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Analysis for Computer Scientists : Foundations, Methods, and Algorithms / by Michael Oberguggenberger, Alexander Ostermann
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Undergraduate Topics in Computer Science | SpringerLink BücherPublisher: London : Springer-Verlag London Limited, 2011Description: Online-Ressource (X, 341p, digital)ISBN:- 9780857294463
- 004.0151
- QA76.9.M35
Contents:
Summary: This textbook presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations. Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book's webpage. Dr. Michael Oberguggenberger is a professor in the Department of Civil Engineering Sciences at the University of Innsbruck, Austria. Dr. Alexander Ostermann is a professor in the Department of Mathematics at the University of Innsbruck, Austria.PPN: PPN: 165084235XPackage identifier: Produktsigel: ZDB-2-SCS
""Analysis for Computer Scientists""; ""Preface""; ""Contents""; ""Chapter 1: Numbers""; ""1.1 The Real Numbers""; ""1.2 Order Relation and Arithmetic on R""; ""1.3 Machine Numbers""; ""1.4 Rounding""; ""1.5 Exercises""; ""Chapter 2: Real-Valued Functions""; ""2.1 Basic Notions""; ""2.2 Some Elementary Functions""; ""Linear Functions (Straight Lines)""; ""Quadratic Parabolas""; ""Power Functions""; ""Absolute Value, Sign and Indicator Function""; ""Exponential Functions and Logarithms""; ""2.3 Exercises""; ""Chapter 3: Trigonometry""; ""3.1 Trigonometric Functions at the Triangle""
""3.2 Extension of the Trigonometric Functions to R""""3.3 Cyclometric Functions""; ""Sine and Arcsine""; ""Cosine and Arccosine""; ""Tangent and Arctangent""; ""3.4 Exercises""; ""Chapter 4: Complex Numbers""; ""4.1 The Notion of Complex Numbers""; ""The Complex Plane""; ""4.2 The Complex Exponential Function""; ""Exponential Function and Polar Coordinates""; ""Euler's Formulae""; ""4.3 Mapping Properties of Complex Functions""; ""4.4 Exercises""; ""Chapter 5: Sequences and Series""; ""5.1 The Notion of an Infinite Sequence""; ""5.2 The Completeness of the Set of Real Numbers""
""5.3 Infinite Series""""5.4 Supplement: Accumulation Points of Sequences""; ""5.5 Exercises""; ""Chapter 6: Limits and Continuity of Functions""; ""6.1 The Notion of Continuity""; ""6.2 Trigonometric Limits""; ""6.3 Zeros of Continuous Functions""; ""6.4 Exercises""; ""Chapter 7: The Derivative of a Function""; ""7.1 Motivation""; ""7.2 The Derivative""; ""Differentiating with maple""; ""7.3 Interpretations of the Derivative""; ""Interpretation as Linear Approximation""; ""Physical Interpretation as Rate of Change""; ""7.4 Differentiation Rules""; ""7.5 Numerical Differentiation""
""Numerical Differentiation of Noisy Functions""""7.6 Exercises""; ""Chapter 8: Applications of the Derivative""; ""8.1 Curve Sketching""; ""8.2 Newton's Method""; ""Derivation of Newton's Method""; ""8.3 Regression Line Through the Origin""; ""8.4 Exercises""; ""Chapter 9: Fractals and L-Systems""; ""9.1 Fractals""; ""Fractal Dimension""; ""9.2 Mandelbrot Sets""; ""9.3 Julia Sets""; ""9.4 Newton's Method in C""; ""9.5 L-Systems""; ""Construction of Fractals""; ""Simulation of Plant Growth""; ""Extensions""; ""9.6 Exercises""; ""Chapter 10: Antiderivatives""; ""10.1 Indefinite Integrals""
""10.2 Integration Formulae""""10.3 Exercises""; ""Chapter 11: Definite Integrals""; ""11.1 The Riemann Integral""; ""11.2 Fundamental Theorems of Calculus""; ""Applications of the First Fundamental Theorem""; ""Applications of the Second Fundamental Theorem""; ""11.3 Applications of the Definite Integral""; ""The Volume of a Solid of Revolution""; ""Arc Length of the Graph of a Function""; ""Lateral Surface Area of a Solid of Revolution""; ""11.4 Exercises""; ""Chapter 12: Taylor Series""; ""12.1 Taylor's Formula""; ""12.2 Taylor's Theorem""; ""12.3 Applications of Taylor's Formula""
""12.4 Exercises""
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