Introduction to L A TEX

Transcription

1 Introduction to L A TEX John McCleary Vassar College 17 September 2013

2 When the first volume of Donald Knuth s The Art of Computer Programming was published in 1969, it was typeset using hot metal type set by a Monotype Corporation typecaster with a hot metal typesetting machine from the 19th century which produced a good classic style appreciated by Knuth. When the second edition of the second volume was published, in 1976, the whole book had to be typeset again because the Monotype technology had been largely replaced by photographic techniques, and the original fonts were no longer available. When Knuth received the galley proofs of the new book on 30 March 1977, he found them awful. Around that time, Knuth saw for the first time the output of a high-quality digital typesetting system, and became interested in digital typography. The disappointing galley proofs gave him the final motivation to solve the problem at hand once and for all by designing his own typesetting system. On 13 May 1977, he wrote a memo to himself describing the basic features of TeX. from Wikipedia, 17.IX.2013

3 30 1 Vectors and Functions the value of f at any point on the 2-interval I (0,0),(1, 1 2 ) =[0, 1] [0, 1 2 ]. Indeed, the image of this 2-interval is [0, 1 2 ] [1, 3 2 ], which is not an interval in R. As indicated by the example in Remark 1.24, a simple modification of the result in Proposition 1.23 yields a characterization of the IVP. Proposition Let D R 2 and let f : D R be a function. Then for any 2-interval I J D, f has the IVP on I J f(e) is an interval in R for every 2-interval E I J. Proof. The implication = follows from Proposition To prove the converse, let (x1,y1), (x2,y2) I J and let r be a real number that lies between f(x1,y1) andf(x2,y2). Let E denote the 2-interval I (x1,y1),(x2,y2). Since f(e) isanintervalinr, it follows that r = f(x0,y0) forsome(x0,y0) E. SinceE I J, it follows that f has the IVP on I J. 1.3 Cylindrical and Spherical Coordinates For points in R 2, one has the familiar notion of polar coordinates. These provide an alternative and useful way to represent points in the plane other than the origin. Recall that the polar coordinates of (x, y) R 2 \{(0, 0)} are given by (r, θ), where r and θ are real numbers determined by the equations x = r cos θ and y = r sin θ and the conditions r>0andθ ( π, π]. The precise relationship is stated below. For a proof of this, one may refer to Proposition 7.20 of ACICARA. Fact If x, y R are such that (x, y) (0, 0), thenr and θ defined by ( x ) r := cos 1 if y 0, r x 2 + y 2 and θ := ( x ) cos 1 if y<0, r satisfy the following properties: r, θ R, r > 0, θ ( π, π], x = r cos θ, and y = r sin θ. Conversely, if r, θ R are such that r>0 and θ ( π, π], thenx := r cos θ and y := r sin θ are real numbers such that (x, y) (0, 0), r = x 2 + y 2,and θ equals cos 1 (x/r) or cos 1 (x/r) according as y 0 or y<0.

4 TEX is a programming language.

5 TEX is a programming language. A TEXfile is a program, that is, it is a series of commands that is compiled by the TEX engine which delivers output.

6 TEX is a programming language. A TEXfile is a program, that is, it is a series of commands that is compiled by the TEX engine which delivers output. LATEX requires a preface declaring certain styles and initiating packages of commands that have been designed by others.

7 A typical setup \documentclass{article} \usepackage{amsmath} \usepackage{amssym} \usepackage{amsfonts} You can put many useful things here. \begin{document} Your text here. \end{document}

8 A scrap of TEX code A {\it binomial} is an algebraic expression of the form $a + b$, on which we can carry out some operation. Most often the expressions are monomials and a binomial is a kind of polynomial. If we raise the monomial $a + b$ to a power, we obtain new terms: Of course, $(a + b)ˆ1 = a + b$, and most of us know that $$(a+b)ˆ2 = aˆ2 + 2ab + bˆ2.$$ If one is willing, we can extend this further: \begin{align*} (a+b)ˆ3 &= aˆ3 + 3aˆ2 b + 3a bˆ2 + bˆ3 \\ (a+b)ˆ4 &= aˆ4 + 4aˆ3 b + 6 aˆ2 bˆ2 + 4 a bˆ3 + bˆ4, \end{align*} and so on. The coefficients appearing in these expressions are called {\it binomial coefficients} and they are defined in general by the notation: $$(a + b)ˆn = aˆn + \binom{n}{1} aˆ{n-1} b + \binom{n}{2} aˆ{n-2} bˆ2 + \cdots + \binom{n}{k} aˆ{n-k} bˆk + \cdots + \binom{n}{n-1} a bˆ{n-1} + bˆn.$$ Thus, $\displaystyle\binom{4}{2} = 6$.

9 Output from that code A binomial is an algebraic expression of the form a + b, on which we can carry out some operation. Most often the expressions are monomials and a binomial is a kind of polynomial. If we raise the monomial a + b to a power, we obtain new terms: Of course, (a + b) 1 = a + b, and most of us know that (a + b) 2 = a 2 + 2ab + b 2. If one is willing, we can extend this further: (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a + b) 4 = a 4 + 4a 3 b + 6a 2 b 2 + 4ab 3 + b 4, and so on. The coefficients appearing in these expressions are called binomial coefficients and they are defined in general by the notation: ( n ( n ( n ( n ) (a + b) n = a n + a 1) n 1 b + a 2) n 2 b a k) n k b k + + ab n 1 + b n. n 1 ( 4 Thus, = 6. 2)

10 Fonts \textit{italic} gives italic. \textbf{bold} gives bold. \textsl{slanted} gives slanted. \textsc{small caps} gives SMALL CAPS. \texttt{typewriter} gives typewriter.

11 Choices align versus align* (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (1) (a + b) 4 = a 4 + 4a 3 b + 6a 2 b 2 + 4ab 3 + b 4, (2) text style versus \displaystyle ( ) ( n ) n 5 versus 5

12 A matrix $$\begin{pmatrix} 7 & 8 & -1 & 0\\ 4 & -2 & 0 & 9 \\ -1 & 0 & 6 & 12 \\ 0 & 3 & -7 & 1 \end{pmatrix}$$

13 Cases $$\int 1ˆx tˆp\,dt = \begin{cases} \displaystyle \frac{xˆ{p+1}}{p+1} - \frac1{p+1} &\mbox{if }p\neq -1,\\ \ln (x) &\mbox{if }p = -1.\end{cases}$$ x 1 x p+1 t p dt = p if p 1, p + 1 ln(x) if p = 1.

14 A commutative diagram 0 C n+1 α Cn+1 β C n C n 0 C n 1 α Cn β C 0 α Cn 1 n β C 0 n 1

15 α \alpha θ \theta o o τ \tau β \beta ϑ \vartheta π \pi υ \upsilon γ \gamma γ \gamma ϖ \varpi φ \phi δ \delta κ \kappa ρ \rho ϕ \varphi ɛ \epsilon λ \lambda ϱ \varrho χ \chi ε \varepsilon µ \mu σ \sigma ψ \psi ζ \zeta ν \nu ς \varsigma ω \omega η \eta ξ \xi Γ \Gamma Λ \Lambda Σ \Sigma Ψ \Psi \Delta Ξ \Xi Υ \Upsilon Ω \Omega Θ \Theta Π \Pi Φ \Phi Greek Letters

16 ± \pm \cap \diamond \oplus \mp \cup \bigtriangleup \ominus \times \uplus \bigtriangledown \otimes \div \sqcap \triangleleft \oslash \ast \sqcup \triangleright \odot \star \vee \lhd b \bigcirc \circ \wedge \rhd b \dagger \bullet \ \setminus \unlhd b \ddagger \cdot \wr \unrhd b \amalg b Not predefined in a format based on basefont.tex. Use one of the style options oldlfont, newlfont, amsfonts or amssymb. Binary Operation Symbols

17 \leq \geq \equiv = \models \prec \succ \sim \perp \preceq \succeq \simeq \mid \ll \gg \asymp \parallel \subset \supset \approx \bowtie \subseteq \supseteq = \cong \Join b \sqsubset b \sqsupset b \neq \smile. \sqsubseteq \sqsupseteq = \doteq \frown \in \ni \propto = = \vdash \dashv < < > > b Not predefined in a format based on basefont.tex. Use one of the style options oldlfont, newlfont, amsfonts or amssymb. Relation Symbols

18 \leftarrow \longleftarrow \uparrow \Leftarrow = \Longleftarrow \Uparrow \rightarrow \longrightarrow \downarrow \Rightarrow = \Longrightarrow \Downarrow \leftrightarrow \longleftrightarrow \updownarrow \Leftrightarrow \Longleftrightarrow \Updownarrow \mapsto \longmapsto \nearrow \hookleftarrow \hookrightarrow \searrow \leftharpoonup \rightharpoonup \swarrow \leftharpoondown \rightharpoondown \nwarrow \rightleftharpoons \leadsto b b Not predefined in a format based on basefont.tex. Use one of the style options oldlfont, newlfont, amsfonts or amssymb. Arrow Symbols

19 ... \ldots \cdots. \vdots... \ddots ℵ \aleph \prime \forall \infty \hbar \emptyset \exists \Box b ı \imath \nabla \neg \Diamond b j \jmath \surd \flat \triangle l \ell \top \natural \clubsuit \wp \bot \sharp \diamondsuit R \Re \ \ \backslash \heartsuit I \Im \angle \partial \spadesuit \mho b b Not predefined in a format based on basefont.tex. Use one of the style options oldlfont, newlfont, amsfonts or amssymb. Miscellaneous Symbols

20 \sum \bigcap \bigodot \prod \bigcup \bigotimes \coprod \bigsqcup \bigoplus \int \bigvee \biguplus \oint \bigwedge Variable-sized Symbols \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 Log-like Symbols

21 1. TEX has the best output. Top ten reasons to learn TEX

22 1. TEX has the best output. 2. TEX knows typsetting. Top ten reasons to learn TEX

23 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. Top ten reasons to learn TEX

24 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. Top ten reasons to learn TEX

25 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. Top ten reasons to learn TEX

26 Top ten reasons to learn TEX 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. 6. TEX input is plain text. (Therefore, small!)

27 Top ten reasons to learn TEX 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. 6. TEX input is plain text. (Therefore, small!) 7. TEX output can be anything.

28 Top ten reasons to learn TEX 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. 6. TEX input is plain text. (Therefore, small!) 7. TEX output can be anything. 8. TEX is free.

29 Top ten reasons to learn TEX 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. 6. TEX input is plain text. (Therefore, small!) 7. TEX output can be anything. 8. TEX is free. 9. TEX runs anywhere.

30 Top ten reasons to learn TEX 1. TEX has the best output. 2. TEX knows typsetting. 3. TEX is fast. 4. TEX is stable. 5. TEX is stable, but not rigid. 6. TEX input is plain text. (Therefore, small!) 7. TEX output can be anything. 8. TEX is free. 9. TEX runs anywhere. 10. TEX is the standard.