Daniel Yorgov 
Assignment MA3610 Exam

Problem for Section 13.3 
Given two vectors (Overscript[a, →]) = 
        2  (Overscript[i, →]) - 3  (Overscript[j, →]) + 4  (Overscript[k, →]) and (Overscript[b, →]) = 
        1  (Overscript[i, →]) + 2  (Overscript[j, →]) + 3  (Overscript[k, →])  represent vector  as a sum of two vectors (Subscript[(Overscript[a, →]), paral]) and (Subscript[(Overscript[a, →]), perp ]) respectively parallel and perpendicular to (Overscript[b, →]).

Proposed Scoring:
-(Overscript[u, →])   from  (Overscript[b, →])   2 pts
- (Subscript[(Overscript[a, →]), paral])=((Overscript[a, →]).(Overscript[u, →])).(Overscript[u, →])   4 pts
-(Subscript[(Overscript[a, →]), perp])= (Overscript[a, →]) - (Subscript[(Overscript[a, →]), paral]) 4 pts
Problem spot:
- need to devide (Overscript[b, →]) by its magnitude to find the unit vector

Problem for Section 14.1
Estimate the values of  (Subscript[f, x])(2; 1) and (Subscript[f, y])(2; 1) from the given contour diagram of f(x, y)

Needs["Graphics`"]
Plot[{-0.5 x + 2, 1 - x,  3 - 0.5  x},{x, 0, 6}, PlotLabel -> "Fig.1", GridLines -> Automatic, PlotRange  ->  {0, 3}, AxesLabel  -> {x, y},PlotStyle -> Thickness[ .01], Epilog -> {Text["z=0", {2, 
                2}, 
Background -> White],  
            Text["z=5", {1, 1.5}, 
Background -> 
                White], 
            Text["z=10", {0.55, 
                0.7}, 
Background -> White]}]

Proposed Scoring:
Each  derivative 5 pts
Problem spot: contour diagram reading