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## CALCULUS 3 FOR ENGINEERS

by: Dr. Filomena Hegmann

43

0

2

# CALCULUS 3 FOR ENGINEERS APPM 2350

Dr. Filomena Hegmann

GPA 3.76

Mary Nelson

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COURSE
PROF.
Mary Nelson
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Applied Math

This 2 page Class Notes was uploaded by Dr. Filomena Hegmann on Thursday October 29, 2015. The Class Notes belongs to APPM 2350 at University of Colorado at Boulder taught by Mary Nelson in Fall. Since its upload, it has received 43 views. For similar materials see /class/231865/appm-2350-university-of-colorado-at-boulder in Applied Math at University of Colorado at Boulder.

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Date Created: 10/29/15
APPM 2350 BASIC TABLE The Frenet Formulas idT vxal dB dT dB K 7 if d5 M3 7 E d5 K 7 d5 The Decomposition of Acceleration dV at aTT LINN7 aT aN RMZ la 7 1 Linear Approximations 1 Error EWy S EMW 960 y 7210 where lfwmlv fzyt fyzt fyyl S M Second Derivative Test Suppose f1 and fy are continuous in a disk centered at cab and fwa7 b fya7 b 0 1 If fmfyy 7 3y gt 0 and fm lt 0 at 17 then f has a local maximum at 17 2 If fmfyy 7 fmzy gt 0 and fm gt 0 at 17 then f has a local minimum at 17 3 If fmfyy 7 3y lt 0 at 17 then f has a saddle at a7b Lagrange Multipliers Vf AVg g 0 Taylor7s Formula about z 07 y 0 f0 0 M0 on mo on M0 W 2mm 0m fyym W Moments and Centers of Mass for three dimensional solids Center of mass 7 7 MW 7 l x i M i MR6yzdl 7 7 M21 7 1 y 7 M 7 MRy5967y72dV7 7 M1 Rz 7yzdl Moments of lnertia Ix y2226zy72 dV7 Iy 22z26zy72 dV7 Iz 2y26xyz dV R R R Radii of Gyration Rm ImM Ry IyM Rz IzM Polar Coordinates z 7 cost97 y rsint97 2 2 2 rz y Spherical and Cylindrical Coordinates Cylindrical to Spherical to Spherical to Rectangular Cylindrical Rectangular rcos0 rpsin zpsin cos0 yrsin0 zpcos ypsin sin0 z z 6 6 z pcos b dV dzdydz dzrdrd pzsinrbdpdrbd Substitutions in Multiple Integrals R mmdzdy G fltzltuwgtyltuwgtgtJltuwgtdudv Green7s Theorem chndsfchyiNdxAdideAA2ltgt dA feudr MdyHNdyAcurlpdeAlt Surface Integrals Flux Circulation d0 V Vfp M1h h dA Ju1 dA dxdy rdrd 7 3m 3y 3y 3m 7 3U 31 3U 31 for the surface 2 hxy7 for the surface fxyz 0 Surface area d07 Flux F IldU39 s s Stokes7s Theorem The Divergence Theorem Gauss7s Theorem fFdrcurlF da C S SF daDdideV gtdA

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