{"id":2784,"date":"2025-06-05T07:43:39","date_gmt":"2025-06-05T07:43:39","guid":{"rendered":"https:\/\/diznr.com\/?p=2784"},"modified":"2025-06-05T07:43:39","modified_gmt":"2025-06-05T07:43:39","slug":"computer-science-numerical-methods-difference-b-w-algebraic-and-transcendental-equation-functions-transcendental","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/computer-science-numerical-methods-difference-b-w-algebraic-and-transcendental-equation-functions-transcendental\/","title":{"rendered":"Computer Science\/Numerical Methods\/. Difference b\/w algebraic and transcendental equation transcendental functions"},"content":{"rendered":"<p>Computer Science\/Numerical Methods\/. Difference b\/w algebraic and transcendental equation transcendental functions<\/p>\n<p>[fvplayer id=&#8221;111&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"79\"><strong data-start=\"4\" data-end=\"77\">Difference Between Algebraic and Transcendental Equations &amp; Functions<\/strong><\/h3>\n<h4 data-start=\"81\" data-end=\"113\"><strong data-start=\"86\" data-end=\"111\">1. Algebraic Equation<\/strong><\/h4>\n<p data-start=\"114\" data-end=\"289\">An <strong data-start=\"117\" data-end=\"139\">algebraic equation<\/strong> is an equation that involves only <strong data-start=\"174\" data-end=\"189\">polynomials<\/strong> with constants and variables, combined using addition, subtraction, multiplication, and division.<\/p>\n<p data-start=\"291\" data-end=\"312\"><strong data-start=\"293\" data-end=\"310\">General Form:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">anxn+an\u22121xn\u22121+\u22ef+a1x+a0=0a_n x^n + a_{n-1} x^{n-1} + \\dots + a_1 x + a_0 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u22ef<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"373\" data-end=\"455\">where <span class=\"katex\"><span class=\"katex-mathml\">an,an\u22121,\u2026,a0a_n, a_{n-1}, \\dots, a_0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"minner\">\u2026<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> are constants, and <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> is the variable.<\/p>\n<p data-start=\"457\" data-end=\"474\"><strong data-start=\"459\" data-end=\"472\">Examples:<\/strong><\/p>\n<ul data-start=\"475\" data-end=\"565\">\n<li data-start=\"475\" data-end=\"501\"><span class=\"katex\"><span class=\"katex-mathml\">x2\u22124x+3=0x^2 &#8211; 4x + 3 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"502\" data-end=\"535\"><span class=\"katex\"><span class=\"katex-mathml\">3&#215;5\u22122&#215;3+x\u22127=03x^5 &#8211; 2x^3 + x &#8211; 7 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"536\" data-end=\"565\"><span class=\"katex\"><span class=\"katex-mathml\">2&#215;4+5&#215;2\u22129=02x^4 + 5x^2 &#8211; 9 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">9<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h4 data-start=\"572\" data-end=\"609\"><strong data-start=\"577\" data-end=\"607\">2. Transcendental Equation<\/strong><\/h4>\n<p data-start=\"610\" data-end=\"792\">A <strong data-start=\"612\" data-end=\"639\">transcendental equation<\/strong> contains <strong data-start=\"649\" data-end=\"677\">transcendental functions<\/strong>, such as exponential, logarithmic, or trigonometric functions, which cannot be expressed as a finite polynomial.<\/p>\n<p data-start=\"794\" data-end=\"811\"><strong data-start=\"796\" data-end=\"809\">Examples:<\/strong><\/p>\n<ul data-start=\"812\" data-end=\"882\">\n<li data-start=\"812\" data-end=\"834\"><span class=\"katex\"><span class=\"katex-mathml\">ex\u22123x=0e^x &#8211; 3x = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"835\" data-end=\"859\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061x\u2212x=0\\sin x &#8211; x = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"860\" data-end=\"882\"><span class=\"katex\"><span class=\"katex-mathml\">xlog\u2061x=5x \\log x = 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mop\">log<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p data-start=\"884\" data-end=\"1063\">\u00a0These equations <strong data-start=\"903\" data-end=\"913\">do not<\/strong> have a closed-form solution and often require <strong data-start=\"960\" data-end=\"981\">numerical methods<\/strong> like <strong data-start=\"987\" data-end=\"1048\">Bisection Method, Newton-Raphson Method, or Secant Method<\/strong> for solving.<\/p>\n<h3 data-start=\"1070\" data-end=\"1138\"><strong data-start=\"1074\" data-end=\"1136\">3. Difference Between Algebraic &amp; Transcendental Functions<\/strong><\/h3>\n<div class=\"overflow-x-auto contain-inline-size\">\n<table data-start=\"1140\" data-end=\"1897\">\n<thead data-start=\"1140\" data-end=\"1211\">\n<tr data-start=\"1140\" data-end=\"1211\">\n<th data-start=\"1140\" data-end=\"1153\"><strong data-start=\"1142\" data-end=\"1152\">Aspect<\/strong><\/th>\n<th data-start=\"1153\" data-end=\"1178\"><strong data-start=\"1155\" data-end=\"1177\">Algebraic Function<\/strong><\/th>\n<th data-start=\"1178\" data-end=\"1211\"><strong data-start=\"1180\" data-end=\"1207\">Transcendental Function<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1274\" data-end=\"1897\">\n<tr data-start=\"1274\" data-end=\"1431\">\n<td><strong data-start=\"1276\" data-end=\"1290\">Definition<\/strong><\/td>\n<td>A function involving polynomials only.<\/td>\n<td>A function that goes beyond polynomials (contains exponentials, logarithms, or trigonometry).<\/td>\n<\/tr>\n<tr data-start=\"1432\" data-end=\"1546\">\n<td><strong data-start=\"1434\" data-end=\"1442\">Form<\/strong><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">f(x)=xn+an\u22121xn\u22121+\u22ef+a1x+a0f(x) = x^n + a_{n-1} x^{n-1} + \\dots + a_1 x + a_0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u22ef<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">f(x)=ex,sin\u2061x,log\u2061x,etc.f(x) = e^x, \\sin x, \\log x, etc.<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">log<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr data-start=\"1547\" data-end=\"1642\">\n<td><strong data-start=\"1549\" data-end=\"1560\">Example<\/strong><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">x2+3x+5x^2 + 3x + 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">4&#215;3\u22122x+74x^3 &#8211; 2x + 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">ex,log\u2061x,sin\u2061x,tan\u2061xe^x, \\log x, \\sin x, \\tan x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">log<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">tan<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr data-start=\"1643\" data-end=\"1781\">\n<td><strong data-start=\"1645\" data-end=\"1660\">Solvability<\/strong><\/td>\n<td>Can be solved algebraically using factorization, quadratic formula, etc.<\/td>\n<td>Requires numerical methods for solving.<\/td>\n<\/tr>\n<tr data-start=\"1782\" data-end=\"1897\">\n<td><strong data-start=\"1784\" data-end=\"1800\">Graph Nature<\/strong><\/td>\n<td>Generally smooth and polynomial-like.<\/td>\n<td>More complex curves, often periodic or asymptotic.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3 data-start=\"1904\" data-end=\"1968\"><strong data-start=\"1908\" data-end=\"1966\">4. Numerical Methods to Solve Transcendental Equations<\/strong><\/h3>\n<p data-start=\"1969\" data-end=\"2062\">Since transcendental equations <strong data-start=\"2000\" data-end=\"2029\">cannot be solved directly<\/strong>, we use <strong data-start=\"2038\" data-end=\"2059\">iterative methods<\/strong>:<\/p>\n<p data-start=\"2064\" data-end=\"2369\"><strong data-start=\"2067\" data-end=\"2087\">Bisection Method<\/strong> \u2013 Divides the interval and checks for root signs.<br data-start=\"2137\" data-end=\"2140\" \/><strong data-start=\"2143\" data-end=\"2168\">Newton-Raphson Method<\/strong> \u2013 Uses derivatives for fast convergence.<br data-start=\"2209\" data-end=\"2212\" \/><strong data-start=\"2215\" data-end=\"2255\">Regula Falsi (False Position) Method<\/strong> \u2013 A modified bisection method.<br data-start=\"2286\" data-end=\"2289\" \/><strong data-start=\"2292\" data-end=\"2309\">Secant Method<\/strong> \u2013 Uses two initial approximations instead of derivatives.<\/p>\n<p data-start=\"2371\" data-end=\"2477\" data-is-last-node=\"\" data-is-only-node=\"\">Would you like a step-by-step example of <strong data-start=\"2412\" data-end=\"2473\">solving a transcendental equation using numerical methods<\/strong>?<\/p>\n<h3 data-start=\"2371\" data-end=\"2477\"><a href=\"https:\/\/csw.uobaghdad.edu.iq\/wp-content\/uploads\/sites\/30\/uploads\/computer%20science\/Lectures\/2nd%20year\/NUM%20ANALYSIS.pdf\" target=\"_blank\" rel=\"noopener\">Computer Science\/Numerical Methods\/. Difference b\/w algebraic and transcendental equation transcendental functions<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/egyankosh.ac.in\/bitstream\/123456789\/10560\/1\/Unit-2.pdf\" target=\"_blank\" rel=\"noopener\">UNIT 2 SOLUTION OF ALGEBRAIC AND &#8230;<\/a><\/h3>\n<p data-start=\"0\" data-end=\"230\">Here\u2019s a clear and concise explanation of the <strong data-start=\"46\" data-end=\"107\">difference between algebraic and transcendental equations<\/strong>, along with an understanding of <strong data-start=\"140\" data-end=\"168\">transcendental functions<\/strong> in the context of <strong data-start=\"187\" data-end=\"229\">Computer Science and Numerical Methods<\/strong>:<\/p>\n<hr data-start=\"232\" data-end=\"235\" \/>\n<h2 data-start=\"237\" data-end=\"269\">\ud83e\uddee <strong data-start=\"243\" data-end=\"269\">1. Algebraic Equations<\/strong><\/h2>\n<h3 data-start=\"271\" data-end=\"293\">\ud83d\udd39 <strong data-start=\"278\" data-end=\"293\">Definition:<\/strong><\/h3>\n<p data-start=\"294\" data-end=\"473\">An <strong data-start=\"297\" data-end=\"319\">algebraic equation<\/strong> is any equation formed using a <strong data-start=\"351\" data-end=\"392\">finite number of algebraic operations<\/strong> (addition, subtraction, multiplication, division, and roots) on <strong data-start=\"457\" data-end=\"472\">polynomials<\/strong>.<\/p>\n<h3 data-start=\"475\" data-end=\"495\">\ud83d\udd39 <strong data-start=\"482\" data-end=\"495\">Examples:<\/strong><\/h3>\n<ul data-start=\"496\" data-end=\"566\">\n<li data-start=\"496\" data-end=\"520\">\n<p data-start=\"498\" data-end=\"520\"><span class=\"katex\"><span class=\"katex-mathml\">x2+3x\u22125=0x^2 + 3x &#8211; 5 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"521\" data-end=\"540\">\n<p data-start=\"523\" data-end=\"540\"><span class=\"katex\"><span class=\"katex-mathml\">x3\u22127=0x^3 &#8211; 7 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"541\" data-end=\"566\">\n<p data-start=\"543\" data-end=\"566\"><span class=\"katex\"><span class=\"katex-mathml\">x+2x=4\\sqrt{x} + 2x = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"svg-align\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"568\" data-end=\"586\">\ud83d\udd39 <strong data-start=\"575\" data-end=\"586\">Nature:<\/strong><\/h3>\n<ul data-start=\"587\" data-end=\"723\">\n<li data-start=\"587\" data-end=\"629\">\n<p data-start=\"589\" data-end=\"629\">Variables appear in <strong data-start=\"609\" data-end=\"623\">polynomial<\/strong> form.<\/p>\n<\/li>\n<li data-start=\"630\" data-end=\"723\">\n<p data-start=\"632\" data-end=\"723\">Can be <strong data-start=\"639\" data-end=\"657\">solved exactly<\/strong> using algebraic methods (e.g., factorization, quadratic formula).<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"725\" data-end=\"728\" \/>\n<h2 data-start=\"730\" data-end=\"767\">\ud83c\udf10 <strong data-start=\"736\" data-end=\"767\">2. Transcendental Equations<\/strong><\/h2>\n<h3 data-start=\"769\" data-end=\"791\">\ud83d\udd39 <strong data-start=\"776\" data-end=\"791\">Definition:<\/strong><\/h3>\n<p data-start=\"792\" data-end=\"996\">A <strong data-start=\"794\" data-end=\"821\">transcendental equation<\/strong> is one that contains at least <strong data-start=\"852\" data-end=\"883\">one transcendental function<\/strong> of the variable \u2014 i.e., a function that <strong data-start=\"924\" data-end=\"947\">cannot be expressed<\/strong> as a finite combination of algebraic operations.<\/p>\n<h3 data-start=\"998\" data-end=\"1018\">\ud83d\udd39 <strong data-start=\"1005\" data-end=\"1018\">Examples:<\/strong><\/h3>\n<ul data-start=\"1019\" data-end=\"1083\">\n<li data-start=\"1019\" data-end=\"1034\">\n<p data-start=\"1021\" data-end=\"1034\"><span class=\"katex\"><span class=\"katex-mathml\">ex=3e^x = 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1035\" data-end=\"1056\">\n<p data-start=\"1037\" data-end=\"1056\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(x)=x\/2\\sin(x) = x\/2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\/2<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1057\" data-end=\"1083\">\n<p data-start=\"1059\" data-end=\"1083\"><span class=\"katex\"><span class=\"katex-mathml\">x\u22c5ln\u2061(x)=1x \\cdot \\ln(x) = 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u22c5<\/span><\/span><span class=\"base\"><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"1085\" data-end=\"1103\">\ud83d\udd39 <strong data-start=\"1092\" data-end=\"1103\">Nature:<\/strong><\/h3>\n<ul data-start=\"1104\" data-end=\"1263\">\n<li data-start=\"1104\" data-end=\"1150\">\n<p data-start=\"1106\" data-end=\"1150\">Cannot be solved analytically in most cases.<\/p>\n<\/li>\n<li data-start=\"1151\" data-end=\"1263\">\n<p data-start=\"1153\" data-end=\"1263\">Requires <strong data-start=\"1162\" data-end=\"1183\">numerical methods<\/strong> (e.g., <strong data-start=\"1191\" data-end=\"1204\">Bisection<\/strong>, <strong data-start=\"1206\" data-end=\"1224\">Newton-Raphson<\/strong>, <strong data-start=\"1226\" data-end=\"1243\">Secant Method<\/strong>) for approximation.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1265\" data-end=\"1268\" \/>\n<h2 data-start=\"1270\" data-end=\"1307\">\ud83d\udcc8 <strong data-start=\"1276\" data-end=\"1307\">3. Transcendental Functions<\/strong><\/h2>\n<h3 data-start=\"1309\" data-end=\"1331\">\ud83d\udd39 <strong data-start=\"1316\" data-end=\"1331\">Definition:<\/strong><\/h3>\n<p data-start=\"1332\" data-end=\"1468\">These are functions that <strong data-start=\"1357\" data-end=\"1380\">go beyond algebraic<\/strong> \u2014 they cannot be expressed as roots of polynomial equations with rational coefficients.<\/p>\n<h3 data-start=\"1470\" data-end=\"1513\">\ud83d\udd39 <strong data-start=\"1477\" data-end=\"1513\">Common Transcendental Functions:<\/strong><\/h3>\n<ul data-start=\"1514\" data-end=\"1739\">\n<li data-start=\"1514\" data-end=\"1552\">\n<p data-start=\"1516\" data-end=\"1552\"><strong data-start=\"1516\" data-end=\"1541\">Exponential functions<\/strong>: <span class=\"katex\"><span class=\"katex-mathml\">exe^x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1553\" data-end=\"1608\">\n<p data-start=\"1555\" data-end=\"1608\"><strong data-start=\"1555\" data-end=\"1580\">Logarithmic functions<\/strong>: <span class=\"katex\"><span class=\"katex-mathml\">ln\u2061(x),log\u206110(x)\\ln(x), \\log_{10}(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">log<span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1609\" data-end=\"1671\">\n<p data-start=\"1611\" data-end=\"1671\"><strong data-start=\"1611\" data-end=\"1638\">Trigonometric functions<\/strong>: <span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(x),cos\u2061(x),tan\u2061(x)\\sin(x), \\cos(x), \\tan(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">tan<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1672\" data-end=\"1739\">\n<p data-start=\"1674\" data-end=\"1739\"><strong data-start=\"1674\" data-end=\"1709\">Inverse trigonometric functions<\/strong>: <span class=\"katex\"><span class=\"katex-mathml\">arcsin\u2061(x),arccos\u2061(x)\\arcsin(x), \\arccos(x)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">arcsin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">arccos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1741\" data-end=\"1744\" \/>\n<h2 data-start=\"1746\" data-end=\"1769\">\ud83e\udde0 <strong data-start=\"1752\" data-end=\"1769\">Summary Table<\/strong><\/h2>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1771\" data-end=\"2522\">\n<thead data-start=\"1771\" data-end=\"1896\">\n<tr data-start=\"1771\" data-end=\"1896\">\n<th data-start=\"1771\" data-end=\"1797\" data-col-size=\"sm\">Feature<\/th>\n<th data-start=\"1797\" data-end=\"1841\" data-col-size=\"sm\">Algebraic Equation<\/th>\n<th data-start=\"1841\" data-end=\"1896\" data-col-size=\"md\">Transcendental Equation<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"2022\" data-end=\"2522\">\n<tr data-start=\"2022\" data-end=\"2146\">\n<td data-start=\"2022\" data-end=\"2047\" data-col-size=\"sm\"><strong data-start=\"2024\" data-end=\"2036\">Involves<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"2047\" data-end=\"2091\">Polynomials only<\/td>\n<td data-col-size=\"md\" data-start=\"2091\" data-end=\"2146\">Transcendental functions (sin, log, exp, etc.)<\/td>\n<\/tr>\n<tr data-start=\"2147\" data-end=\"2271\">\n<td data-start=\"2147\" data-end=\"2172\" data-col-size=\"sm\"><strong data-start=\"2149\" data-end=\"2164\">Solvability<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"2172\" data-end=\"2216\">Often solved exactly<\/td>\n<td data-col-size=\"md\" data-start=\"2216\" data-end=\"2271\">Usually solved approximately (numerical methods)<\/td>\n<\/tr>\n<tr data-start=\"2272\" data-end=\"2397\">\n<td data-start=\"2272\" data-end=\"2297\" data-col-size=\"sm\"><strong data-start=\"2274\" data-end=\"2285\">Example<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"2297\" data-end=\"2342\"><span class=\"katex\"><span class=\"katex-mathml\">x2+2x\u22123=0x^2 + 2x &#8211; 3 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/td>\n<td data-col-size=\"md\" data-start=\"2342\" data-end=\"2397\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(x)\u2212x\/2=0\\sin(x) &#8211; x\/2 = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\/2<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr data-start=\"2398\" data-end=\"2522\">\n<td data-start=\"2398\" data-end=\"2423\" data-col-size=\"sm\"><strong data-start=\"2400\" data-end=\"2415\">Application<\/strong><\/td>\n<td data-start=\"2423\" data-end=\"2467\" data-col-size=\"sm\">Found in basic modeling<\/td>\n<td data-start=\"2467\" data-end=\"2522\" data-col-size=\"md\">Found in complex physical, engineering simulations<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr data-start=\"2524\" data-end=\"2527\" \/>\n<h2 data-start=\"2529\" data-end=\"2582\">\ud83d\udcbb <strong data-start=\"2535\" data-end=\"2582\">In Numerical Methods (Computer Science Use)<\/strong><\/h2>\n<ul data-start=\"2584\" data-end=\"2796\">\n<li data-start=\"2584\" data-end=\"2657\">\n<p data-start=\"2586\" data-end=\"2657\"><strong data-start=\"2586\" data-end=\"2609\">Algebraic Equations<\/strong>: Often solved with direct or iterative methods.<\/p>\n<\/li>\n<li data-start=\"2658\" data-end=\"2796\">\n<p data-start=\"2660\" data-end=\"2731\"><strong data-start=\"2660\" data-end=\"2688\">Transcendental Equations<\/strong>: Require <strong data-start=\"2698\" data-end=\"2725\">root-finding algorithms<\/strong> like:<\/p>\n<ul data-start=\"2734\" data-end=\"2796\">\n<li data-start=\"2734\" data-end=\"2757\">\n<p data-start=\"2736\" data-end=\"2757\">Newton-Raphson Method<\/p>\n<\/li>\n<li data-start=\"2760\" data-end=\"2778\">\n<p data-start=\"2762\" data-end=\"2778\">Bisection Method<\/p>\n<\/li>\n<li data-start=\"2781\" data-end=\"2796\">\n<p data-start=\"2783\" data-end=\"2796\">Secant Method<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p data-start=\"2798\" data-end=\"2880\">These are essential in simulations, control systems, machine learning models, etc.<\/p>\n<hr data-start=\"2882\" data-end=\"2885\" \/>\n<p data-start=\"2887\" data-end=\"2972\" data-is-last-node=\"\" data-is-only-node=\"\">Would you like visual examples or Python code for solving such equations numerically?<\/p>\n<h3 data-start=\"2887\" data-end=\"2972\"><a href=\"https:\/\/csw.uobaghdad.edu.iq\/wp-content\/uploads\/sites\/30\/uploads\/computer%20science\/Lectures\/2nd%20year\/NUM%20ANALYSIS.pdf\" target=\"_blank\" rel=\"noopener\">Computer Science\/Numerical Methods\/. Difference b\/w algebraic and transcendental equation transcendental functions<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/ijarsct.co.in\/Paper12754.pdf\" target=\"_blank\" rel=\"noopener\">Algebraic and Transcendental Equation and It&#8217;s Applications<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/epgp.inflibnet.ac.in\/epgpdata\/uploads\/epgp_content\/S000025MS\/P001476\/M016970\/ET\/1468564867EText(Ch-4,M-1.pdf\" target=\"_blank\" rel=\"noopener\">Numerical Analysis by Dr. Anita Pal Assistant Professor &#8230;<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/kahedu.edu.in\/naac\/C-3\/Additional%20documents\/E-content\/242.pdf\" target=\"_blank\" rel=\"noopener\">Semester\u2013V L T P C 15PHU505A NUMERICAL METHODS 5<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Computer Science\/Numerical Methods\/. Difference b\/w algebraic and transcendental equation transcendental functions [fvplayer id=&#8221;111&#8243;] Difference Between Algebraic and Transcendental Equations &amp; Functions 1. Algebraic Equation An algebraic equation is an equation that involves only polynomials with constants and variables, combined using addition, subtraction, multiplication, and division. General Form: anxn+an\u22121xn\u22121+\u22ef+a1x+a0=0a_n x^n + a_{n-1} x^{n-1} + \\dots + [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[110],"tags":[],"class_list":["post-2784","post","type-post","status-publish","format-standard","hentry","category-numerical-methods"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=2784"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2784\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}