HW
Math 273
Name_________________________
1. One dimensional coordinate changes: Substitution
Recall how to integrate composite functions such as f(x) = e2x+3 . Show in detail how to integrate this
function by letting u = 2x+3. Integrate from x = 0 to x =10, but DO NOT CHANGE BACK TO x
coordinates at the end; instead do the evaluations in the new coordinates.
2. Cylindrical to Rectangular
a) Calculate the 3x3 matrix representing the linear transformations from cylindrical to rectangular
coordinates using the non-linear coordinate change functions on p.1107. (Answer on that page)
b) Given r=1, θ=0, and z=1, Δr=.1, Δθ=.2 (radians) and Δz= .3 (radians), find Δx, Δy, and Δz.
c) Given Δx= .1, Δy=.2, and Δz=.3, calculate Δr, Δθ, and Δz.
d) By taking the absolute value of the determinant (Jacobian) of the matrix in a), show the local
coordinate relationship between cylindrical and rectangular coordinates.
3. Spherical to Rectangular
a) Calculate the 3x3 matrix representing the linear transformations from spherical to rectangular
coordinates using the non-linear coordinate change functions on p.1107.
b) Given ρ=1, θ=0, and φ=0, Δρ=.1, Δθ=.2 (radians) and Δφ= .3 (radians), find Δx, Δy, and Δz.
c) By taking the absolute value of the determinant (Jacobian) of the matrix in a), show the local
coordinate relationship between spherical and rectangular coordinates (problem 17, section 5.7).