) = 2[|(x1,y1)||(x2,y2)| - (x1,y1).(x2,y2)] (in vector form) = 2[|(x1,y1)||(x2,y2)| - |(x1,y1)||(x2,y2)| cos å] = 2 |(x1,y1)||(x2,y2)| (1 - cos å ) ≥ 0, giving the result. Note The .advanced engineering math ii

Proof We square both sides and compare them. Write z1 = x1 + iy1 and z2 = x2 + iy2. Then |z1 + z2|2 = (x1+x2)2 + (y1+y2)2 = x12 + x22 + 2x1x2 + y12 + y22 + 2y1y2. On the other hand, (|z1| + |z2|)2= |z1|2 + 2|z1||z2| + |z2|2 = x12 + x22 + y12 + y22 + 2|z1||z2|. Subtracting, (|z1| + |z2|)2 - |z1 + z2|2 = 2|z1||z2| - 2(x1x2 + y1y2) = 2[|(x1,y1)||(x2,y2)| - (x1,y1).(x2,y2)] (in vector form) = 2[|(x1,y1)||(x2,y2)| - |(x1,y1)||(x2,y2)| cos å] = 2 |(x1,y1)||(x2,y2)| (1 - cos å ) ≥ 0, giving the result. Note The .advanced engineering mathematics, 10th edition iust personal

. helped to pave the way for the present development of engineering mathematics. This new edition will prepare the student for the. tools for the students to get a good foundation of engineering mathematics that will help them in their careers and in.advanced engineering mathematics alan jeffrey.pdf

The ability to formulate physical problems in mathematical terms is an essential part of all mathematics applications. Although this is not a text on mathematical modeling, where more complicated physical applications are considered, the essential background is ﬁrst developed to the point at which the physical nature of the problem becomes clear. Some examples, such as the ones involving the determination of the forces acting in the struts of a framed structure, the damping of vibrations caused by a .advanced-engineering-mathematics

The ability to formulate physical problems in mathematical terms is an essential part of all mathematics applications. Although this is not a text on mathematical modeling, where more complicated physical applications are considered, the essential background is ﬁrst developed to the point at which the physical nature of the problem becomes clear. Some examples, such as the ones involving the determination of the forces acting in the struts of a framed structure, the damping of vibrations caused by a .
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