1 Infinite Series, Power Series 2 Complex Numbers 3 Linear Algebra 4 Partial Differentitation 5 Multiple Integreals 6 Vector Analysis 7 Fourier Series And Transforms 8 Ordinary Differential Equations 9 Calculus Of Variations 10 Tensor Analysis 11 Special Functions 12 Series Solutions Of Differential Equations; Legendre, Bessel, Hermite, And Laguerre Functions 13 Partial Differential Equations 14 Functions Of A Complex Variable 15 Probability And Statistics expand_more
4.1 Introduction And Notation 4.2 Power Series In Two Variables 4.3 Total Differentials 4.4 Approximations Using Differentials 4.5 Chain Rule Or Differentiating A Function Of A Function 4.6 Implicit Differentiation 4.7 More Chain Rule 4.8 Application Of Partial Differentiation To Maximum And Minimum Problems 4.9 Maximum And Minimum Problems With Constraints; Lagrange Multipliers 4.10 Endpoint Or Boundary Point Problems 4.11 Change Of Variables 4.12 Differentiation Of Integrals; Leibniz' Rule 4.13 Miscellaneous Problem expand_more
Problem 1P: If x=yz and y=2sin(y+z), find dx/dy and d2x/dy2. Problem 2P: IfP=rcostandrsint2ter=0,finddP/dt. Problem 3P: Ifz=xeyandx=cosht,y=coss,findz/sandz/t. Problem 4P Problem 5P Problem 6P Problem 7P: If x=rcos and y=rsin, find (y/)r and (y/)x. Also find (/y)x in two ways (by eliminating r from the... Problem 8P: If xs2+yt2=1 and x2s+y2t=xy4, find x/s,x/t,y/s,y/t, at (x,y,s,t)=(1,3,2,1). Hint: To simplify the... Problem 9P: Verify (7.16) in three ways: (a) Differentiate equations (7.6). (b) Take differentials of (7.5) and... Problem 10P Problem 11P: Finish Example 4 above, both for the general case and for the given numerical values. Substitute the... Problem 12P: Ifw=x+ywithx3+xy+y3=sandx2y+xy2=t,findw/s,w/t. Problem 13P Problem 14P: Ifu=x2+y2+xyzandx4+y4+z4=2x2y2z2+10, find (u/x)z at the point (x, y, z)=(2,1,1). Problem 15P Problem 16P: Let w=x2+xy+z2 (a) If x3+x=3t,y4+y=4t,z5+z=5t, find dw/dt. (b) If y3+xy=1 and z3xz=2, find dw/dx.... Problem 17P: Ifp3+sq=t,andq3+tp=s,find(p/s)t,(p/s)qat(p,q,s,t)=(1,2,3,5). Problem 18P: Ifm=a+bandn=a2+b2find(b/m)nand(m/b)a. Problem 19P Problem 20P Problem 21P Problem 22P: If w=f(ax+by), show that bwxawy=0. Hint: Let ax+by=z. Problem 23P Problem 24P Problem 25P: The formulas of this problem are useful in thermodynamics. (a) Given f(x,y,z)=0, find formulas for... Problem 26P: Given f(x,y,z)=0 and g(x,y,z)=0, find a formula for dy/dx. Problem 27P: Given u(x,y) and y(x,z), show that uxz=uxy+uyxyxz. Problem 28P format_list_bulleted