gar
Senior Member
- Location
- Ann Arbor, Michigan
- Occupation
- EE
090704-1243 EST
iwire:
I stopped at Barnes & Noble this morning, and took a quick look at Algebra for Dummies. The book is accurate, but I think you would find it laborious.
What you need has a lot to do with your background. Did you have a high school class in algebra? What have you learned about numbers and operations on them form your work experience and various classes?
I found two other books that you might find more useful than the Dummies book. These are
Quick Algebra Review by Peter Selby ISBN 0-471-57843-6, and
Practical Algebra by Peter Selby ISBN 0-471-53012-3.
Some quick hints for you:
1. Always look for the possibility of a divide by 0. This is indeterminate unless you know how the equation responds as the divisor approaches 0. The result could be anything including infinity.
For example:
y = 1/sin x approaches infinity as x approaches 0.
y = 2*sin x / sin x = 2 for any value of x.
2. +, -, *, /, ^ are operators. You need to be very familiar with their precedence. For example:
z = x + y*x^2 . By convention you calculate x^2 first, then its result times y, and last add x. This precedence can be clarified by parens as follows:
z = x + ( y * (x^2) ) .
A quite different result would occur if the parens were shifted as follows:
z = ( x + y ) * ( x^2 )
3. Note I have used * instead of x for multiplication because much of the time x, y, z, and t are used as variables. Also / for division because most typewriters do not have the conventional ./. division symbol. Also sometimes a large centered dot is used for multiplication, but that is not on most keyboards, and thus * is really the common symbol for multiplication. Also it is quite common to use caps for constants. For example:
y = A*x + C*x^2 = A*x + C*x*x = x ( A + C*x )
4. You can always add, subtract, multiply, or divide the same value to both sides of an equation. You can always multiply or divide both the numerator and denominator of a fraction by the same value. For example:
y = A + B*x
y/x = A/x + B
5. The equation
y = C*x + A when plotted produces a straight line that intersects the Y-axis at a value of A, and the X-axis at a value of
0 = C*x + A or
X = - A/C .
This curve has a positive slope of C . In other words a change of +1 in x produces a change of +C*1 in y .
6. The equation
x^2 + y^2 = C^2
is a circle of radius C . This you can check with y = 0 and separately with x = 0. Note the solution to
x^2 = C^2 has two values which are x = +C and -C. (-C)^2 = C^2 because (-1)^2*(C)^2 = 1*C^2 . Also consider the point where x and y are equal (45 deg). 2*x^2 = C^2 has a solution of x = +/- C/sq-root of 2, or C/1.414 = 0.707*C . And sin 45 = 0.707 .
.
iwire:
I stopped at Barnes & Noble this morning, and took a quick look at Algebra for Dummies. The book is accurate, but I think you would find it laborious.
What you need has a lot to do with your background. Did you have a high school class in algebra? What have you learned about numbers and operations on them form your work experience and various classes?
I found two other books that you might find more useful than the Dummies book. These are
Quick Algebra Review by Peter Selby ISBN 0-471-57843-6, and
Practical Algebra by Peter Selby ISBN 0-471-53012-3.
Some quick hints for you:
1. Always look for the possibility of a divide by 0. This is indeterminate unless you know how the equation responds as the divisor approaches 0. The result could be anything including infinity.
For example:
y = 1/sin x approaches infinity as x approaches 0.
y = 2*sin x / sin x = 2 for any value of x.
2. +, -, *, /, ^ are operators. You need to be very familiar with their precedence. For example:
z = x + y*x^2 . By convention you calculate x^2 first, then its result times y, and last add x. This precedence can be clarified by parens as follows:
z = x + ( y * (x^2) ) .
A quite different result would occur if the parens were shifted as follows:
z = ( x + y ) * ( x^2 )
3. Note I have used * instead of x for multiplication because much of the time x, y, z, and t are used as variables. Also / for division because most typewriters do not have the conventional ./. division symbol. Also sometimes a large centered dot is used for multiplication, but that is not on most keyboards, and thus * is really the common symbol for multiplication. Also it is quite common to use caps for constants. For example:
y = A*x + C*x^2 = A*x + C*x*x = x ( A + C*x )
4. You can always add, subtract, multiply, or divide the same value to both sides of an equation. You can always multiply or divide both the numerator and denominator of a fraction by the same value. For example:
y = A + B*x
y/x = A/x + B
5. The equation
y = C*x + A when plotted produces a straight line that intersects the Y-axis at a value of A, and the X-axis at a value of
0 = C*x + A or
X = - A/C .
This curve has a positive slope of C . In other words a change of +1 in x produces a change of +C*1 in y .
6. The equation
x^2 + y^2 = C^2
is a circle of radius C . This you can check with y = 0 and separately with x = 0. Note the solution to
x^2 = C^2 has two values which are x = +C and -C. (-C)^2 = C^2 because (-1)^2*(C)^2 = 1*C^2 . Also consider the point where x and y are equal (45 deg). 2*x^2 = C^2 has a solution of x = +/- C/sq-root of 2, or C/1.414 = 0.707*C . And sin 45 = 0.707 .
.
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