+++ For an angle of 60 degrees, enter it in radians as
+pi/3or +1.04719..., but not60. ++ By default, trig functions are evaluated in radians, so +
+cos(pi/3) = 1/2, but +cos(60) = -0.9524since it is radians. + You must convert degrees to radians before applying a trig function to an angle. +
+ If asked for units on an angle, enter, for example,+pi/6 rad+ (including rad) or30 deg(including deg). +
+pi,e = e^1
+ Sometimesg+pi/6is allowed, but0.524+ is not. +
+ Sometimesg+0.866025403784is allowed, but +cos(pi/6)is not. +
+ Typically, if your answer is correct to 5 decimal places it will be marked correct, although the number of + decimal places required may vary from problem to problem. When in doubt, give more decimal places. ++
+ For example, if your answers are+-3/2, 4/3, 2pi, e^3, 5enter them as +-1.5, 1.3333333, 6.2831853, 20.0855369, 5. +
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
++y = 5x+2will be incorrect if the answer is +w = 5y+2+
+++
+ +32 = 5*x + 2is the same as30 = 5x+ orx = 6++
+y = (x-1)^2 + 3is the same as +y - 3 = (x-1)^2++
+x^2 + xy + y^2 = 13xis the same as +y*(y+x) = 13x - x^2+
+ Enter+NONEorDNE(this may vary from + problem to problem). +
+pi,e = e^1
++sqrt(x) = sqrt(5)is valid, but +sqrt(x=5)is not +
+ For example,+x^2andx**2are the same, + as aree^(-x/2)and1/(e**(x/2)). +
+ For example, the square root of 2 can be entered as+sqrt(2), +2^(1/2), or2**(1/2), but the cube root + of 2 must be entered as2^(1/3)or +2**(1/3). The parentheses in2^(1/3)are + required, since2^1/3will be interpreted as +(2^1)/3 = 2/3. +
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/. When these operations are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+ For example, a function of time+tcould be +-16t^2 + 12, while-16x^2 + 12would be + incorrect. +
+++
+- +
+5*sin((pi*x)/2)or5 sin(pi x/2)+- +
+e^(-x)ore**(-x)or +1/(e^x)+- +
+abs(5y)or|5y|+- +
+sqrt(9 - z^2)or(9 - z^2)^(1/2)+- +
+24or4!or +4 * 3 * 2 * 1+- +
+pior4 arctan(1)or +4 atan(1)or4 tan^(-1)(1)+
+ In this question, use+ln(x)orlog(x)+ for natural log, andlogten(x)or +log10(x)for the base 10 logarithm. Enter log base b as +ln(x)/ln(b). +
+pi,e = e^1
+ Addition++, subtraction-, + multiplication*, division/, + exponentiation^(or**), + factorial!+
+++
+- +
sqrt(x) = x^(1/2)- +
abs(x) = |x|- +
2^x- +
e^x- +
ln(x)- +
log10(x)- +
sin(x)- +
cos(x)- +
tan(x)- +
csc(x)- +
sec(x)- +
cot(x)- +
arcsin(x) = asin(x) = sin^(-1)(x)- +
arccos(x) = acos(x) = cos^(-1)(x)- +
arctan(x) = atan(x) = tan^(-1)(x)
+ For example,+6x + 5 - 2xshould be simplified to +4x + 5+
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+ For example, a function of time+tcould be +-16t^2 + 12, while-16x^2 + 12would be + incorrect. +
+++
+- +
+5*sin((pi*x)/2)or5 sin(pi x/2)+- +
+e^(-x)ore**(-x)or +1/(e^x)+- +
+abs(5y)or|5y|+- +
+sqrt(9 - z^2)or(9 - z^2)^(1/2)+- +
+24or4!or +4 * 3 * 2 * 1+- +
+pior4 arctan(1)or +4 atan(1)or4 tan^(-1)(1)+
+ In this question, use+ln(x)for natural log, and +log(x),logten(x)or +log10(x)for the base 10 logarithm. Enter log base b as +ln(x)/ln(b). +
+pi,e = e^1
+ Addition++, subtraction-, + multiplication*, division/, + exponentiation^(or**), + factorial!+
+++
+- +
sqrt(x) = x^(1/2)- +
abs(x) = |x|- +
2^x- +
e^x- +
ln(x)- +
log10(x)- +
sin(x)- +
cos(x)- +
tan(x)- +
csc(x)- +
sec(x)- +
cot(x)- +
arcsin(x) = asin(x) = sin^(-1)(x)- +
arccos(x) = acos(x) = cos^(-1)(x)- +
arctan(x) = atan(x) = tan^(-1)(x)
+ For example,+6x + 5 - 2xshould be simplified to +4x + 5+
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+ 5/2, -1/3, pi/3, 4, sqrt(2)/2
+
+
+ 15/6, (3-4)/3, 2*pi/6, (16/2)/2
+
+ ++Allowed:
+5/2, -1/3, pi/3, 4, sqrt(2)/2, 2^(1/2)Not allowed:
+2.5, -0.33333, 3.14159/3, 0.707106/2, 2^(0.5)
+ Enter+1 2/3(for 1 and 2/3) with a space between the 1 and the 2 instead of +5/3. +
+ Enter+4/1instead of4. +
+ For example, if your answers are+-3/2, 4/3, 2pi, e^3, 5enter +3/2, 4/3, 2*pi, e^3, 5. +
+ Enter+NONEorDNE+ (this may vary from problem to problem). +
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + and exponentiation^(or**). When these + operations are not allowed, it is usually because you are expected to be able to simplify your answer, often + without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+++
+- +
<less than- +
+<=less than or equal to + (=<might also work) +- +
=equals- +
!=not equal to (uses exclamation point)- +
>greater than- +
+>=greater than or equal to + (=>might also work) +
+++
+- +
+infinityorinf+ means positive infinity +- +
+-infinityor-inf+ means negative infinity +- +
Rmeans all real numbers- +
+Ris the same as +-inf < x < infor +(-inf,inf)+- +
{2,4,5}using curly braces denotes a finite set- +
+NONEor a pair of curly braces +{}means the empty set +- +
Udenotes the union of intervals
+++
+ * Some questions may not allow interval notation to be used ++ +Inequality Notation ++ Interval Notation* + +Remarks ++ ++ +x<2++ +(-infinity,2)++ Use rounded parentheses +(or +)at infinite endpoints. ++ ++ +x>2++ +(2,infinity)++ + ++ +x<=2++ +(-infinity,2]++ + ++ +x>=2++ +[2,infinity)++ + ++ +0<x<=2++ +(0,2]++ + ++ +0<x and x<2++ +(0,2)++ +andis special ++ ++ +x<0 or x>2++ +(-inf,0)U(2,inf)++ +oris special, +Udenotes union ++ ++ +x=0 or x=2++ +{0,2}++ finite sets are allowed using curly braces +{a,b,c}++ ++ +x < 3 or x > 3++ ++
+- +
(-inf,3)U(3,inf)- +
x != 3- +
R-{3}set differences are allowed +
+++
+- + If an interval includes an endpoint, use square brackets:
+[or +]+- + If an interval excludes an endpoint or an endpoint is infinite, use rounded parentheses: +
+(or)+- + Use curly braces to enclose finite sets and commas to separate elements the set: +
+{ -3, pi, 2/5, 0.75 }+- + All sets should be expressed in their simplest form in interval notation with no overlapping + intervals. For example,
+[2,4]U[3,5]is not equivalent to +[2,5]+- + If you are asked to find the range of a function
+y = f(x), your + inequality should be in terms of the variabley+
[ or ].
+ If not, then use ( or ). For example, the
+ interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].
+ Inf for
+ ∞ (infinity) and
+ -Inf for -∞
+ (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed
+ [6,Inf).
+ [-8,-5)U(-3,7].
+ { }
+ R as a shorthand for all real numbers. So, it is equivalent to
+ entering (-Inf, Inf).
+ R-{3} or (-Inf, 3)U(3,Inf) (they are the
+ same). Similarly, [1,10)-{3,4} is the same as
+ [1,3)U(3,4)U(4,10).
+ [2,4]U[3,5] as equivalent to
+ [2,5], unless a problem tells you otherwise. All sets should be expressed in
+ their simplest interval notation form, with no overlapping intervals.
+
+ For example, limx → ∞ arctan(x) = π/2, so you would enter
+ pi/2
+
+ + Enter+infinity,inf, +-infinity,-inf+
+ Enter+DNEorNONE+ (this may vary from question to question) +
+ Enter the function using appropriate syntax, for example: +++
+- +
sqrt(x) = x^(1/2)- +
abs(x) = |x|- +
2^x, e^x, ln(x), log10(x)- +
sin(x), cos(x), tan(x), csc(x), sec(x), cot(x)- +
arcsin(x) = asin(x) = sin^(-1)(x)- +
arccos(x) = acos(x) = cos^(-1)(x)- +
arctan(x) = atan(x) = tan^(-1)(x)
+ For example,+6x + 5 - 2x + 7should be simplified to +4x + 12+
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
ln(x) or log(x).
+ log10(x) or logten(x).
+ ln(x)/ln(b) or
+ log(x)/log(b)
+ + WeBWorK does not recognize logarithms to other bases, so you must use the change of base formula for + logarithms to enter your answer. For example, enter log base 2 of x as ++ln(x)/ln(2)orlog(x)/log(2). +
++ln(2x+8)andln2x+8 = ln(2)*x+8are very + different. +
+ For example, the required answer may be+ln(6) + ln(x)or +ln(6x). +
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
ln(x).
+ log(x), log10(x), or
+ logten(x).
+ ln(x)/ln(b) or
+ log(x)/log(b)
+ + WeBWorK does not recognize logarithms to other bases, so you must use the change of base formula for + logarithms to enter your answer. For example, enter log base 2 of x as ++ln(x)/ln(2)orlog(x)/log(2). +
++ln(2x+8)andln2x+8 = ln(2)*x+8are very + different. +
+ For example, the required answer may be+ln(6) + ln(x)or +ln(6x). +
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+
+ 4, 5/2, -1/3, pi/3, e^3, 3.1415926535, sqrt(2) = 2^(1/2), ln(2), sin(2pi/3)
+
+
+ ++For example, enter
+-1.5, 4/3, 2pi, e^3, 5+ Do not use commas in large numbers: enter
+4321(not +4,321) +
+ Enter+NONEorDNE+ (this may vary from problem to problem) +
+ Typically, if your answer is correct to 5 decimal places it will be marked correct, although the number of + decimal places required may vary from problem to problem. When in doubt, give more decimal places. ++
+ Usually, the operations that are not allowed include addition++, + subtraction-, multiplication*, + division/, and exponentiation^(or +**). When these operations are not allowed, it is usually because you are + expected to be able to simplify your answer, often without using a calculator. +
+ Usually, the functions that are not allowed include square root+sqrt( ), + absolute value| |(orabs( )), as well + as other named functions such assin( ), +ln( ), etc. When these functions are not allowed, it is usually because + you are expected to be able to simplify your answer, often without using a calculator. +
+++
(4.5, 3/7)is a valid point in 2 dimensions.+
(pi,e,2)is a valid point in 3 dimensions.
+ Enter your answer as a comma-separated list of points, for example:
+ (4,3), (5,10)
+
+ + Enter+NONEorDNE(this may vary from + problem to problem) +
+pi,e = e^1
++(sqrt(2),sqrt(5))is valid, but +(sqrt(2,5))is not. +
+ Addition.- Subtraction.* Multiplication. Multiplication can also be indicated by a space or
+ juxtaposition, e.g., 2x, 2 x or
+ 2*x, also 2(3+4).
+ / Division.^ or ** Exponent. You can use either
+ ^ or ** for exponentiation, e.g.,
+ 3^2 or 3**2.
+ ( ) Parentheses. You can also use square brackets,
+ [ ], and braces, { }, for grouping, e.g.,
+ [1+2]/[3(4+5)]
+ 1+2/3*4 and
+ [1+2]/[3*4] click the "Preview Button".
+ * symbol to indicate mutiplication makes things easier to
+ read. For example (1+2)*(3+4) and (1+2)(3+4)
+ are both valid. So are 3*4 and 3 4
+ (3 space 4, not 34) but using a
+ * makes things clearer.
+ ('s and )'s to make your meaning clear.
+ You can also use ['s and ]'s and
+ {'s and }'s.
+ 2/4+5 (which is 5.5) when you
+ really want 2/(4+5) (which is 2/9).
+ 2/3*4 (which is 8/3) when you
+ really want 2/(3*4) (which is 2/12).
+ [1+2+3+4]/[5+6+7+8], is a
+ good practice.
+ sin(t) instead of sint or
+ sin t even though WeBWorK is smart enough to usually accept
+ sin t or even sint. For example,
+ sin 2t is interpreted as sin(2)t, i.e.
+ (sin(2))*t so be careful.
+ sin^2(t) as a short cut although mathematically speaking
+ sin^2(t) is shorthand for (sin(t))^2 (the
+ square of sin of t). (You can enter it as sin(t)^2 or even
+ sint^2, but don't try such things unless you really understand the
+ precedence of operations. The "sin" operation has highest precedence, so it is
+ performed first, using the next token (i.e. t) as an argument. Then the result
+ is squared.) You can always use the Preview button to see a typeset version of what you entered and check
+ whether what you wrote was what you meant.
+ 2+3sin^2(4x) will work and is equivalent to
+ 2+3(sin(4x))^2 or 2+3sin(4x)^2. Why does the
+ last expression work? Because things in parentheses are always done first
+ [ i.e. (4x)], next all functions, such as sin, are evaluated
+ [giving sin(4x)], next all exponents are taken
+ [giving sin(4x)^2], next all multiplications and divisions are performed in
+ order from left to right [giving 3sin(4x)^2], and finally all additions and
+ subtractions are performed [giving 2+3sin(4x)^2].
+ -5^2 positive or negative? It's negative. This is because the square
+ operation is done before the negative sign is applied. Use (-5)^2 if you want
+ to square negative 5.
+ 2/3*4 = (2/3)*4 = 8/3.
+ 1-2+3 = (1-2)+3 = 2.
+ 2^3^4 = 2^(3^4) = 2^81 = a big number.
+ pi This gives 3.14159265358979, e.g.
+ cos(pi) is -1
+ e This gives 2.71828182845905, e.g.
+ ln(e*2) is 1 + ln(2)
+ 2.1E2 is the same as 2102.1E-2 is the same as 0.021+ Note that sometimes one or more of these functions is disabled for a WeBWorK problem because the instructor wants + you to calculate the answer by some means other than just using the function. +
+abs( ) The absolute valuecos( ) Note: Uses radian measure.sin( ) Note: Uses radian measure.tan( ) Note: Uses radian measure.sec( ) Note: Uses radian measure.cot( ) Note: Uses radian measure.csc( ) Note: Uses radian measure.exp( ) The same function as e^x.log( )
+ This is usually the natural log but your instructor may have redined this to be log base 10.
+ ln( ) The natural log.logten( ) The log to the base 10.arcsin( )asin( ) or sin^-1( )
+ Another name for arcsin.
+ arccos( )acos( ) or cos^-1( )
+ Another name for arccos.
+ arctan( )atan( ) or tan^-1( )
+ Another name for arctan.
+ arccot( )acot( ) or cot^-1( )
+ Another name for arccot.
+ arcsec( )asec( ) or sec^-1( )
+ Another name for arcsec
+ arccsc( )acsc( ) or csc^-1( )
+ Another name for arccsc.
+ sinh( )cosh( )tanh( )sech( )csch( )coth( )arcsinh( )asinh( ) or sinh^-1( )
+ Another name for arcsinh.
+ arccosh( )acosh( ) or cosh^-1( )
+ Another name for arccosh.
+ arctanh( )atanh( ) or tanh^-1( )
+ Another name for arctanh.
+ arcsech( )asech( ) or sech^-1( )
+ Another name for arcsech.
+ arccsch( )acsch( ) or csch^-1( )
+ Another name for arccsch.
+ arccoth( )acoth( ) or coth^-1( )
+ Another name for arccoth.
+ sqrt( )n! n factorial. This is defined for integers
+ n such that n ≥ 0.
+ These functions may not always be available for every problem.
+sgn( ) The sign function. Its value is one of
+ -1, 0, or
+ 1.
+ step( ) The step function. Its value is
+ 0 if x ≤ 0 and
+ 1 if x > 0.
+ fact(n)
+ The factorial function n! (defined only for nonnegative integers)
+ P(n,k) = n*(n-1)*(n-2)...(n-k+1), the number of ordered sequences of
+ k elements chosen from n elements
+ C(n,k) = "n choose k", the number of unordered sequences of
+ k elements chosen from n elements
+
+ Some WeBWorK problems ask for answers with units. Below is a list of basic units and how they need to be abbreviated
+ in WeBWorK answers. In some problems, you may need to combine units (e.g, velocity might be in
+ ft/s for feet per second).
+
| Unit | +Abbreviation | +
|---|---|
| Time | +|
| Seconds | +s | +
| Minutes | +min | +
| Hours | +hr | +
| Days | +day | +
| Years | +yr | +
| Milliseconds | +ms | +
| Distance | +|
| Feet | +ft | +
| Inches | +in | +
| Miles | +mi | +
| Meters | +m | +
| Centimeters | +cm | +
| Millimeters | +mm | +
| Kilometers | +km | +
| Angstroms | +A | +
| Light years | +light-year | +
| Mass | +|
| Grams | +g | +
| Kilograms | +kg | +
| Slugs | +slug | +
| Volume | +|
| Liters | +L | +
| Cubic Centimeters | +cc | +
| Milliliters | +ml | +
| Force | +|
| Newtons | +N | +
| Dynes | +dyne | +
| Pounds | +lb | +
| Tons | +ton | +
| Work/Energy | +|
| Joules | +J | +
| kilo Joule | +kJ | +
| ergs | +erg | +
| foot pounds | +lbf | +
| calories | +cal | +
| kilo calories | +kcal | +
| electron volts | +eV | +
| kilo Watt hours | +kWh | +
| Misc | +|
| Amperes | +amp | +
| Moles | +mol | +
| Degrees Centrigrade | +degC | +
| Degrees Fahrenheit | +degF | +
| Degrees Kelvin | +degK | +
| Angle degrees | +deg | +
| Angle radians | +rad | +
+ More details on units in WeBWorK +
diff --git a/htdocs/helpFiles/Entering-Vectors.html b/htdocs/helpFiles/Entering-Vectors.html new file mode 100644 index 0000000000..7a1523b13b --- /dev/null +++ b/htdocs/helpFiles/Entering-Vectors.html @@ -0,0 +1,71 @@ +i, j, and
+ k
+
+ +++
+iis the same as<1,0,0>++
+jis the same as<0,1,0>++
+kis the same as<0,0,1>+
i, j, and
+ k:
+
+ +++
+<4.5, 3/7>and4.5i + 3/7j+ are valid vectors in 2 dimensions. ++
+<pi,e,2>andpi i + e j + 2 k+ are valid vectors in 3 dimensions. +
+ Enter your answer as a comma-separated list of vectors, for example:
+ <4,3>, <5,10>
+
+ + Enter+NONEorDNE+ (this may vary from problem to problem). +
+pi,e = e^1
++<sqrt(2),sqrt(5)>is valid, but +<sqrt(2,5)>is not. +
[ or ].
+ If not, then use ( or ). For example, the
+ interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].
+ Inf for
+ ∞ (infinity) and
+ -Inf for -∞
+ (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed
+ [6,Inf).
+ [-8,-5)U(-3,7].
+ { }
+ R as a shorthand for all real numbers. So, it is equivalent to
+ entering (-Inf, Inf).
+ R-{3} or (-Inf, 3)U(3,Inf) (they are the
+ same). Similarly, [1,10)-{3,4} is the same as
+ [1,3)U(3,4)U(4,10).
+ [2,4]U[3,5] as equivalent to
+ [2,5], unless a problem tells you otherwise. All sets should be expressed in
+ their simplest interval notation form, with no overlapping intervals.
+ | Partial Derivative | +Enter into WeBWork | +
|---|---|
| \(\frac{\partial u}{\partial x}\) | +ux | +
| \(\frac{\partial u}{\partial t}\) | +ut | +
| \(\frac{\partial u}{\partial y}\) | +uy | +
| \(\frac{\partial^2 u}{\partial x^2}\) | +uxx | +
| \(\frac{\partial^2 u}{\partial t^2}\) | +utt | +
| \(\frac{\partial^2 u}{\partial y^2}\) | +uyy | +
+ To answer questions that require you to input a PDE you will also need to know the form of the PDE WeBWorK is + expecting. In particular you will need to use the same letters for constants that WeBWorK is expecting. Below is a + table of the PDE's you may encounter. +
+ +| Model | +PDE | +
|---|---|
| heat equation | ++ \(k \frac{\partial^2 u}{\partial x^2} = \frac{\partial u}{\partial t}\) + | +
| + heat equation with lateral heat transfer - \(u_m\) is the temperature of the surrounding medium and will be + given, and h is the constant from Newton's $ + | ++ \(k \frac{\partial^2 u}{\partial x^2}-h (u-u_m) = \frac{\partial u}{\partial t}\) + | +
| wave equation | ++ \(a^2 \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2}\) + | +
| wave equation with damping | ++ \(a^2 \frac{\partial^2 u}{\partial x^2} = + \frac{\partial^2 u}{\partial t^2}+c \frac{\partial u}{\partial t}\) + | +
| + wave equation with an external force (f(x,t) will specified in the problem + | ++ \(a^2 \frac{\partial^2 u}{\partial x^2} + f(x,t) = \frac{\partial^2 u}{\partial t^2}\) + | +
| Laplace's equation | ++ \(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} = 0\) + | +
For problems with proportional quantities the constant of proportionality is c.
+ ++ Suppose that we want to enter the boundary condition \(\frac{\partial u}{\partial x}\big\vert_{x=0}=0\). You will be + given two answer blanks: the first is to input the partial derivative and the point, \(ux(0,t)\), and the second + will be for the right hand side. In WeBWorK notation the boundary condition would be given as + \(ux(0,t) = 0\). +
diff --git a/htdocs/helpFiles/Syntax.html b/htdocs/helpFiles/Syntax.html new file mode 100644 index 0000000000..a95067272b --- /dev/null +++ b/htdocs/helpFiles/Syntax.html @@ -0,0 +1,249 @@ ++ Addition.- Subtraction.* Multiplication. Multiplication can also be indicated by a space or
+ juxtaposition, e.g., 2x, 2 x or
+ 2*x, also 2(3+4).
+ / Division.^ or ** Exponent. You can use either
+ ^ or ** for exponentiation, e.g.,
+ 3^2 or 3**2.
+ ( ) Parentheses. You can also use square brackets,
+ [ ], and braces, { }, for grouping, e.g.,
+ [1+2]/[3(4+5)]
+ 1+2/3*4 and
+ [1+2]/[3*4] click the "Preview Button".
+ * symbol to indicate mutiplication makes things easier to
+ read. For example (1+2)*(3+4) and (1+2)(3+4)
+ are both valid. So are 3*4 and 3 4
+ (3 space 4, not 34) but using a
+ * makes things clearer.
+ ('s and )'s to make your meaning clear.
+ You can also use ['s and ]'s and
+ {'s and }'s.
+ 2/4+5 (which is 5.5) when you
+ really want 2/(4+5) (which is 2/9).
+ 2/3*4 (which is 8/3) when you
+ really want 2/(3*4) (which is 2/12).
+ [1+2+3+4]/[5+6+7+8], is a
+ good practice.
+ sin(t) instead of sint or
+ sin t even though WeBWorK is smart enough to usually accept
+ sin t or even sint. For example,
+ sin 2t is interpreted as sin(2)t, i.e.
+ (sin(2))*t so be careful.
+ sin^2(t) as a short cut although mathematically speaking
+ sin^2(t) is shorthand for (sin(t))^2 (the
+ square of sin of t). (You can enter it as sin(t)^2 or even
+ sint^2, but don't try such things unless you really understand the
+ precedence of operations. The "sin" operation has highest precedence, so it is
+ performed first, using the next token (i.e. t) as an argument. Then the result
+ is squared.) You can always use the Preview button to see a typeset version of what you entered and check
+ whether what you wrote was what you meant.
+ 2+3sin^2(4x) will work and is equivalent to
+ 2+3(sin(4x))^2 or 2+3sin(4x)^2. Why does the
+ last expression work? Because things in parentheses are always done first
+ [ i.e. (4x)], next all functions, such as sin, are evaluated
+ [giving sin(4x)], next all exponents are taken
+ [giving sin(4x)^2], next all multiplications and divisions are performed in
+ order from left to right [giving 3sin(4x)^2], and finally all additions and
+ subtractions are performed [giving 2+3sin(4x)^2].
+ -5^2 positive or negative? It's negative. This is because the square
+ operation is done before the negative sign is applied. Use (-5)^2 if you want
+ to square negative 5.
+ 2/3*4 = (2/3)*4 = 8/3.
+ 1-2+3 = (1-2)+3 = 2.
+ 2^3^4 = 2^(3^4) = 2^81 = a big number.
+ pi This gives 3.14159265358979, e.g.
+ cos(pi) is -1
+ e This gives 2.71828182845905, e.g.
+ ln(e*2) is 1 + ln(2)
+ 2.1E2 is the same as 2102.1E-2 is the same as 0.021+ Note that sometimes one or more of these functions is disabled for a WeBWorK problem because the instructor wants + you to calculate the answer by some means other than just using the function. +
+abs( ) The absolute valuecos( ) Note: Uses radian measure.sin( ) Note: Uses radian measure.tan( ) Note: Uses radian measure.sec( ) Note: Uses radian measure.cot( ) Note: Uses radian measure.csc( ) Note: Uses radian measure.exp( ) The same function as e^x.log( )
+ This is usually the natural log but your instructor may have redined this to be log base 10.
+ ln( ) The natural log.logten( ) The log to the base 10.arcsin( )asin( ) or sin^-1( )
+ Another name for arcsin.
+ arccos( )acos( ) or cos^-1( )
+ Another name for arccos.
+ arctan( )atan( ) or tan^-1( )
+ Another name for arctan.
+ arccot( )acot( ) or cot^-1( )
+ Another name for arccot.
+ arcsec( )asec( ) or sec^-1( )
+ Another name for arcsec
+ arccsc( )acsc( ) or csc^-1( )
+ Another name for arccsc.
+ sinh( )cosh( )tanh( )sech( )csch( )coth( )arcsinh( )asinh( ) or sinh^-1( )
+ Another name for arcsinh.
+ arccosh( )acosh( ) or cosh^-1( )
+ Another name for arccosh.
+ arctanh( )atanh( ) or tanh^-1( )
+ Another name for arctanh.
+ arcsech( )asech( ) or sech^-1( )
+ Another name for arcsech.
+ arccsch( )acsch( ) or csch^-1( )
+ Another name for arccsch.
+ arccoth( )acoth( ) or coth^-1( )
+ Another name for arccoth.
+ sqrt( )n! n factorial. This is defined for integers
+ n such that n ≥ 0.
+ These functions may not always be available for every problem.
+sgn( ) The sign function. Its value is one of
+ -1, 0, or
+ 1.
+ step( ) The step function. Its value is
+ 0 if x ≤ 0 and
+ 1 if x > 0.
+ fact(n)
+ The factorial function n! (defined only for nonnegative integers)
+ P(n,k) = n*(n-1)*(n-2)...(n-k+1), the number of ordered sequences of
+ k elements chosen from n elements
+ C(n,k) = "n choose k", the number of unordered sequences of
+ k elements chosen from n elements
+
+ Some WeBWorK problems ask for answers with units. Below is a list of basic units and how they need to be abbreviated
+ in WeBWorK answers. In some problems, you may need to combine units (e.g, velocity might be in
+ ft/s for feet per second).
+
| Unit | +Abbreviation | +
|---|---|
| Time | +|
| Seconds | +s | +
| Minutes | +min | +
| Hours | +hr | +
| Days | +day | +
| Years | +yr | +
| Milliseconds | +ms | +
| Distance | +|
| Feet | +ft | +
| Inches | +in | +
| Miles | +mi | +
| Meters | +m | +
| Centimeters | +cm | +
| Millimeters | +mm | +
| Kilometers | +km | +
| Angstroms | +A | +
| Light years | +light-year | +
| Mass | +|
| Grams | +g | +
| Kilograms | +kg | +
| Slugs | +slug | +
| Volume | +|
| Liters | +L | +
| Cubic Centimeters | +cc | +
| Milliliters | +ml | +
| Force | +|
| Newtons | +N | +
| Dynes | +dyne | +
| Pounds | +lb | +
| Tons | +ton | +
| Work/Energy | +|
| Joules | +J | +
| kilo Joule | +kJ | +
| ergs | +erg | +
| foot pounds | +lbf | +
| calories | +cal | +
| kilo calories | +kcal | +
| electron volts | +eV | +
| kilo Watt hours | +kWh | +
| Misc | +|
| Amperes | +amp | +
| Moles | +mol | +
| Degrees Centrigrade | +degC | +
| Degrees Fahrenheit | +degF | +
| Degrees Kelvin | +degK | +
| Angle degrees | +deg | +
| Angle radians | +rad | +
+ More details on units in WeBWorK +
diff --git a/htdocs/js/apps/AppletSupport/ww_applet_support.js b/htdocs/js/apps/AppletSupport/ww_applet_support.js new file mode 100644 index 0000000000..605f584bc3 --- /dev/null +++ b/htdocs/js/apps/AppletSupport/ww_applet_support.js @@ -0,0 +1,357 @@ +// ################################################################################ +// # WeBWorK Online Homework Delivery System +// # Copyright © 2000-2022 The WeBWorK Project, https://github.com/openwebwork +// # +// # This program is free software; you can redistribute it and/or modify it under +// # the terms of either: (a) the GNU General Public License as published by the +// # Free Software Foundation; either version 2, or (at your option) any later +// # version, or (b) the "Artistic License" which comes with this package. +// # +// # This program is distributed in the hope that it will be useful, but WITHOUT +// # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// # FOR A PARTICULAR PURPOSE. See either the GNU General Public License or the +// # Artistic License for more details. +// ################################################################################ + +// List of web applets on the page. +const ww_applet_list = {}; + +// Utility functions + +// Dummy function provided to prevent console errors for problems written for lecacy code. +const applet_loaded = () => {}; + +const getApplet = (appletName) => window[appletName]; + +// Get Question Element in problemMainForm by name +const getQE = (name1) => { + const obj = document.getElementById(name1) ?? document.problemMainForm[name1]; + if (!obj || obj.name != name1) { + console.log(`Can't find element ${name1}`); + } else { + return obj; + } +} + +const getQuestionElement = getQE; + +// WW_Applet class definition +class ww_applet { + constructor(appletName) { + this.appletName = appletName; + this.type = ''; + this.initialState = ''; + this.configuration = ''; + this.getStateAlias = ''; + this.setStateAlias = ''; + this.setConfigAlias = ''; + this.getConfigAlias = ''; + this.submitActionScript = ''; + this.onInit = 0; + this.debug = 0; + } + + // Determine whether an XML string has been base64 encoded. + // This returns false if the string is empty, or if it contains a < or > character. + // The empty string is not a base64 string, and + // base64 can't contain < or > and xml strings contain lots of them. + base64Q(str) { return str && !/[<>]+/.exec(str); } + + // Make sure that the applet has this function available + methodDefined(methodName) { + const applet = getApplet(this.appletName); + if (methodName && typeof(applet[methodName]) == 'function') return true; + if (this.debug) console.log(`${this.appletName}: Method name ${methodName} is not defined`); + return false; + } + + // CONFIGURATIONS + // Configurations are "permanent" + setConfig() { + if (this.debug) console.log(`${this.appletName}: calling setConfig`); + const applet = getApplet(this.appletName); + try { + if (this.methodDefined(this.setConfigAlias)) { + if (this.debug) console.log(`${this.appletName}: calling ${this.setConfigAlias}${ + this.debug > 1 ? `with configuration:\n${this.configuration}` : ''}`); + applet[this.setConfigAlias](this.configuration); + } + } catch(e) { + console.log(`Error configuring ${this.appletName} using command ${this.setConfigAlias}: ${e}`); + } + } + + // Gets the configuration from the applet. + getConfig() { + if (this.debug) console.log(`${this.appletName}: calling getConfig`); + const applet = getApplet(this.appletName); + try { + if (this.methodDefined(this.getConfigAlias)) { + if (this.debug) console.log(`${this.appletName}: calling ${this.getConfigAlias}`); + console.log(applet[this.getConfigAlias]()); + } + } catch(e) { + console.log(`Error getting configuration for ${this.appletName} using command ${this.getConfigAlias}: ${e}`); + } + } + + // Set the state stored on the HTML page + setHTMLAppletState(newState) { + if (this.debug) console.log(`${this.appletName}: setHTMLAppletState${this.debug > 1 ? ` to:\n${newState}` : ''}`); + if (typeof(newState) === 'undefined') newState = '