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Calculus III

by: Mrs. Preston Lehner

Calculus III MATH 215

Mrs. Preston Lehner
GPA 3.87


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Class Notes
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This 1 page Class Notes was uploaded by Mrs. Preston Lehner on Thursday October 29, 2015. The Class Notes belongs to MATH 215 at University of Michigan taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/231504/math-215-university-of-michigan in Mathematics (M) at University of Michigan.

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Date Created: 10/29/15
Math 215 Calculus HI Maple Quick Reference Card The University of Michigan Ann Arbor General Maple l Example Description command l Input l Output asic quot 39 operations and constants Command termination gt22 4 Suppressing output gt22 Math operations never omit gt239 2 87 the multiplication symbol gt336 Conversion to decimals evalf gtevalf 336 5 500000000 7r Pi gtevalf Pi 3141592654 e exp1 gteva1f exp1 2718281828 Elementary functions sinzcoszemlnz etci sqrtx gtsqrt18 32 sin x gtevalf sqrt18 41242640686 cosx gtsin3Pi4 5V2 exp x 1 lnx gtarcsinsqrt22 17quot De ning your own functions and expressions Expressions gty x 2 12 gty I2 gteva1yx2 4 gtsubsx 3y 9 Functions gt gtf xgtx 2 12 gtfx 12 gtf4 16 P and J J Differentiation diff gtdiff x 2x 2r gtdiff x 2 y 3x 2r gtdiff x 2 y 3y 3f lntegration int gtint sin x x 7 cosz 7r De nite zsinzdz gtintxsinxx0 Pi 7r 01 x2 1 lterated ydydz gtintint yy0 x 2 x0 1 E 0 0 Solving equations and systems of equations Equations solve gtsolve x 24x 2 72 Systems I y 7 gtsolvexy3xy7xy z 5y 72 z 7 y De ning the intervals of change of variables for plotting integration etc a lt I S b l l gtxa b a plotting functions are in the plots package lncluding the plots package Working with packages eg many h l wit gtwithplots Plotting plane curves Equations implicitplot gtimplicitplot x 2yquot21 Useful options color red blue x1 1y1 1 green yellow etc axes boxed or normal thickness linestyle solid dot dash dashdot scaling labels title etci Graphs plot gtplot x 2 x1 1 Useful options color red blue gtplot x 2x1 1colorblue green yellow etc axes boxed color thickness2 or normal thickness linestyle thickness linestyleDASHDOT x solid dot dash dashdot linestyle scaling labels title etci Parametric curves plot gtplot 1 21 1 quot31 Useful options color red blue t12 12 green yellow etc axes boxed scaling gt plottquot21t 3t or normal thickness linestyle axes t1 2 1 2 solid dot dash dashdot labels scalingconstrained scaling labels title etci axesboxedlabels quotxquot quotyquot


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