The Student's Introduction to <I>Mathematica</I> and the Wolfram Language最新文献

{"title":"Functions and Their Graphs","authors":"Michael Penna","doi":"10.1017/9781108290937.004","DOIUrl":"https://doi.org/10.1017/9781108290937.004","url":null,"abstract":"Since MATLAB’s library of functions cannot include all functions of interest to you, MATLAB provides several ways for you to define your own functions. In this project we illustrate how you can define your own functions using “in-line” functions. MATLAB also provides several ways to graph functions, not only its own built-in functions, but also “in-line” functions. In this project we illustrate how you can graph functions using the ezplot command:","PeriodicalId":360335,"journal":{"name":"The Student's Introduction to <I>Mathematica</I> and the Wolfram Language","volume":"259 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122768654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Index","authors":"","doi":"10.1017/9781108290937.011","DOIUrl":"https://doi.org/10.1017/9781108290937.011","url":null,"abstract":"","PeriodicalId":360335,"journal":{"name":"The Student's Introduction to <I>Mathematica</I> and the Wolfram Language","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117297913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear Algebra","authors":"H. Helson","doi":"10.1017/9781108290937.008","DOIUrl":"https://doi.org/10.1017/9781108290937.008","url":null,"abstract":"","PeriodicalId":360335,"journal":{"name":"The Student's Introduction to <I>Mathematica</I> and the Wolfram Language","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123415096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Working with Mathematica","authors":"","doi":"10.1017/9781108290937.003","DOIUrl":"https://doi.org/10.1017/9781108290937.003","url":null,"abstract":"","PeriodicalId":360335,"journal":{"name":"The Student's Introduction to <I>Mathematica</I> and the Wolfram Language","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125962970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multivariable Calculus","authors":"Khalid Khan, T. Graham","doi":"10.1201/9781315104270-10","DOIUrl":"https://doi.org/10.1201/9781315104270-10","url":null,"abstract":"This is an extended syllabus for this summer. It tells the story of the entire course in a condensed form. These 8 pages can be a guide through the semester. The material is arranged in 6 chapters and delivered in the 6 weeks of the course. Each chapter has 4 sections, two sections for each day. While it make sense to read in a text book beside following the lectures, I want you to focus on the lectures. Textbooks have a lot of additional material and notation. Some of it can distract, other can even confuse. While a selected read in an other source can be helpful to get a second opinion and reconciliation of confusion and merging of different sources is an important aspect of learning, it can be sufficient and save time, to focus on the lectures delivered in class. It goes without saying that homework is extremely important. Mathematics can only be learned by solving problems. Chapter 1. Geometry and Space Section 1.1: Space, distance, geometrical objects After an overview over the syllabus, we use coordinates like P = (3, 4, 5) to describe points P in space. As promoted by Descartes in the 16’th century, geometry can be described algebraically when a coordinate system is introduced. A fundamental notion is the distance d(P,Q) = √ (x− a) + (y − b) + (z − c) between two points P = (x, y, z) and Q = (a, b, c). This formula makes use of Pythagoras theorem. In order to get a feel about space, we look at some geometric objects in space. We will focus on simple examples like cylinders and spheres and learn how to find the center and radius of a sphere given as a quadratic expression in x, y, z. This method is called the completion of the square and is based on one of the oldest techniques discovered in mathematics. Section 1.2: Vectors, dot product, projections Two points P,Q in space define a vector ~ PQ at P . It has its head at Q and its tail at P . The vector connects the initial point P with the end point Q. Vectors can be attached everywhere in space, but they are identified if they have the same length and the same direction. Vectors can describe velocities, forces or color or data. The components of a vector ~ PQ connecting a point P = (a, b, c) with a point Q = (x, y, z) are the entries of the vector 〈x− a, y− b, z − c〉. 1 Examples of vectors are the zero vector ~0 = 〈0, 0, 0〉, and the standard basis vectors ~i = 〈1, 0, 0〉,~j = 〈0, 1, 0〉, ~k = 〈0, 0, 1〉. Addition, subtraction and scalar multiplication of vectors can be done both geometrically and algebraically. The dot product ~v · ~ w between two vectors results is a scalar. It allows to define the length |~v| = √ ~v · ~v of a vector. The trigonometric cos-formula leads to the angle formula ~v · ~ w = |~v||~ w| cosα. By the CauchySchwarz inequality we can define the angle between two vectors using this formula. Vectors satisfying ~v · ~ w = 0 are called perpendicular. Pythagoras formula |~v + ~ w|2 = |~v|2 + |~ w|2 follows now from the definitions. Section 1.3: The cross product and triple s","PeriodicalId":360335,"journal":{"name":"The Student's Introduction to <I>Mathematica</I> and the Wolfram Language","volume":"73 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131773633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}