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/* M. Beeson, for MathXpert
Status line help for the topics menus
Must list every topic in tdefn.h
Original date, 9.7.95
Last modified 1.7.99
9.4.04 added an include and added 'const' in declaration of topichelp
*/
#include <assert.h>
#define ENGLISH_DLL
#include "export.h"
#include "tdefn.h"
#include "english1.h"
/*__________________________________________________________*/
MEXPORT_ENGLISH const char * topichelp(int n)
/* supply a status-line string for a topic menu, in English */
{ switch(n)
{ case 0 : return ""; // on disabled menu items, labels like "Algebra 1"
case _ordinary_graph : return "Make an ordinary graph of a function.";
case _ordinary_graph_quadratic : return "Example: y = 3x^2 + 2x + 1";
case _ordinary_graph_polynomial : return "Example: y = x^3 - ax";
case _ordinary_graph_linear : return "Example: y = 3x - 2";
case _ordinary_graph_rational : return "A rational function is a quotient of polynomials.";
case _ordinary_graph_fractexp : return "Example: y = x^(4/5)";
case _ordinary_graph_exponential : return "Learn about exponential growth and decay.";
case _ordinary_graph_log : return "Example: y = ln(x/a)";
case _ordinary_graph_algvariety : return "Example: y = sqrt(x^2-9)/(x-1)";
case _ordinary_graph_sincos : return "Learn about frequency, phase, and amplitude.";
case _ordinary_graph_trig : return "Learn the graphs of all six trig functions.";
case _ordinary_graph_arctrig : return "Learn the graphs of all six inverse trig functions.";
case _ordinary_graph_htrig : return "Learn the graphs of the hyperbolic functions.";
case _ordinary_graph_trigvariety : return "Graph functions composed of trig and algebraic components.";
case _ordinary_graph_bessel : return "Learn the graphs of the different kinds of Bessel functions.";
case _ordinary_graph_calcvariety : return "Graph functions composed of trig, log, exponential, and algebraic components.";
case _graph_taylor : return "Compare the partial sums of a series with the complete sum.";
case _graph_fourier : return "Compare the partial sums of a series with the complete sum.";
case _compare_same : return "Two or more graphs will be drawn on the same axes.";
case _compare_different : return "Two or more graphs will be drawn, on separate axes.";
case _graph_ineq : return "Examples: y <= tan x, or x <= y <= tan x";
case _graph_set : return "Example: y^2 < tan x.";
case _graph_circle : return "Learn how the radius and center depend on the formula.";
case _graph_ellipse : return "Learn how the shape of an ellipse depends on the formula.";
case _graph_parabola : return "Learn how the shape of a parabola depends on the formula.";
case _graph_hyperbola : return "Learn how the shape of a hyperbola depends on the formula.";
case _graph_relation : return "Example, $3x^2 + 5y^2 = 1$ will plot an ellipse";
case _polyroots : return "Use a parameter in the polynomial to see how the roots move.";
case _parametric_graph : return "Plot a graph defined by equations x = f(t), y = g(t).";
case _polar_graph : return "Plot a graph defined by an equation $r = f(\\theta )$";
case _comparefandfprime : return "f' will be calculated, and f and f' will be plotted on different axes.";
case _comparetwoderivs : return "f'' and f'' will be calculated and f, f', and f'' will all be plotted.";
case _contour_plot : return "Plot the level lines f(x,y) = z for regularly-spaced z values.";
case _complex_contour_plot: return "Makes a contour plot of the real part of a complex function.";
case _solve_ode : return "Plot solutions through points you specify by clicking.";
case _solve_two_odes : return "Plot equations of the form dx/dt = f(t,x,y), dy/dt = g(t,x,y)";
case _high_order_ode : return "Plot equations of the form y'' = f(t,x,y,y'), also for higher order.";
case _riemann_sums : return "Show the function and the approximating rectangles used in a Riemann sum.";
case _trapezoid_rule : return "Show the function and approximating trapezoids used in the trapezoid rule.";
case _simpsons_rule : return "Show the function and approximating regions used in Simpson's rule.";
case _space_curve : return "Plot a curve defined by three functions x(t), y(t), z(t).";
case _nonparametric_surface: return "Three-dimensional graph of a function of two variables.";
case _polar_nonparametric_surface: return "Three-dimensional graph of a function of two variables in polar coordinates.";
case _parametric_surface : return "A parametric surface is defined by three functions x(u,v), y(u,v), z(u,v).";
/* Algebra 1 */
case _evaluate_numerically: return "Evaluate a given expression at specified values of the variable(s).";
case _verify_algebraic_identity: return "Verify identities using the basic axioms of commutativity, distributivity, etc.";
case _solve_linear_equation: return "Example: 3x + 2 = 11";
case _simplify_polynomial : return "Collect, regroup, and cancel terms to simplify an expression.";
case _multiply_polynomials : return "Multiply out products of sums, then simplify.";
case _alg1_absolute_value : return "Solve simple inequalities involving absolute value";
case _numerical_exponents : return "Practice the laws of exponents on purely numerical problems.";
case _alg1_exponents : return "Simplify expresssions involving exponents";
case _simple_factoring : return "Factor out explicit common factors and use simple factoring identities";
case _alg1_factor_quadratic: return "Example: $x^2-x-2 = (x-1)(x-2)$. Factor by trying all possibilities";
case _factor_by_grouping : return "Factor out the greatest common divisor of two groups of terms.";
case _alg1_quadratic_equation : return "Example: $x^2+1 = x+3$. Bring terms to the left and factor.";
case _complete_the_square : return "Solve quadratic equations by completing the square. Example: $x^2-4x = 17$.";
case _alg1_quadratic_formula: return "Solve quadratic equations using $x = -b/2a \\pm (1/2a)\\sqrt (b^2-4ac)$";
case _alg1_linear_inequality: return "Example: 3x + 2 < 11";
case _alg1_linear_systems : return "Example: x + y = 3, x - y = 1";
case _alg1_simplify : return "Simplify algebraic expressions using the laws of exponents.";
case _add_numerical_fractions : return "Review your arithmetic skills: example, 3/4 + 2/3";
case _alg1_common_denoms : return "Add algebraic fractions using common denominators";
case _simplify_fractions : return "Simplify fractions by factoring, and cancelling common factors.";
case _numerical_compound_fractions : return "Use the laws of fractions to simplify some purely numerical examples.";
case _alg1_compound_fractions : return "Eliminate compound fractions in examples containing variables.";
case _equations_containing_fractions : return "Example: 3/x + 2/(x-1) = 1";
case _numerical_radicals : return "Simplify numerical expressions involving roots. Example: $\\sqrt 28 + \\sqrt 63$";
case _alg1_radicals : return "Simplify algebraic expressions involving roots.";
/* Linear Algebra */
case _solve_linear_eqn : return "Example: 3x + 2 = 11";
case _eqns_by_substitution : return "Solve a system of linear equations by eliminating one variable at a time.";
case _eqns_by_adding_eqns : return "Solve by adding or subtracting multiples of one row to another";
case _eqns_in_matrix_form : return "Write the system in matrix form and perform row operations.";
case _gauss_jordan : return "Calculate the matrix inverse while solving by row operations.";
case _eqns_by_matrix_inverse : return "Use matrix algebra and let MathXpert compute the matrix inverse.";
case _cramers_rule : return "Solve equations using the theory of determinants.";
/* Algebra 2 */
case _simplify : return "You can enter any expression, but not an equation or inequality.";
case _simple_commondenom : return "Choose this topic to learn or review common denominators.";
case _advanced_commondenom : return "Sometimes you must factor in order to find the best common denominator.";
case _compound_fractions : return "Eliminate compound fractions using all the laws of algebra.";
case _simplify_polynomials : return "Collect, regroup, and cancel terms to simplify an expression.";
case _simple_exponents : return "Simplify algebraic expressions using the laws of exponents.";
case _simplify_rational_functions: return "A rational function is a quotient of polynomials.";
case _negative_exponents : return "Express fractions using negative exponents";
case _eliminate_negative_exponents: return "Replace negative exponents by equivalent fractions and simplify.";
case _radicals : return "Simplify expressions involving roots and square roots.";
case _absolute_value : return "Solve inequalities involving absolute value.";
case _fractional_exponents : return "Change roots and square roots to fractional exponents.";
case _eliminate_fractional_exponents: return "Use roots and square roots to eliminate fractional exponents.";
case _factor_quadratics : return "Example: $x^2-x-2 = (x-1)(x-2)$. Factor by trying all possibilities.";
case _quadratic_formula : return "Solve quadratic equations using $x = -b/2a \\pm (1/2a)\\sqrt (b^2-4ac)$.";
case _solve_quadratic_equation : return "Solve by factoring, completing the square, or quadratic formula as required.";
case _advanced_factoring : return "Factor expressions using several steps or advanced factoring formulas.";
case _solve_higher_degree_equation: return "Equations that can be solved after several factoring steps.";
case _solve_rational_equation : return "Solve equations requiring common denominators and simplification.";
case _solve_root_equation : return "Example: $2\\sqrt n = 5$";
case _solve_fractions_and_roots : return "Example: $3 \\sqrt (x-2)/x + x/\\sqrt (x-2) = 4$";
case _solve_linear_inequality : return "Example: 3x + 2 < 11";
case _solve_polynomial_inequality : return "Example: x^3 - x < 0";
case _solve_rational_inequality : return "Example: (x-2) / (x-8) < 0";
case _solve_root_inequality : return "Example: $\\sqrt (x^2-x-1) < x$";
case _cubic_one_root : return "Example: x^3 + 3x + 1 = 0";
case _solve_equation : return "Problems will be of different types. Choose this to enter a new equation.";
case _simplify_roots_and_powers : return "Example: $(\\sqrt x + \\sqrt y)^2/\\sqrt (xy)$";
case _simplify_roots_and_fractions: return "Example: $3 \\sqrt (x-2)/x + x/\\sqrt (x-2)$";
case _simplify_any_function : return "Example: ln x^x";
case _verify_alg2_identity : return "Verify an identity by simplifying both sides to the same form.";
/* end Algebra 2 */
/* Precalculus */
case _evaluate_trig : return "Learn common values such as $sin(\\pi /4) = 1/\\sqrt 2$";
case _basic_trig : return "Identities that can be verified using the most basic laws of trig.";
case _trig_addition : return "Identities requiring the use of formulas for sin(u+v) etc.";
case _double_angle : return "Identities requiring the use of formulas for $sin 2\\theta $ etc.";
case _half_angle : return "Identities requiring the use of formulas for $sin(\\theta /2)$ etc.";
case _trig_product : return "Simplify an expression such as $sin \\theta sin 2\\theta $ using product identities.";
case _trig_factor : return "Identities expressing $sin x \\pm sin y$ as a product of trig functions, etc.";
case _trig_simplify : return "Simplify an arbitrary trigonometric expression.";
case _trig_identities : return "A variety of trig identities; or enter an identity of your own";
case _inverse_trig_functions : return "First exercises in the evaluation of expressions involving arcsin, etc.";
case _simple_trig_eqn : return "Equations solved using inverse trig functions. Example: tan x = -1.309.";
case _trig_eqn : return "Example: 4 cos^2 x - 3 = 0";
case _complex_arithmetic : return "First exercises in complex numbers: addition and subtraction.";
case _logarithms : return "Simplify using laws of logarithms. Example: log(u^2 v^7).";
case _change_log_base : return "Simplify expressions involving logarithms to a base other than 10 or e.";
case _exponentials : return "Simplify using the inverse relation between powers and logarithms.";
case _simplify_logpower : return "Simplify expressions involving logarithms and exponents.";
case _log_eqn : return "Example: log (x-9) + log (100 x) = 3";
case _exp_eqn : return "Solve equations that require using logarithms. Example: e^(4x) = 5e^2x.";
case _polar_form : return "Express complex numbers in polar form.";
case _de_moivre : return "Calculate integer powers of complex numbers.";
case _hyperfunctions : return "Basic identities defining or involving sinh, cosh, tanh, etc.";
case _hyperfunctions2 : return "Identities involving sinh, cosh, tanh, etc.";
case _complex_trig : return "Express trig functions using complex exponentials.";
case _complex_quadratics : return "Find complex roots of quadratic equations";
case _complex_cubics : return "Cubic equations led to the discovery of complex numbers";
case _sigma_notation : return "Basic laws of indexed sums";
case _binomial_theorem : return "Expand integer powers of sums using the binomial theorem.";
case _complex_roots : return "Find all the n-th roots of a complex number.";
/* Calculus 1 */
case _polynomial_limits : return "Under other topics, MathXpert will compute a polynomial limit in one step.";
case _simple_limits : return "Basic laws of limits: limit of a root, logarithm, quotient, etc.";
case _diff_from_def : return "Express a derivative as a limit and evaluate that limit if possible.";
case _diff_polynomial : return "Under other topics, MathXpert will differentiate a polynomial in one step.";
case _diff_basics : return "Product rule, quotient rule, etc.";
case _lim_trig : return "Limits of functions involving sin, cos, tan, etc.";
case _diff_trig : return "Simple differentiation problems involving sin, cos, tan, etc.";
case _chain_rule : return "First chain-rule exercises. Example: $d/dx (x^2 + 1)^100$";
case _difreview : return "Exercises in differentiation, using all the rules on a variety of functions.";
case _higher_order_diff : return "Compute the second (or third or higher) derivative.";
case _implicit_diff : return "Find dy/dx when y is not given explicitly but by an equation in x and y.";
case _related_rates : return "Given an equation between y,t,and dy/dt, find them all at a certain time.";
case _minmax : return "Find the maximum and minimum of $f(x)$ on an interval $a \\le x \\le b$";
case _rational_limits : return "A rational function is a quotient of polynomials";
case _limits_at_infinity : return "Limits as x tends to plus or minus infinity.";
case _infinite_limits : return "Limits in which the function increases or decreases without bound.";
case _sigma_notation1 : return "Indexed sums are used in calculus as one way to define an integral.";
case _int_poly : return "Under other topics, MathXpert will integrate a polynomial in one step.";
case _simple_int : return "These problems can be done before learning integration by substitution.";
case _fundamental_theorem : return "Differentiation and integration are inverse processes.";
case _int_by_substitution : return "Under other topics, MathXpert integrates by substitution in one step.";
case _int_by_parts1 : return "$\\int u dv = uv - \\int v du$";
case _intreview : return "Mixed problems. Choose the best method. Enter your own integral here.";
/* Calculus 2 */
case _lim_exp : return "Behavior of exponential functions at infinity";
case _eulere_as_limit : return "Limits which can be solved using the limit definition of e";
case _lhopitals_rule : return "In an indeterminate limit, differentiate numerator and denominator.";
case _limleadingterm : return "Learn to use leading terms to simplify limit calculations.";
case _limits_any_function : return "A variety of limit problems. Enter your own limit problem here.";
case _diff_exp_from_defn : return "Express a derivative as a limit and evaluate that limit if possible.";
case _diff_exp : return "Differentiate expressions containing the variable in an exponent.";
case _diff_logs : return "Differentiate expressions involving logarithms.";
case _logarithmic_differentiation: return "Logarithmic differentiation is this: dy/dx = y (d/dx) ln y.";
case _diff_arctrig : return "Differentiate expressions involving arcsin, arctan, etc.";
case _diff_hyperbolic : return "Differentiate expressions involving sinh, cosh, tanh, etc.";
case _diff_any_function : return "Differentiate all kinds of expressions. Enter your own here.";
case _int_by_parts2 : return "Applied to exponentials, logs, inverse trig functions, etc.";
case _int_logs : return "Integration problems in which the answer involves a logarithm.";
case _trigpower_integrals : return "Integrate polynomials in sin, cos, tan, sec, csc, cot.";
case _trig_substitution : return "Also known as inverse substitutions. Example: x = sin u in $\\int \\sqrt (1-x^2)dx$.";
case _integrate_rational_functions: return "Methods: polynomial division, partial fractions, reduce to trig integrals.";
case _rationalizing_substitutions: return "Eliminate a root or other complication by a well-chosen substitution.";
case _integrate_any_function : return "Mixed problems. Choose the best method. Enter your own integral here.";
case _improper_integrals : return "Integrals in which the integrand has a singularity, usually at an endpoint.";
case _sum_series : return "Find the sum of an infinite series.";
case _integral_test : return "Test convergence of a series using the integral test.";
case _comparison_test : return "Test convergence of a series using the comparison test.";
case _root_ratio_tests : return "Test convergence of a series using the root or ratio tests.";
case _power_series1 : return "Expand a function in a power series.";
case _power_series2 : return "Expand a function in a power series.";
case _separable_ode : return "Get the variables on different sides of the equation and integrate.";
case _arc_length : return "Compute the arc length of y = f(x) using an integral formula.";
case _area_revolution : return "Compute the area of a surface of revolution using an integral formula.";
case _volume_revolution : return "Compute the volume of a surface of revolution using an integral formula.";
default: assert(0); // all cases are covered
}
return "oops"; // avoid a warning message
}
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