MAT331, January 28th, 2010 ssh Compute 145+2333 145+2333 ;

IiV5Qw==

145+2333 = 1;

LyIleUMiIiI=

Compute 3(5+123) 3(5+123);

IiIk

3*(5+123);

IiQlUQ==

Compute 45/25 45/25;

IyIiKiIiJg==

Give a decimal expression for 45/25. 45/25.;

JCIrKysrKz0hIio=

Give a decimal expression for 125/31 evalf(125/31);

JCIrbCFlQS4lISIq

Round 125/31 to 25 decimal places. Digits:=25;

IiNE

evalf(125/31);

JCI6bCFlQS5IaF5rIWVBLiUhI0M=

digits:=100;

IiQrIg==

Colon and semicolon, go to next line, prompts. myExpression:=sin(x)+cos(x^2);

LCYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1JJGNvc0dGJTYjKiRGKiIiI0Yr

myExpression + 1;

LCgtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1JJGNvc0dGJTYjKiRGKiIiI0YrRitGKw==

myNewExpression:=myExpression^2;

KiQsJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ4R0YpIiIiLUkkY29zR0YmNiMqJEYrIiIjRixGMQ==

myNewNewExpression:=x*y: example1:=5+6;

IiM2

Give the first 100 decimal numbers after the 3. of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYy pi;

SSNwaUc2Ig==

%;

SSNwaUc2Ig==

evalf(Pi);

JCI6VkVZUUt6KmVgRWZUSiEjQw==

Assign the value 45 to the variable x. xx:=45;

IiNY

x;

SSJ4RzYi

Not a good idea to use x as 45. y;

SSJ5RzYi

"Check" whether x is equal to 9 times five. Find all the prime divisors of 56. ?factor ifactor(56);

KiYtSSFHNiI2IyIiIyIiJC1GJDYjIiIoIiIi

Answer: The prime divisors of 56 are 2 and 7. The importance of the order in time and not in the worksheet. %, %%, restart. x:='x'; a:=x^2+x^3; %;

SSJ4RzYi

LCYqJEkieEc2IiIiIyIiIiokRiQiIiRGJw==

LCYqJEkieEc2IiIiIyIiIiokRiQiIiRGJw==

restart; Main library, packages. ?divisor QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJKm51bXRoZW9yeUdGJSIiIg==

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

QyQtSSlkaXZpc29yc0c2IjYjIiNjIiIi

PCoiIiIiIiMiIiUiIigiIikiIzkiI0ciI2M=

SSN4eEc2Ig==

Functions and Composition. Expressions f:=x->sin(x)+sin(x^2);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYtSSRzaW5HRiU2IzkkIiIiLUYrNiMqJEYtIiIjRi5GJUYlRiU=

f(Pi);

LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJEkjUGlHRiUiIiM=

f(y+17);

LCYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJ5R0YoIiIiIiM8RixGLC1GJDYjKiRGKiIiI0Ys

x*f(z);

KiZJInhHNiIiIiIsJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJ6R0YkRiUtRig2IyokRi0iIiNGJUYl

evalf(f(Pi));

JCErJz43SUklISM1

Common mistakes: misspelling, forget ; , multiplication sign * Simplify, expand, collect pol:=(x+3)*(x^2-1);

KiYsJkkieEc2IiIiIiIiJEYmRiYsJiokRiQiIiNGJiEiIkYmRiY=

pol1:=expand(pol); collect(pol,x); factor(pol1); simplify(x+y-x);

LCoqJEkieEc2IiIiJCIiIkYkISIiKiRGJCIiI0YmISIkRic=

LCoqJEkieEc2IiIiJCIiIkYkISIiKiRGJCIiI0YmISIkRic=

KigsJkkieEc2IiIiIiEiIkYmRiYsJkYkRiYiIiRGJkYmLCZGJEYmRiZGJkYm

SSJ5RzYi

?collect solving equations: solve, fsolve. solve(b*x^3+a=0,x);

NiUqJkkiYkc2IiEiIiwkKiZJImFHRiUiIiJGJCIiI0YmI0YqIiIkLCZGIyNGJkYrKipeI0YvRipGLSNGKkYrRiRGJkYnRixGKiwmRiNGLyoqXiNGMkYqRi1GMkYkRiZGJ0YsRio=

solve(2*x^3+3=0,x);

NiUsJCokIiM3IyIiIiIiJCMhIiIiIiMsJkYkI0YnIiIlKiheIyNGKkYuRidGKCNGJ0YrRiVGJkYnLCZGJEYtKiheI0YtRidGKEYyRiVGJkYn

solve(cos(x)+x+x^2=2,x);

LUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKi1JJGNvc0dGJDYjSSNfWkdGJCIiIkYtRi4qJEYtIiIjRi4hIiNGLg==

solve(a*x^2+b*x+c,x);

NiQsJComSSJhRzYiISIiLCZJImJHRiZGJyokLCYqJEYpIiIjIiIiKiZGJUYuSSJjR0YmRi4hIiUjRi5GLUYuRi5GMiwkKiYsJkYpRi5GKkYuRi5GJUYnI0YnRi0=

solve(f*x^6+a*x^2+b*x+c,x);

LUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKiomSSJmR0YnIiIiSSNfWkdGJCIiJ0YsKiZJImFHRidGLEYtIiIjRiwqJkkiYkdGJ0YsRi1GLEYsSSJjR0YnRiw=

fsolve(cos(x)+x+x^2=2,x);

JCIrUyMqKltEKCEjNQ==

fsolve(x^2-3*x-3,x);

NiQkISt2JXlHInohIzUkIitaeUcieiQhIio=

plot(cos(x)+x+x^2-2,x=-5..5);

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

sequences, for loop, seq(cos(Pi*i), i=1..10);

NiwhIiIiIiJGI0YkRiNGJEYjRiRGI0Yk

for j from 1 to 10 do cos(Pi/j); end do;

ISIi

IiIh

IyIiIiIiIw==

LCQqJCIiIyMiIiJGJEYl

LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkjUGlHRiUjIiIiIiIm

LCQqJCIiJCMiIiIiIiNGJQ==

LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkjUGlHRiUjIiIiIiIo

LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkjUGlHRiUjIiIiIiIp

LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkjUGlHRiUjIiIiIiIq

LUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkjUGlHRiUjIiIiIiM1

20 differentiation and integration. pol;

KiYsJkkieEc2IiIiIiIiJEYmRiYsJiokRiQiIiNGJiEiIkYmRiY=

diff(pol,x);

LCgqJEkieEc2IiIiIyIiIiEiIkYnKiYsJkYkRiciIiRGJ0YnRiRGJ0Ym

int(pol,x); int(%, x=-2..222);

LCpJInhHNiIhIiQqJEYjIiIlIyIiIkYnKiRGIyIiJEYpKiRGIyIiIyMhIiJGLQ==

IyItMyM9Ulw4JSIjOg==

Diff(pol,x);

LUklRGlmZkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkKiYsJkkieEdGJyIiIiIiJEYsRiwsJiokRisiIiNGLCEiIkYsRixGKw==

Difference between = and := n=5;

L0kibkc2IiIiJg==

pol=x;

LyomLCZJInhHNiIiIiIiIiRGJ0YnLCYqJEYlIiIjRichIiJGJ0YnRiU=

evalb(pol=x);

SSZmYWxzZUclKnByb3RlY3RlZEc=

myNumber:=subs(x=6,pol);

IiQ6JA==

x;

SSJ4RzYi

Restart Find all the values of x which make x^4-4 equal to 2. Add all these values. mySol:=solve(x^4-4=2,x);

NiYqJCIiJyMiIiIiIiUqJl4jRiZGJkYkRiUsJEYjISIiKiZeI0YrRiZGJEYl

Find a decimal approximation of each the values of x which make x^4-4 equal to 2 mySol[2];

KiZeIyIiIkYkIiInI0YkIiIl

Find the solutions of the system of equations 3x+y=24, 2x-y=9. Illustrate Storing and expressing answers Find the sum of the first ten positive integers. Simplify your answer. Find the sum of the first n positive integers. Simplify your answer. Find the sum of the first n squares positive integers. Simplify your answer. JSFH Consider the expression LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2KS1JI21uR0YkNiRRIzI1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSi1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRictRi82JFEiM0YnRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjUtRiw2Jy1GUTYlUSNsbkYnL0ZVRjtGMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0YyRjlGPEY+RkBGQkZERkZGSEZLLUYsNiYtRjY2LVEiKEYnRjIvRjpGVkY8L0Y/RlZGQEZCRkRGRi9GSVEsMC4xNjY2NjY3ZW1GJy9GTEZqby1GLDYmLUZRNiNRIUYnLUYsNiYtRlE2JVEiYUYnRlRGV0Y1RlBGMkZecEYyLUY2Ni1RIilGJ0YyRmdvRjxGaG9GQEZCRkRGRkZpby9GTFEsMC4xMTExMTExZW1GJ0YyRl5wRjJGXnBGMi1GLDYmRl5wLUYsNidGW29GX28tRiw2JkZkby1GLDYkLUYvNiRRIzEwRidGMkYyRmZwRjJGXnBGMkZecEYyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zbci8lKWJldmVsbGVkR0Y7 a. Rewrite this expression as a function of the variable x b. Rewrite this expression as a function of the variables x and a. c. Evaluate the expression for x=3. d. Evaluate the expression for x=z^{1/2} e. Assign this expression to the variable VAR and take the square root of VAR. Lists and sets. Plot the graph of your favorite polynomial of degree 6. How do you think Maple "decides" the vertical and horizontal scales? Plot options Parametric plots Plot several functions Plot a set of points.