دانلود کتاب Analysis for Computer Scientists: Foundations, Algorithms and Applications

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\"\"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\"\"