001451101 000__ 06870cam\a2200577\i\4500
001451101 001__ 1451101
001451101 003__ OCoLC
001451101 005__ 20230310004643.0
001451101 006__ m\\\\\o\\d\\\\\\\\
001451101 007__ cr\cn\nnnunnun
001451101 008__ 221111s2022\\\\gw\a\\\\o\\\\\001\0\eng\d
001451101 019__ $$a1350687525
001451101 020__ $$a9783662654583$$q(electronic bk.)
001451101 020__ $$a366265458X$$q(electronic bk.)
001451101 020__ $$z9783662654576
001451101 020__ $$z3662654571
001451101 0247_ $$a10.1007/978-3-662-65458-3$$2doi
001451101 035__ $$aSP(OCoLC)1350617258
001451101 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001451101 0411_ $$aeng$$hger
001451101 049__ $$aISEA
001451101 050_4 $$aQA303.2
001451101 08204 $$a515$$223/eng/20221122
001451101 1001_ $$aKarpfinger, Christian,$$eauthor.
001451101 24510 $$aCalculus and linear algebra in recipes :$$bterms, phrases and numerous examples in short learning units /$$cChristian Karpfinger.
001451101 250__ $$aThird edition.
001451101 264_1 $$aBerlin :$$bSpringer,$$c[2022]
001451101 264_4 $$c©2022
001451101 300__ $$a1 online resource (xxvi, 1038 pages) :$$billustrations
001451101 336__ $$atext$$btxt$$2rdacontent
001451101 337__ $$acomputer$$bc$$2rdamedia
001451101 338__ $$aonline resource$$bcr$$2rdacarrier
001451101 500__ $$aIncludes index.
001451101 5050_ $$aIntro -- Foreword to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Speech, Symbols and Sets -- 1.1 Speech Patterns and Symbols in Mathematics -- 1.1.1 Junctors -- 1.1.2 Quantifiers -- 1.2 Summation and Product Symbol -- 1.3 Powers and Roots -- 1.4 Symbols of Set Theory -- 1.5 Exercises -- 2 The Natural Numbers, Integers and Rational Numbers -- 2.1 The Natural Numbers -- 2.2 The Integers -- 2.3 The Rational Numbers -- 2.4 Exercises -- 3 The Real Numbers -- 3.1 Basics -- 3.2 Real Intervals -- 3.3 The Absolute Value of a Real Number
001451101 5058_ $$a3.4 n-th Roots -- 3.5 Solving Equations and Inequalities -- 3.6 Maximum, Minimum, Supremum and Infimum -- 3.7 Exercises -- 4 Machine Numbers -- 4.1 b-adic Representation of Real Numbers -- 4.2 Floating Point Numbers -- 4.2.1 Machine Numbers -- 4.2.2 Machine Epsilon, Rounding and Floating Point Arithmetic -- 4.2.3 Loss of Significance -- 4.3 Exercises -- 5 Polynomials -- 5.1 Polynomials: Multiplication and Division -- 5.2 Factorization of Polynomials -- 5.3 Evaluating Polynomials -- 5.4 Partial Fraction Decomposition -- 5.5 Exercises -- 6 Trigonometric Functions -- 6.1 Sine and Cosine
001451101 5058_ $$a6.2 Tangent and Cotangent -- 6.3 The Inverse Functions of the Trigonometric Functions -- 6.4 Exercises -- 7 Complex Numbers: Cartesian Coordinates -- 7.1 Construction of C -- 7.2 The Imaginary Unit and Other Terms -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Exercises -- 8 Complex Numbers: Polar Coordinates -- 8.1 The Polar Representation -- 8.2 Applications of the Polar Representation -- 8.3 Exercises -- 9 Linear Systems of Equations -- 9.1 The Gaussian Elimination Method -- 9.2 The Rank of a Matrix -- 9.3 Homogeneous Linear Systems of Equations -- 9.4 Exercises
001451101 5058_ $$a10 Calculating with Matrices -- 10.1 Definition of Matrices and Some Special Matrices -- 10.2 Arithmetic Operations -- 10.3 Inverting Matrices -- 10.4 Calculation Rules -- 10.5 Exercises -- 11 LR-Decomposition of a Matrix -- 11.1 Motivation -- 11.2 The LR-Decomposition: Simplified Variant -- 11.3 The LR-Decomposition: General Variant -- 11.4 The LR-Decomposition-with Column Pivot Search -- 11.5 Exercises -- 12 The Determinant -- 12.1 Definition of the Determinant -- 12.2 Calculation of the Determinant -- 12.3 Applications of the Determinant -- 12.4 Exercises -- 13 Vector Spaces
001451101 5058_ $$a13.1 Definition and Important Examples -- 13.2 Subspaces -- 13.3 Exercises -- 14 Generating Systems and Linear (In)Dependence -- 14.1 Linear Combinations -- 14.2 The Span of X -- 14.3 Linear (In)Dependence -- 14.4 Exercises -- 15 Bases of Vector Spaces -- 15.1 Bases -- 15.2 Applications to Matrices and Systems of Linear Equations -- 15.3 Exercises -- 16 Orthogonality I -- 16.1 Scalar Products -- 16.2 Length, Distance, Angle and Orthogonality -- 16.3 Orthonormal Bases -- 16.4 Orthogonal Decomposition and Linear Combination with Respect to an ONB -- 16.5 Orthogonal Matrices -- 16.6 Exercises
001451101 506__ $$aAccess limited to authorized users.
001451101 520__ $$aHave you ever cooked a 3-course meal from a recipe? That generally works out pretty well, even if you're not much of a cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise, too: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems in the following topics: Calculus in one and more variables, linear algebra, vector analysis, theory on differential equations, ordinary and partial, and complex analysis. We have tried to summarize these recipes as good and also as understandable as possible in this book. It is often said that one must understand higher mathematics in order to be able to apply it. We show in this book that understanding also comes naturally by doing: no one learns the grammar of a language from cover to cover if he wants to learn a language. You learn a language by reading up a bit on the grammar and then getting going; you have to speak, make mistakes, have mistakes pointed out to you, know example sentences and recipes, work out topics in tidbits, then it works. In higher mathematics it is no different. Other features of this book include: The division of calculus and linear algebra into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture. Numerous examples. Many tasks, the solutions to which can be found in the accompanying workbook. Many problems in calculus and linear algebra can be solved with computers. We always indicate how it works with MATLAB. Due to the clear presentation, the book can also be used as an annotated collection of formulas with numerous examples. Prof. Dr. Christian Karpfinger teaches at the Technical University of Munich; in 2004 he received the State Teaching Award of the Free State of Bavaria. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com).
001451101 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 22, 2022).
001451101 650_0 $$aCalculus.
001451101 650_0 $$aAlgebras, Linear.
001451101 655_0 $$aElectronic books.
001451101 77608 $$iPrint version: $$z3662654571$$z9783662654576$$w(OCoLC)1313385181
001451101 852__ $$bebk
001451101 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-662-65458-3$$zOnline Access$$91397441.1
001451101 909CO $$ooai:library.usi.edu:1451101$$pGLOBAL_SET
001451101 980__ $$aBIB
001451101 980__ $$aEBOOK
001451101 982__ $$aEbook
001451101 983__ $$aOnline
001451101 994__ $$a92$$bISE