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I & I $ > � yyy/english/topichlp.c /home/beeson/Otter-Lambda GNU C 3.3.5 (Debian 1:3.3.5-13) � topichelp � Un � � � � char int * �
yyy/english topichlp.c c�����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������$ Make an ordinary graph of a function. Example: y = 3x^2 + 2x + 1 Example: y = x^3 - ax Example: y = 3x - 2 A rational function is a quotient of polynomials. Example: y = x^(4/5) Learn about exponential growth and decay. Example: y = ln(x/a) Example: y = sqrt(x^2-9)/(x-1) Learn about frequency, phase, and amplitude. Learn the graphs of all six trig functions. Learn the graphs of all six inverse trig functions. Learn the graphs of the hyperbolic functions. Graph functions composed of trig and algebraic components. Learn the graphs of the different kinds of Bessel functions. Graph functions composed of trig, log, exponential, and algebraic components. Compare the partial sums of a series with the complete sum. Two or more graphs will be drawn on the same axes. Two or more graphs will be drawn, on separate axes. Examples: y <= tan x, or x <= y <= tan x Example: y^2 < tan x. Learn how the radius and center depend on the formula. Learn how the shape of an ellipse depends on the formula. Learn how the shape of a parabola depends on the formula. Learn how the shape of a hyperbola depends on the formula. Example, $3x^2 + 5y^2 = 1$ will plot an ellipse Use a parameter in the polynomial to see how the roots move. Plot a graph defined by equations x = f(t), y = g(t). Plot a graph defined by an equation $r = f(\theta )$ f' will be calculated, and f and f' will be plotted on different axes. f'' and f'' will be calculated and f, f', and f'' will all be plotted. Plot the level lines f(x,y) = z for regularly-spaced z values. Makes a contour plot of the real part of a complex function. Plot solutions through points you specify by clicking. Plot equations of the form dx/dt = f(t,x,y), dy/dt = g(t,x,y) Plot equations of the form y'' = f(t,x,y,y'), also for higher order. Show the function and the approximating rectangles used in a Riemann sum. Show the function and approximating trapezoids used in the trapezoid rule. Show the function and approximating regions used in Simpson's rule. Plot a curve defined by three functions x(t), y(t), z(t). Three-dimensional graph of a function of two variables. Three-dimensional graph of a function of two variables in polar coordinates. A parametric surface is defined by three functions x(u,v), y(u,v), z(u,v). Evaluate a given expression at specified values of the variable(s). Verify identities using the basic axioms of commutativity, distributivity, etc. Example: 3x + 2 = 11 Collect, regroup, and cancel terms to simplify an expression. Multiply out products of sums, then simplify. Solve simple inequalities involving absolute value Practice the laws of exponents on purely numerical problems. Simplify expresssions involving exponents Factor out explicit common factors and use simple factoring identities Example: $x^2-x-2 = (x-1)(x-2)$. Factor by trying all possibilities Factor out the greatest common divisor of two groups of terms. Example: $x^2+1 = x+3$. Bring terms to the left and factor. Solve quadratic equations by completing the square. Example: $x^2-4x = 17$. Solve quadratic equations using $x = -b/2a \pm (1/2a)\sqrt (b^2-4ac)$ Example: 3x + 2 < 11 Example: x + y = 3, x - y = 1 Simplify algebraic expressions using the laws of exponents. Review your arithmetic skills: example, 3/4 + 2/3 Add algebraic fractions using common denominators Simplify fractions by factoring, and cancelling common factors. Use the laws of fractions to simplify some purely numerical examples. Eliminate compound fractions in examples containing variables. Example: 3/x + 2/(x-1) = 1 Simplify numerical expressions involving roots. Example: $\sqrt 28 + \sqrt 63$ Simplify algebraic expressions involving roots. Example: 3x + 2 = 11 Solve a system of linear equations by eliminating one variable at a time. Solve by adding or subtracting multiples of one row to another Write the system in matrix form and perform row operations. Calculate the matrix inverse while solving by row operations. Use matrix algebra and let MathXpert compute the matrix inverse. Solve equations using the theory of determinants. You can enter any expression, but not an equation or inequality. Choose this topic to learn or review common denominators. Sometimes you must factor in order to find the best common denominator. Eliminate compound fractions using all the laws of algebra. Express fractions using negative exponents Replace negative exponents by equivalent fractions and simplify. Simplify expressions involving roots and square roots. Solve inequalities involving absolute value. Change roots and square roots to fractional exponents. Use roots and square roots to eliminate fractional exponents. Example: $x^2-x-2 = (x-1)(x-2)$. Factor by trying all possibilities. Solve quadratic equations using $x = -b/2a \pm (1/2a)\sqrt (b^2-4ac)$. Solve by factoring, completing the square, or quadratic formula as required. Factor expressions using several steps or advanced factoring formulas. Equations that can be solved after several factoring steps. Solve equations requiring common denominators and simplification. Example: $2\sqrt n = 5$ Example: $3 \sqrt (x-2)/x + x/\sqrt (x-2) = 4$ Example: 3x + 2 < 11 Example: x^3 - x < 0 Example: (x-2) / (x-8) < 0 Example: $\sqrt (x^2-x-1) < x$ Example: x^3 + 3x + 1 = 0 Problems will be of different types. Choose this to enter a new equation. Example: $(\sqrt x + \sqrt y)^2/\sqrt (xy)$ Example: $3 \sqrt (x-2)/x + x/\sqrt (x-2)$ Example: ln x^x Verify an identity by simplifying both sides to the same form. Learn common values such as $sin(\pi /4) = 1/\sqrt 2$ Identities that can be verified using the most basic laws of trig. Identities requiring the use of formulas for sin(u+v) etc. Identities requiring the use of formulas for $sin 2\theta $ etc. Identities requiring the use of formulas for $sin(\theta /2)$ etc. Simplify an expression such as $sin \theta sin 2\theta $ using product identities. Identities expressing $sin x \pm sin y$ as a product of trig functions, etc. Simplify an arbitrary trigonometric expression. A variety of trig identities; or enter an identity of your own First exercises in the evaluation of expressions involving arcsin, etc. Equations solved using inverse trig functions. Example: tan x = -1.309. Example: 4 cos^2 x - 3 = 0 First exercises in complex numbers: addition and subtraction. Simplify using laws of logarithms. Example: log(u^2 v^7). Simplify expressions involving logarithms to a base other than 10 or e. Simplify using the inverse relation between powers and logarithms. Simplify expressions involving logarithms and exponents. Example: log (x-9) + log (100 x) = 3 Solve equations that require using logarithms. Example: e^(4x) = 5e^2x. Express complex numbers in polar form. Calculate integer powers of complex numbers. Basic identities defining or involving sinh, cosh, tanh, etc. Identities involving sinh, cosh, tanh, etc. Express trig functions using complex exponentials. Find complex roots of quadratic equations Cubic equations led to the discovery of complex numbers Basic laws of indexed sums Expand integer powers of sums using the binomial theorem. Find all the n-th roots of a complex number. Under other topics, MathXpert will compute a polynomial limit in one step. Basic laws of limits: limit of a root, logarithm, quotient, etc. Express a derivative as a limit and evaluate that limit if possible. Under other topics, MathXpert will differentiate a polynomial in one step. Product rule, quotient rule, etc. Limits of functions involving sin, cos, tan, etc. Simple differentiation problems involving sin, cos, tan, etc. First chain-rule exercises. Example: $d/dx (x^2 + 1)^100$ Exercises in differentiation, using all the rules on a variety of functions. Compute the second (or third or higher) derivative. Find dy/dx when y is not given explicitly but by an equation in x and y. Given an equation between y,t,and dy/dt, find them all at a certain time. Find the maximum and minimum of $f(x)$ on an interval $a \le x \le b$ A rational function is a quotient of polynomials Limits as x tends to plus or minus infinity. Limits in which the function increases or decreases without bound. Indexed sums are used in calculus as one way to define an integral. Under other topics, MathXpert will integrate a polynomial in one step. These problems can be done before learning integration by substitution. Differentiation and integration are inverse processes. Under other topics, MathXpert integrates by substitution in one step. $\int u dv = uv - \int v du$ Mixed problems. Choose the best method. Enter your own integral here. Behavior of exponential functions at infinity Limits which can be solved using the limit definition of e In an indeterminate limit, differentiate numerator and denominator. Learn to use leading terms to simplify limit calculations. A variety of limit problems. Enter your own limit problem here. Differentiate expressions containing the variable in an exponent. Differentiate expressions involving logarithms. Logarithmic differentiation is this: dy/dx = y (d/dx) ln y. Differentiate expressions involving arcsin, arctan, etc. Differentiate expressions involving sinh, cosh, tanh, etc. Differentiate all kinds of expressions. Enter your own here. Applied to exponentials, logs, inverse trig functions, etc. Integration problems in which the answer involves a logarithm. Integrate polynomials in sin, cos, tan, sec, csc, cot. Also known as inverse substitutions. Example: x = sin u in $\int \sqrt (1-x^2)dx$. Methods: polynomial division, partial fractions, reduce to trig integrals. Eliminate a root or other complication by a well-chosen substitution. Integrals in which the integrand has a singularity, usually at an endpoint. Find the sum of an infinite series. Test convergence of a series using the integral test. Test convergence of a series using the comparison test. Test convergence of a series using the root or ratio tests. Expand a function in a power series. Get the variables on different sides of the equation and integrate. Compute the arc length of y = f(x) using an integral formula. Compute the area of a surface of revolution using an integral formula. 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