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  • 1. Indian TEX Users Group : http://www.river-valley.com/tug Introduction Maths in text Fraction 11 A On-line Tutorial on LTEX Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page The Tutorial Team Indian TEX Users Group,  Buildings, Cotton Hills Trivandrum 695014,  2000 Prof. (Dr.) K. S. S. Nambooripad, Director, Center for Mathematical Sciences, Trivandrum, (Editor); Dr. E. Krishnan, Reader in Mathematics, University College, Trivandrum; Mohit Agarwal, Department of Aerospace Engineering, Indian Institute of Science, Bangalore; T. Rishi, Focal Image (India) Pvt. Ltd., Trivandrum; L. A. Ajith, Focal Image (India) Pvt. Ltd., Trivandrum; A. M. Shan, Focal Image (India) Pvt. Ltd., Trivandrum; C. V. Radhakrishnan, River Valley Technologies, Software Technology Park, Trivandrum constitute the Tutorial team A A This document is generated from LTEX sources compiled with pdfLTEX v. 14e in an INTEL Pentium III 700 MHz system running Linux kernel version 2.2.14-12. The packages used are hyperref.sty and pdfscreen.sty A c 2000, Indian TEX Users Group. This document may be distributed under the terms of the LTEX A Project Public License, as described in lppl.txt in the base LTEX distribution, either version 1.0 or, at your option, any later version Page 1 of 31 Go Back Full Screen Close Quit
  • 2. 11 Mathematics Introduction Maths in text Fraction Equation 11.1. Introduction Definitions for . . . AMS-LaTeX TEX is at its best while producing mathematical documents. If you want to test the power of TEX, do typeset some mathematics. In the foreword of the TEX book, Knuth writes: “TEX is a new typesetting system intended for the creation of beautiful books—and especially for books that contain a lot of mathematics”. Mathematical . . . Accents and For . . . Title Page A LTEX has a special mode for typesetting mathematics. Mathematical text within a paragraph (inline) is entered between ( and ), between $ and $ or between begin{math} and end{math}. Normally larger mathematical equations and formula are typesetted in separate lines, in display mode. To produce this, we enclose them between [ and ], between $$ and $$ or between begin{displaymath} and end{displaymath}. This produces formula, which are not numbered. If we want to produce equation number, we have to use equation environment. The spacing for both in-line and displayed mathematics is completely controlled by TEX. Page 2 of 31 Go Back Full Screen Close Quit
  • 3. 11.2. Maths in text input—file Using˜(5.64) and the fact that the $c_n=langlepsi_nvertPsirangle$ and $d_nˆ*=langle Xpsi_nrangle$, the scalar product $langle Xvert Psirangle$ can be expressed in the way as $langle XvertPsirangle= sum_nd_nˆ*c_n = mathbf{d}ˆdagger boldsymbol{cdot}mathbf{c}$ where (mathbf{c}) is a column vector with elements $c_n$ and row vector $mathbf{d}ˆdagger$ with elements $d_nˆ*$. The inverse $mathbf{A}ˆ{-1}$ of a matrix $mathbf{A}$ is such that $mathbf{AA}ˆ{-1}=mathbf{A}ˆ{-1} mathbf{A}= mathbf{I}$. output—dvi Using (5.64) and the fact that the cn = ψn |Ψ ∗ and dn = Xψn , the scalar product X|Ψ can be expressed in the way as ∗ X|Ψ = n dn cn = d† · c where c is a column vector with elements cn and row vector d† ∗ with elements dn . The inverse A−1 of a matrix A is such that AA−1 = A−1 A = I. Where I is the unit matrix, elements Imn = δmn . For a stationary state ΨE = ψE exp(−iEt/ ) and a time-independent operator A it is clear that the expectation value ΨE |A|ΨE = ψE |A|ψE does not depend on the time. Where $mathbf{I}$ is the unit matrix, elements $I_{mn}=delta_{mn}$. For a emph{stationary state} $Psi_E=psi_Eexp(-{rm i}Et/hbar)$ and a emph{time-independent} operator $A$ it is clear that the expectation value begin{math}langlePsi_Evert AvertPsi_Erangle=langlepsi_Evert Avertpsi_Erangleend{math} does not depend on the time. Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Page 3 of 31 Go Back Full Screen Close Quit
  • 4. 11.3. Fraction $$ frac{{rm d}varepsilon}{{rm d}varepsilon}qquad frac{frac{a}{x-y}+frac{b}{x+y}}{1+frac{a-b}{a+b}} $$ dε dε a x−y + 1+ b x+y a−b a+b Introduction Maths in text Fraction Equation Definitions for . . . 11.4. AMS-LaTeX Equation Mathematical . . . Accents and For . . . Don’t put blank lines between the dollar signs delimiting the mathematical text. TEX assumes that all the mathematical text being typeset is in one paragraph, and a blank line starts a new paragraph; consequently, this will generate an error message. 11.4.1. Title Page Equation with numbers begin{equation} varphi(x,z) = z - gamma_{10} x - sum_{m+nge2} gamma{mn} xˆm zˆn end{equation} Page 4 of 31 Go Back ϕ(x, z) = z − γ10 x − γmnx z m n m+n≥2 (1) Full Screen Close Quit
  • 5. 11.4.2. Equation without numbers begin{displaymath} left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right) =int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy end{displaymath} Introduction Maths in text OR Fraction Equation $$ Definitions for . . . left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right) =int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy $$ AMS-LaTeX Mathematical . . . Accents and For . . . Title Page ∞ e−x 2 −∞ ∞ ∞ = e−(x −∞ 2 +y2 ) dx dy −∞ [ left(int_{-infty}ˆ{infty} eˆ{-xˆ2}right) =int_{-infty}ˆ{infty}int_{-infty}ˆ{infty}eˆ{-(xˆ2+yˆ2)}dx,dy Page 5 of 31 ] ∞ −x2 e −∞ ∞ ∞ −∞ −∞ = Go Back −(x2 +y2 ) e dx dy Full Screen Close Quit
  • 6. 11.4.3. Subequations1 begin{subequations} begin{equation} langlePsi_1vertPsi_2rangleequivintPsi_1ˆ* (mathbf{r})Psi_2 (mathbf{r}){rm d}mathbf{r} end{equation} and begin{equation} langlePsi_1vertPsi_2rangleequivPsi_1ˆ*(mathbf{r}_1,ldots, mathbf{r}_N)Psi_2(mathbf{r}_1,ldots,mathbf{r}_N){rm d} mathbf{r}_1ldots{rm d}mathbf{r}_N. end{equation} end{subequations} Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Ψ1 |Ψ2 ≡ Ψ∗ (r)Ψ2 (r)dr 1 (2a) and Ψ1 |Ψ2 ≡ Ψ∗ (r1 , . . . , rN )Ψ2 (r1 , . . . , rN )dr1 . . . drN . 1 11.4.4. Framed displayed equation begin{equation} fbox{$displaystyleint_0ˆinfty f(x),{rm d}x approxsum_{i=1}ˆnw_i{rm e}ˆ{x_i}f(x_i)$} end{equation} 1 (2b) Page 6 of 31 Go Back Full Screen subeqn.sty package should be loaded. Close Quit
  • 7. n ∞ wi e xi f (xi ) f (x) dx ≈ 0 11.4.5. (3) i=1 Introduction Multiline equations – Eqnarray Maths in text Fraction begin{eqnarray} barvarepsilon &=& frac{int_0ˆinftyvarepsilon exp(-betavarepsilon),{rm d}varepsilon}{int_0ˆinfty exp(-betavarepsilon),{rm d}varepsilon}nonumber &=& -frac{{rm d}}{{rm d}beta}logBiggl[int_0ˆinftyexp (-betavarepsilon),{rm d}varepsilonBiggr]=frac1beta=kT. end{eqnarray} Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page ¯ ε= ∞ ε exp(−βε) dε 0 ∞ exp(−βε) dε 0 ∞ = − d log dβ exp(−βε) dε = 0 1 = kT. β (4) nonumber is used for suppressing number. 11.4.6. Page 7 of 31 Go Back Matrix $$ matrix{1 & 2 & 3cr 2 & 3 & 4cr 3 & 4 & 5}qquad left(matrix{1 & cdots & 3cr 2 & vdots & 4cr 3 & ddots & 5}right) $$ 1 2 3 2 3 4 3 4 5  1      2        3 ··· . . .  3       4     ..  . 5 Full Screen Close Quit
  • 8. 11.4.7. Array $$ begin{array}{lcll} Psi(x,t) &=& A({rm e}ˆ{{rm i}kx}-{rm e}ˆ{-{rm i}kx}) {rm e}ˆ{-{rm i}omega t}& &=& Dsin kx{rm e}ˆ{-{rm i}omega t}, & D=2{rm i}A end{array} Introduction Maths in text Fraction $$ Equation Definitions for . . . AMS-LaTeX Ψ(x, t) = A(eikx − e−ikx )e−iωt = D sin kxe−iωt , D = 2iA Mathematical . . . Accents and For . . . Title Page 11.4.8. Cases $$ psi(x)=cases{A{rm e}ˆ{{rm i}kx}+B{rm e}ˆ{{-rm i}kx}, & for $x=0$cr D{rm e}ˆ-{kappa x}, & for $x=0$.} $$ Page 8 of 31  Aeikx + Be−ikx ,   ψ(x) =  −κx De ,  for x = 0 for x = 0. Go Back Full Screen Close Quit
  • 9. 11.4.9. Stackrel $$ astackrel{def}{=} alpha + betaquad stackrel{thermo}{longrightarrow} de f a = α+β thermo −→ $$ Introduction Maths in text Fraction 11.4.10. Equation Atop Definitions for . . . AMS-LaTeX $$ sum_{k=1 atop k=0} qquad sum_{123 atop{234 atop {890 atop 456}}} $$ Mathematical . . . k=1 k=0 123 234 890 456 Accents and For . . . Title Page 11.4.11. Square root $$ sqrt[n]{frac{xˆn-yˆn}{1+uˆ{2n}}} n $$ x n − yn 1 + u2n Page 9 of 31 11.4.12. Choose $$ {123 choose 456}qquad {xˆn-yˆn choose 1+uˆ{2n}} $$ Go Back 123 456 xn − yn 1 + u2n Full Screen Close Quit
  • 10. 11.5. Definitions for Theorems We should define newtheorem{thm}{Theorem} etc in preamble. Introduction newtheorem{thm}{Theorem} begin{thm} This is body matter for testing this environment. end{thm} Maths in text Theorem 1 This is body matter for testing this environment. Fraction Equation Definitions for . . . AMS-LaTeX newtheorem{rmk}{Remark}[section] begin{rmk} This is body matter for testing this environment. end{rmk} Remark 11.5.1 This is body matter for testing this environment. Mathematical . . . Accents and For . . . Title Page newtheorem{col}{Corollary} begin{col}[Richard, 1987] This is body matter for testing this environment. end{col} Corollary 1 (Richard, 1987) This is body matter for testing this environment. newtheorem{lem}{Lemma}[thm] begin{lem} This is body matter for testing this environment. end{lem} Lemma 1.1 This is body matter for testing this environment. newtheorem{exa}{Example}[lem] begin{exa} This is body matter for testing this environment. end{exa} Page 10 of 31 Go Back Full Screen Example 1.1.1 This is body matter for testing this environment. Close Quit
  • 11. 11.6. A AMS-LTEX2 Following are some of the component parts of the amsmath package, available individually and can be used separately in a usepackage command: Introduction amsbsy defines the amsmath boldsymbol and (poor man’s bold) pmb commands. amscd defines some command for easing the generation of commutative diagrams. defines the frak and Bbb commands and set up the fonts msam (extra math amsfonts symbols A), msbm (extra math symbols B, and blackboard bold), eufm (Euler Fraktur), extra sizes of cmmib (bold math italic and bold lowercase Greek), and cmbsy (bold math symbols and bold script), for use in mathematics. amssymb lection. amstext 11.6.1. defines the names of all the math symbols available with the AMS fonts col- Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page defines the amsmath text command. Align environment Page 11 of 31 Align environment is used for two or more equations when vertical alignment is desired (usually binary relations such as equal signs are aligned). Go Back 2 CTAN: /tex-archive/macros/latex/packages/amslatex Full Screen Close Quit
  • 12. begin{align} F_{rm fer}(k) =& -frac{16 x_0 ˆ3 t}{3pi }bigg( sum_{l=1}ˆinfty -frac{nuˆ5}{tˆ4 (x_0ˆ2-l-frac{1}{4})ˆ3}bigg[S bigg(frac{sqrt{x_0ˆ2+lˆ2}}{t};2 bigg) + 2Sbigg(frac{nu}{t};2 bigg)bigg] bigg) F_{rm red}(t) =& -frac{16 x_0 ˆ3 t}{3pi }sum_{l=1}ˆinfty bigg{ frac{1}{2nu (x_0ˆ2+lˆ2)ˆ2} nonumber & -frac{nuˆ5}{tˆ4 (x_0ˆ2-l-frac{1}{4})ˆ3}bigg[S bigg( frac{sqrt{x_0ˆ2+lˆ2}}{t};2 bigg) +2Sbigg(frac{nu}{t};2 bigg)bigg] nonumber & +V(x_e ,x_{alpha}) -g delta (x_e - x_{alpha}) bigg}. end{align} Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page 3 16x0 t Ffer (k) = − 3π Fred (t) = − 3 16x0 t 3π ∞ − l=1 ∞ l=1 ν S 2 t4 (x0 − l − 1 )3 4 5 t ; 2 + 2S ν ;2 t (5) 1 + l2 )2 2 2ν(x0 ν5 S − 2 t4 (x0 − l − 1 )3 4 2 x0 + l2 t + V(xe , xα ) − gδ(xe − xα ) . 11.6.2. 2 x0 + l2 ; 2 + 2S ν ;2 t Page 12 of 31 (6) Gather environment Gather environment is used for two or more equations, but when there is no alignment desired among them each one is centered separately between the left and right margins. Go Back Full Screen Close Quit
  • 13. begin{gather} frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d} varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d}varepsilon} frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}varepsilon} {int_0ˆinftyexp(-betavarepsilon)} int_0ˆinftyexp(-betavarepsilon),{rm d}exp(-betavarepsilon)nonumber frac{int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d}varepsilon} {int_0ˆinftyexp(-betavarepsilon)} int_0ˆinftyexp(-betavarepsilon),{rm d}exp(-betavarepsilon) end{gather} Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . ∞ ∞ ε exp(−βε) dε 0 ε exp(−βε) dε 0 ∞ ∞ exp(−βε) dε exp(−βε) 0 0 ∞ exp(−βε) d exp(−βε) 0 ∞ 0 ∞ ε exp(−βε) dε ∞ 0 exp(−βε) exp(−βε) d exp(−βε) (7) (8) (9) (10) 0 11.6.3. Title Page Alignat environment The align environment takes up the whole width of a display. If you want to have several “align”-type structures side by side, you can use an alignat environment. It has one required argument, for specifying the number of “align” structures. For an argument of n, the number of ampersand characters per line is 2n − 1 (one ampersand for alignment within each align structure, and ampersands to separate the align structures from one another). Page 13 of 31 Go Back Full Screen Close Quit
  • 14. begin{alignat}{2} L_1 & = R_1 &qquad L_2 & = R_2 L_3 & = R_3 &qquad L_4 & = R_4 end{alignat} Introduction Maths in text Fraction L1 = R 1 L3 = R 3 L2 = R2 L4 = R4 (11) (12) Equation Definitions for . . . AMS-LaTeX 11.6.4. Alignment Environments as Parts of Displays There are some other equation alignment environments that do not constitute an entire display. They are self-contained units that can be used inside other formulae, or set side by side. The environment names are: aligned, gathered and alignedat. These environments take an optional argument to specify their vertical positioning with respect to the material on either side. The default alignment is centered ([c]), and its effect is seen in the following example. begin{equation*} begin{aligned} xˆ2 + yˆ2 & = 1 x & = sqrt{1-yˆ2} end{aligned} qquad begin{gathered} (a+b)ˆ2 = aˆ2 + 2ab + bˆ2 (a+b) cdot (a-b) = aˆ2 - bˆ2 end{gathered} end{equation*} Mathematical . . . Accents and For . . . Title Page Page 14 of 31 Go Back Full Screen Close Quit
  • 15. x2 + y2 = 1 x= 1 − y2 (a + b)2 = a2 + 2ab + b2 (a + b) · (a − b) = a2 − b2 The same mathematics can now be typeset using vertical alignments for the environments. Introduction Maths in text begin{equation*} begin{aligned}[b] xˆ2 + yˆ2 & = 1 x & = sqrt{1-yˆ2} end{aligned} qquad begin{gathered}[t] (a+b)ˆ2 = aˆ2 + 2ab + bˆ2 (a+b) cdot (a-b) = aˆ2 - bˆ2 end{gathered} end{equation*} Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page x2 + y2 = 1 x= 11.6.5. 1 − y2 (a + b)2 = a2 + 2ab + b2 (a + b) · (a − b) = a2 − b2 Multline environment The multline environment is a variation of the equation environment used for equations that do not fit on a single line. The first line of a multline will be at the left margin and the last line at the right margin except for an indentation on both sides whose amount is equal to multline-gap. Page 15 of 31 Go Back Full Screen Close Quit
  • 16. begin{multline} {int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d} varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d} varepsilon}{int_0ˆinftyvarepsilonexp(-betavarepsilon), {rm d}varepsilon}{int_0ˆinftyexp(-betavarepsilon)} {int_0ˆinftyvarepsilonexp(-betavarepsilon),{rm d} varepsilon}{int_0ˆinftyexp(-betavarepsilon),{rm d} varepsilon}{int_0ˆinftyvarepsilon} {int_0ˆinftyexp(-betavarepsilon)} end{multline} Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . ∞ ∞ ε exp(−βε) dε 0 ∞ ε exp(−βε) dε exp(−βε) dε 0 ∞ 0 ∞ ε exp(−βε) dε 0 11.6.6. Accents and For . . . ∞ exp(−βε) 0 ∞ 0 ∞ ε exp(−βε) dε 0 Title Page exp(−βε) (13) 0 Split environment The split environment is for single equations that are too long to fit on a single line and hence must be split into multiple lines. Unlike multline, however, the split environment provides for alignment among the split lines. Page 16 of 31 Go Back begin{equation} begin{split} (a+b)ˆ4 & = (a+b)ˆ2(a+b)ˆ2 & = (aˆ2+2ab+bˆ2)(aˆ2+2ab+bˆ2) & = aˆ4+4aˆ3b+6aˆ2bˆ2+4abˆ3+bˆ4 end{split} end{equation} Full Screen Close Quit
  • 17. (a + b)4 = (a + b)2 (a + b)2 = (a2 + 2ab + b2 )(a2 + 2ab + b2 ) = a4 + 4a3 b + 6a2 b2 + 4ab3 + b4 (14) Introduction 11.6.7. Maths in text Cases Fraction begin{equation} P_{r-j}= begin{cases} 0 & text{if $r-j$ is odd}, r!,(-1)ˆ{(r-j)/2} & text{if $r-j$ is even}. end{cases} end{equation} Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Pr− j 11.6.8.  0   = r! (−1)(r− j)/2  if r − j is odd, if r − j is even. (15) Matrix begin{gather*} begin{matrix} begin{pmatrix} begin{bmatrix} begin{vmatrix} begin{Vmatrix} end{gather*} Page 17 of 31 0 & 1 1 & 0 0 & -i i & 0 a & b c & d 0 & 1 -1 & 0 f & g e & v end{matrix}qquad end{pmatrix}qquad end{bmatrix}qquad end{vmatrix}qquad end{Vmatrix} Go Back Full Screen Close Quit
  • 18. 0 1 1 0 11.6.9. 0 −i i 0 a b c d 0 1 −1 0 f g e v Introduction substack environment Maths in text begin{equation*} sum_{substack{0leq ileq m 0jn}} end{equation*} Fraction Equation 0≤i≤m 0> j>n Definitions for . . . AMS-LaTeX begin{equation*} sumˆ{substack{0leq ileq m 0jn}} end{equation*} Mathematical . . . 0≤i≤m 0> j>n Accents and For . . . Title Page 11.6.10. Commutative Diagram3 begin{equation*} begin{CD} S_Lambdaˆ{mathcal{W}}otimes T @j> T @VVV @VV{{rm End}P}V (Sotimes T)/I @= (Zotimes T)/J end{CD} end{equation*} 3 Page 18 of 31 Go Back amscd.sty package should be loaded. Full Screen Close Quit
  • 19. j W SΛ ⊗ T −−− −−→      (S ⊗ T )/I T     EndP (Z ⊗ T )/J Introduction Maths in text begin{equation*} begin{CD} S_Lambdaˆ{mathcal{W}}otimes T @j> @V{{Out}p}VV & (Sotimes T)/I @= end{CD} end{equation*} Fraction T_{XF} @xyz> T & @AA{{rm End}P}A X_{mathcal{F}} @fg> (Zotimes T)/J Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . j xyz W S Λ ⊗ T − − − T XF − − − −−→ −−→      Outp (S ⊗ T )/I 11.6.11. Equation Title Page T  EndP    fg XF − − − (Z ⊗ T )/J −−→ Binom Page 19 of 31 begin{equation*} binom{x}{y} end{equation*} x y Go Back Full Screen 11.6.12. AMS symbols Close iint iiint iiiint Quit
  • 20. 11.7. Mathematical Symbols 11.7.1. Lowercase Greek letters α β γ δ ε ζ η 11.7.2. θ ϑ ι κ λ µ ν ξ theta vartheta iota kappa lambda mu nu xi o π ρ σ ς o pi varpi rho varrho sigma varsigma τ υ φ ϕ χ ψ ω tau upsilon phi varphi chi psi omega Gamma Delta Theta Λ Ξ Π Lambda Xi Pi hat{a} check{a} a ´ a ` Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Title Page Σ Υ Φ Sigma Upsilon Phi Ψ Ω Psi Omega Math mode accents a ˆ a ˇ Introduction Accents and For . . . Uppercase Greek letters Γ ∆ Θ 11.7.3. alpha beta gamma delta epsilon varepsilon zeta eta acute{a} grave{a} Page 20 of 31 a ¯ a bar{a} vec{a} a ˙ a ¨ dot{a} ddot{a} a ˘ a ˜ breve{a} tilde{a} Go Back Full Screen Close Quit
  • 21. 11.7.4. Binary Operation Symbols ± × ÷ ∗ ◦ • · a 11.7.5. pm mp times div ast star circ bullet cdot ∩ ∪ ∨ ∧ cap cup uplus sqcap sqcup vee wedge setminus wr ⊕ diamond bigtriangleup bigtriangledown triangleleft triangleright lhda rhda unlhda unrhda ⊗ † ‡ oplus ominus otimes oslash odot bigcirc dagger ddagger amalg Not predefined in NFSS. Use the latexsym or amssymb package. Relation symbols ≤ ⊂ ⊆ ∈ leq prec preceq ll subset subseteq sqsubset sqsubseteq in vdash Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page ≥ ⊃ ⊇ geq succ succeq gg supset supseteq sqsupset sqsupseteq ni dashv ≡ ∼ ≈ equiv sim simeq asymp approx cong neq doteq notin |= ⊥ | ∝ models perp mid parallel bowtie Join smile frown propto Page 21 of 31 Go Back Full Screen Close Quit
  • 22. 11.7.6. Arrow symbols ← ⇐ → ⇒ ↔ ⇔ |→ ← 11.7.7. leftarrow Leftarrow rightarrow Rightarrow leftrightarrow Leftrightarrow mapsto hookleftarrow leftharpoonup leftharpoondown rightleftharpoons ←− ⇐= −→ =⇒ ←→ ⇐⇒ −→ → longleftarrow Longleftarrow longrightarrow Longrightarrow longleftrightarrow Longleftrightarrow longmapsto hookrightarrow rightharpoonup rightharpoondown leadsto ↑ ⇑ ↓ ⇓ uparrow Uparrow downarrow Downarrow updownarrow Updownarrow nearrow searrow swarrow nwarrow ldots prime exists Diamonda ∃ ⊥ ··· ∀ top bot mho cdots forall ı flat clubsuit Re . . . ∞ √  vdots infty surd jmath natural Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Title Page imath ♣ Maths in text Accents and For . . . Miscellaneous symbols ... Introduction Im .. . ♥ ∠ ℵ aleph ddots hbar Boxa ∅ emptyset triangle neq ell sharp heartsuit angle nabla ℘ ♠ ∂ wp spadesuit partial ♦ diamondsuit Page 22 of 31 Go Back Full Screen a Not predefined in NFSS. Use the latexsym or amssymb package. Close Quit
  • 23. 11.7.8. Variable-sized symbols sum bigcap bigodot prod bigcup bigotimes coprod bigsqcup bigoplus int bigvee biguplus oint bigwedge Introduction Maths in text 11.7.9. Delimiters Fraction Equation ↑ { | ⇑ uparrow { lfloor langle } | ↓ Uparrow } rfloor rangle | downarrow updownarrow / ⇓ Definitions for . . . lceil / Downarrow Updownarrow rceil backslash AMS-LaTeX Mathematical . . . Accents and For . . . Title Page 11.7.10. A LTEX math constructs abc ←− − abc abc widetilde{abc} overleftarrow{abc} overline{abc} abc −→ − abc abc widehat{abc} overrightarrow{abc} underline{abc} Page 23 of 31 abc √ abc f overbrace{abc} sqrt{abc} f’ abc √ n abc abc xyz underbrace{abc} sqrt[n]{abc} frac{abc}{xyz} Go Back Full Screen 11.7.11. AMS Greek and Hebrew (available with amssymb package) Close digamma κ varkappa beth daleth gimel Quit
  • 24. 11.7.12. AMS delimiters (available with amssymb package) ulcorner 11.7.13. urcorner llcorner lrcorner AMS miscellaneous (available with amssymb package) ∅ hbar triangledown circledS nexists Game varnothing blacksquare sphericalangle diagup ∠ k hslash square angle mho Bbbk blacktriangle blacklozenge complement diagdown ♦ ð vartriangle lozenge measuredangle Finv backprime blacktrinagledown bigstar eth Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page a Not defined in old releases of the amssymb package; define with the DeclareMathSymbol command. 11.7.14. AMS negated arrows (available with amssymb package) Page 24 of 31 nleftarrow nRightarrow nrightarrow nleftrightarrow nLeftarrow nLeftrightarrow Go Back Full Screen Close Quit
  • 25. 11.7.15. AMS binary relations (available with amssymb package) ≈ ∝ leqq lesssim lessdot lesseqgtr risingdotseq backsimeq sqsubset precsim trianglelefteq smallsmile Bumpeq eqslantgtr gtrdot gtreqless circeq thickapprox sqsupset succsim trianglerighteq shortparallel varpropto backepsilon leqslant lessapprox lll lesseqqgtr fallingdotseq subseteqq preccurlyeq precapprox vDash smallfrown geqq gtrsim ggg gtreqqless triangleq supseteqq succcurlyeq succapprox Vdash between blacktriangleleft blacktriangleright ∼ ∴ eqslantless approxeq lessgtr doteqdot backsim Subset curlyeqprec vartriangleleft Vvdash bumpeq geqslant gtrapprox gtrless eqcirc thicksim Supset curlyeqsucc vartriangleright shortmid pitchfork therefore because Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Page 25 of 31 Go Back Full Screen Close Quit
  • 26. 11.7.16. AMS binary operators (available with amssymb package) dotplus Cup doublebarwedge boxdot ltimes rightthreetimes circleddash centerdot smallsetminus barwedge boxminus boxplus rtimes curlywedge circledast intercal Cap veebar boxtimes divideontimes leftthreetimes curlyvee circledcirc Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX 11.7.17. AMS negated binary relations (available with amssymb package) nless nleqq lvertneqq nprec precnapprox nmid ntriangleleft subsetneq varsubsetneqq ngeqslant gneqq gnapprox succnsim nshortparallel nVDash nsupseteq varsupsetneq nleq lneq lnsim npreceq nsim nvdash ntrianglelefteq varsubsetneq ngtr ngeqq gvertneqq nsucc succnapprox nparallel ntriangleright nsupseteqq supsetneqq nleqslant lneqq lnapprox precnsim nshortmid nvDash nsubseteq subsetneqq ngeq gneq gnsim nsucceq ncong nvDash ntrianglerighteq supsetneq varsupsetneqq Mathematical . . . Accents and For . . . Title Page Page 26 of 31 Go Back Full Screen Close Quit
  • 27. 11.7.18. AMS arrows (available with amssymb package) dashrightarrow leftrightarrows leftarrowtail curvearrowleft upuparrows multimap rightleftarrows twoheadrightarrow rightleftharpoons Rsh downharpoonright 11.7.19. dashleftarrow Lleftarrow looparrowleft circlearrowleft upharpoonleft leftrightsquigarrow rightrightarrows rightarrowtail curvearrowright downdownarrows rightsquigarrow leftleftarrows twoheadleftarrow leftrightharpoons Lsh downharpoonleft rightrightarrows rightleftarrows looparrowright circlearrowright upharpoonright arccos cos csc exp ker limsup min sinh Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Log-like symbols arccos cos csc exp ker lim sup min sinh Introduction arcsin cosh deg gcd lg ln Pr sup arcsin cosh deg gcd lg ln Pr sup arctan cot det hom lim log sec tan arctan cot det hom lim log sec tan arg coth dim inf lim inf max sin tanh arg coth dim inf liminf max sin tanh Page 27 of 31 Go Back Full Screen Close Quit
  • 28. 11.7.20. Double accents in math (available with amssymb package) ´ ´ A ˘ ˘ A ¨ A ` ` A ˜ A Bar{Bar{A}} Grave{Grave{A}} ¯ A ˇ ˇ A ˙ A ˆ ˆ A Tilde{Tilde{A}} A Vec{Vec{A}} Acute{Acute{A}} Breve{Breve{A}} Ddot{Ddot{A}} Check{Check{A}} Dot{Dot{A}} Introduction Hat{Hat{A}} Maths in text Fraction Equation Definitions for . . . 11.7.21. Other Styles AMS-LaTeX Mathematical . . . 11.7.21.1. Accents and For . . . Caligraphic letters ABCDEF GH IJ K LMN OPQRST UVWXYZ Title Page use mathcal{} 11.7.21.2. Mathbb letters ABCDEFGHIJKLMNOPQRSTUVWXYZ Page 28 of 31 use mathbb{} Go Back 11.7.21.3. Mathfrak letters Full Screen ABCDEFGHIJKLMNOPQRSTUVWXYZ Close use mathfrak{} with amssymb package Quit
  • 29. 11.7.21.4. Math bold italic letters ABCDEFGHIJKLMNOPQRSTUVWXYZ use mathbi{} Introduction Maths in text 11.7.21.5. Math Sans serif letters Fraction Equation ABCDEFGHIJKLMNOPQRSTUVWXYZ Definitions for . . . AMS-LaTeX use mathsf{} Mathematical . . . Accents and For . . . 11.7.21.6. Math bold letters Title Page ABCDEFGHIJKLMNOPQRSTUVWXYZ use mathbf{} 11.7.22. Accents–Symbols ´ o ` o ˙ o oo o ¯ ß ø Ø s . ’{o} ‘{o} .{o} t{oo} b{o} ¨ o ˜ o ˘ o o ¸ Å "{o} ˜{o} u{o} c{o} AA ˆ o ¯ o ˝ o o . å ˆ{o} ={o} H{o} d{o} aa ss o O d s ı s ¶ ˚ s i t s P r s  ˇ s § ˝ s j v s S H s Page 29 of 31 Go Back Full Screen Close Quit
  • 30. 11.8. 11.8.1. Accents and Foreign Letters Printing command characters Introduction The characters # $ ˜ ˆ % { } are interpreted as commands. If they are to be printed as text, the character must precede them: $ = $ & = & % = % # = # = _ { = { } = } Maths in text Fraction Equation Definitions for . . . AMS-LaTeX 11.8.2. Mathematical . . . The special characters Accents and For . . . These special characters do not exist on the computer keyboard. They can however be generated by special commands as follows: §= S 11.8.3. †= dag ‡= ddag ¶= P c = copyright Title Page £= pounds Foreign letters Special letters that exist in European languages other than English can also be generated with TEX. These are: Page 30 of 31 Go Back œ= oe ø= o Œ= OE Ø= O æ= ae ł= l Æ= AE Ł= L å= aa ß= ss Å= AA SS= SS ¡ = !‘ ¿ = ?‘ Full Screen Close Quit
  • 31. 11.8.4. Accents ` o = ‘o ¯ o = =o oo = t{oo} ´ o = ’o ˙ o = .o o = c o ¸ ˆ o = ˆo ˘ o = u o o = d o . ¨ o = "o ˇ o = v o o = b o ¯ ˜ o = ˜o ˝ o = H o ˚ o = r o A The last command, r, is new to LTEX 2ε . The o above is given merely as an example: any letter may be used. With i and j it should be pointed out that the dot must first be removed. This is carried out by prefixing these letters with . The command i yield ı. Introduction Maths in text Fraction Equation Definitions for . . . AMS-LaTeX Mathematical . . . Accents and For . . . Title Page Page 31 of 31 Go Back Full Screen Close Quit