Introduction to L T EX (Part 3) A http://www.win.tue.nl/ ∼ jknopper/latex/ October 2012 Jan Willem Knopper (jknopper@win.tue.nl) Where innovation starts
Contents 2/43 9 Mathematical formulas 3 10 The amsmath package 30 11 Define your own commands 34 12 Theorem, proposition, lemma 41 / department of mathematics and computer science October 2012
9 Mathematical formulas 3/43 In a text: For a rectangular triangle, we know from Pythagoras’ theorem that a 2 + b 2 = c 2 where a and b are the length of two sides adjoining the straight angle while c is the length of the side opposite the straight angle. Compare this with: For a rectangular triangle, we know from Pythagoras’ theorem that a 2 +b 2 =c 2 where a and b are the length of two sides adjoin- ing the straight angle while c is the length of the side opposite the straight angle. / department of mathematics and computer science October 2012
4/43 Mathematical formulas are created as follows: We get: $a^2+b^2=c^2$, $a^{13}$, $b_3$ or $b_13$ results in We get: a 2 + b 2 = c 2 , a 13 , b 3 or b 1 3 / department of mathematics and computer science October 2012
5/43 Mathematical formulas are created as follows: We get \[ a^2+b^2=c^2, a^{13}, b_3 \ mbox { or } b_13 \] results in We get a 2 + b 2 = c 2 , a 13 , b 3 or b 1 3 / department of mathematics and computer science October 2012
6/43 We can also number our equations: We get \ begin {equation} \ label {one} a^2+b^2=c^2, a^{13}, b_3 \ mbox { or } b_13 \ end {equation} results in We get a 2 + b 2 = c 2 , a 13 , b 3 or b 1 3 (1) / department of mathematics and computer science October 2012
7/43 We can also have multiple equations: \ begin {eqnarray} x & = & r\ sin \ varphi \ label {11} \\ y & = & r\ cos \ varphi \ nonumber \\ z & = & z \ label {33} \ end {eqnarray} (2) x = r sin ϕ y = r cos ϕ (3) z = z / department of mathematics and computer science October 2012
8/43 or without numbers: \ begin {eqnarray*} x & = & r\ sin \ varphi \\[-0.2cm] y & = & r\ cos \ varphi \\ z & = & z \ end {eqnarray*} x = r sin ϕ y = r cos ϕ z = z / department of mathematics and computer science October 2012
9/43 We have the following \ documentclass options: fleqn Displayed formulas will be flushed left leqno Equation number on the left \ documentclass [11pt,a4paper,fleqn]{article} / department of mathematics and computer science October 2012
10/43 Obviously we can do more: $\ frac {n}{n+p^2} \ int _0^\ infty \ sqrt [n]{x^n-\ sin y} \ textrm {d}x$ √ x n − sin y d x � ∞ n n n + p 2 0 / department of mathematics and computer science October 2012
11/43 On the other hand: \[ \ frac {n}{n+p^2} \ int _0^\ infty \ sqrt [n]{x^n-\ sin y}\, \ textrm {d}x \] � ∞ n x n − sin y d x � n n + p 2 0 / department of mathematics and computer science October 2012
12/43 and finally: $\ displaystyle \ frac {n}{n+p^2} \ int _0^\ infty \ sqrt [n]{x^n-\ sin y}\; \ textrm {d}x$ � ∞ n � x n − sin y d x n n + p 2 0 / department of mathematics and computer science October 2012
Dots 13/43 $x_1,...,x_n$ or $x_1+...+x_n$ versus $x_1, \ ldots , x_n$ or $x_1+ \ cdots + x_n$ x 1 , ..., x n or x 1 + ... + x n versus x 1 , . . . , x n or x 1 + · · · + x n / department of mathematics and computer science October 2012
Functions 14/43 $\ sin x,\; sin x, \; \ mbox {sin} x$ sin x , sinx , sin x / department of mathematics and computer science October 2012
Symbols 15/43 a ˆ ´ a ¯ a a ˙ a ˘ \hat{a} \acute{a} \bar{a} \dot{a} \breve{a} a ˇ \check{a} ` a \grave{a} � a \vec{a} a ¨ \ddot{a} a ˜ \tilde{a} Table 8.1: Math mode accents (available in L TEX) A α β γ δ ǫ \alpha \beta \gamma \delta \epsilon ε ζ η θ ϑ \varepsilon \zeta \eta \theta \vartheta ι \iota κ \kappa λ \lambda µ \mu ν \nu ξ o π ̟ ρ \xi o \pi \varpi \rho ̺ σ ς τ υ \varrho \sigma \varsigma \tau \upsilon φ \phi ϕ \varphi χ \chi ψ \psi ω \omega Γ ∆ Θ Λ Ξ \Gamma \Delta \Theta \Lambda \Xi Π \Pi Σ \Sigma Υ \Upsilon Φ \Phi Ψ \Psi Ω \Omega Table 8.2: Greek letters (available in L TEX) A / department of mathematics and computer science October 2012
Symbols 16/43 ± ∩ ⋄ ⊕ \pm \cap \diamond \oplus ∓ ∪ △ ⊖ \mp \cup \bigtriangleup \ominus × ⊎ ▽ ⊗ \times \uplus \bigtriangledown \otimes ÷ ⊓ ⊳ ⊘ \div \sqcap \triangleleft \oslash ∗ ⊔ ⊙ \ast \sqcup ⊲ \triangleright \odot ⋆ ∨ � \star \vee ✁ \lhd a \bigcirc ◦ ∧ † \circ \wedge ✄ \rhd a \dagger • \bullet \ \setminus \unlhd a ‡ \ddagger ✂ · ≀ ∐ \cdot \wr ☎ \unrhd a \amalg a Not predefined in NFSS . Use the latexsym or amssymb package. Table 8.3: Binary operation symbols (available in L TEX) A ≤ \leq , \le ≥ \geq , \ge ≡ | = ≺ \equiv \models \prec ≻ ∼ ⊥ � � \succ \sim \perp \preceq \succeq ≃ | ≪ ≫ ≍ \simeq \mid \ll \gg \asymp � ⊂ ⊃ ≈ ⊲ ⊳ \parallel \subset \supset \approx \bowtie ∼ ⊆ \subseteq ⊇ \supseteq = \cong \Join \sqsubset ✶ ❁ � = ⌣ ⊑ ⊒ ❂ \sqsupset \neq \smile \sqsubseteq \sqsupseteq . ∈ ∋ ∝ = \doteq ⌢ \frown \in \ni \propto = ⊢ ⊣ < > = \vdash \dashv < > Table 8.4: Relation symbols (available in L TEX) A / department of mathematics and computer science October 2012
Symbols 17/43 ← ← − ↑ \leftarrow \longleftarrow \uparrow ⇐ ⇐ = ⇑ \Leftarrow \Longleftarrow \Uparrow → − → ↓ \rightarrow \longrightarrow \downarrow ⇒ ⇒ ⇓ \Rightarrow = \Longrightarrow \Downarrow ↔ \leftrightarrow ← → \longleftrightarrow � \updownarrow ⇔ ⇐ ⇒ � \Leftrightarrow \Longleftrightarrow \Updownarrow �→ �− → ր \mapsto \longmapsto \nearrow ← ֓ ֒ → ց \hookleftarrow \hookrightarrow \searrow ւ ↼ \leftharpoonup ⇀ \rightharpoonup \swarrow ↽ \leftharpoondown ⇁ \rightharpoondown տ \nwarrow Table 8.5: Arrow symbols (available in L TEX) A . ... . ℵ . . . \ldots · · · \cdots . \vdots \ddots \aleph � ′ ∀ ∞ ∅ \prime \forall \infty \hbar \emptyset √ ∃ ∇ △ \exists \nabla \surd ✷ \Box a \triangle ı ℓ ¬ ✸ \Diamond a \imath \jmath \ell \neg ⊤ \top ♭ \flat ♮ \natural ♯ \sharp ℘ \wp ⊥ \bot ♣ \clubsuit ♦ \diamondsuit ♥ \heartsuit ♠ \spadesuit ∠ ℜ ℑ ∂ ✵ \mho a \Re \Im \angle \partial a Not predefined in NFSS . Use the latexsym or amssymb package. Table 8.6: Miscellaneous symbols (available in L TEX) A / department of mathematics and computer science October 2012
Symbols 18/43 � � � � � \sum \prod \coprod \int \oint � \bigcap � \bigcup � \bigsqcup � \bigvee � \bigwedge � � � � \bigodot \bigotimes \bigoplus \biguplus Table 8.7: Variable-sized symbols (available in L TEX) A \arccos \cos \csc \exp \ker \limsup \min \sinh \arcsin \cosh \deg \gcd \lg \ln \Pr \sup \arctan \cot \det \hom \lim \log \sec \tan \arg \coth \dim \inf \liminf \max \sin \tanh Table 8.8: Log-like symbols (available in L A TEX) ↑ ⇑ ↓ ⇓ \uparrow \Uparrow \downarrow \Downarrow { } � � \{ \} \updownarrow \Updownarrow ⌊ ⌋ ⌈ ⌉ \lfloor \rfloor \lceil \rceil � � / \ \langle \rangle / \backslash | � | \| Table 8.9: Delimiters (available in L TEX) A / department of mathematics and computer science October 2012
Symbols 19/43 Several packages exist that extend the number of available symbols: \ usepackage {amssymb} / department of mathematics and computer science October 2012
Symbols 20/43 ≦ � � \leqq \leqslant \eqslantless � � ≅ \lesssim \lessapprox \approxeq ≪ ≶ ⋖ \lessdot \lll , \llless \lessgtr ⋚ � � \lesseqgtr \lesseqqgtr \doteqdot , \Doteq � � ∽ \risingdotseq \fallingdotseq \backsim ⋍ � ⋐ \backsimeq \subseteqq \Subset � � ❁ \sqsubset \preccurlyeq \curlyeqprec � ⊳ � \precsim \precapprox \vartriangleleft � � � \trianglelefteq \vDash \Vvdash � � ≏ \smallsmile \smallfrown \bumpeq ≎ ≧ � \Bumpeq \geqq \geqslant � � � \eqslantgtr \gtrsim \gtrapprox ≫ ≷ ⋗ \ggg , \gggtr \gtrdot \gtrless � � ≖ \gtreqless \gtreqqless \eqcirc ⊜ � ∼ \circeq \triangleq \thicksim � ⋑ ≈ \thickapprox \supseteqq \Supset � � ❂ \sqsupset \succcurlyeq \curlyeqsucc � ⊲ � \succsim \succapprox \vartriangleright � � � \trianglerighteq \Vdash \shortmid ≬ ⋔ � \shortparallel \between \pitchfork ∝ ◭ ∴ \varpropto \blacktriangleleft \therefore ◮ ∵ � \backepsilon \blacktriangleright \because Table 8.16: AMS binary relations (available with amssymb package) / department of mathematics and computer science October 2012
Brackets 21/43 $\ displaystyle (\ frac {n}{\ frac {n}{n+p}+1}) + \ left ( \ frac {n}{\ tfrac {n}{n+p}+1} \ right )$ � � n n ( n + p + 1 ) + n n n + p + 1 / department of mathematics and computer science October 2012
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