دانلود کتاب The Humongous Book of Calculus Problems (Humongous Books)

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Contents iii\nIntroduction ix\nChapter 1: Linear Equations and Inequalities 1\n Linear Geometry 2\n Linear Inequalities and Interval Notation 5\n Absolute Value Equations and Inequalities 8\n Systems of Equations and Inequalities 11\nChapter 2: Polynomials 15\n Exponential and Radical Expressions 16\n Operations on Polynomial Expressions 18\n Factoring Polynomials 21\n Solving Quadratic Equations 23\nChapter 3: Rational Expressions 27\n Adding and Subtracting Rational Expressions 28\n Multiplying and Dividing Rational Expressions 30\n Solving Rational Equations 33\n Polynomial and Rational Inequalities 35\nChapter 4: Functions 41\n Combining Functions 42\n Graphing Function Transformations 45\n Inverse Functions 50\n Asymptotes of Rational Functions 53\nChapter 5: Logarithmic and Exponential Functions 57\n Exploring Exponential and Logarithmic Functions 58\n Natural Exponential and Logarithmic Functions 62\n Properties of Logarithms 63\n Solving Exponential and Logarithmic Equations 66\nChapter 6: Conic Sections 69\n Parabolas 70\n Circles 76\n Ellipses 79\n Hyperbolas 85\nChapter 7: Fundamentals of Trigonometry 91\n Measuring Angles 92\n Angle Relationships 93\n Evaluating Trigonometric Functions 95\n Inverse Trigonometric Functions 102\nChapter 8: Trigonometric Graphs, Identities, and Equations 105\n Graphing Trigonometric Transformations 106\n Applying Trigonometric Identities 110\n Solving Trigonometric Equations 115\nChapter 9: Investigating Limits 123\n Evaluating One-Sided and General Limits Graphically 124\n Limits and Infinity 129\n Formal Definition of the Limit 134\nChapter 10: Evaluating Limits 137\n Substitution Method 138\n Factoring Method 141\n Conjugate Method 146\n Special Limit Theorems 149\nChapter 11: Continuity and the Difference Quotient 151\n Continuity 152\n Types of Discontinuity 153\n The Difference Quotient 163\n Differentiability 166\nChapter 12: Basic Differentiation Methods 169\n Trigonometric, Logarithmic, and Exponential Derivatives 170\n The Power Rule 172\n The Product and Quotient Rules 175\n The Chain Rule 179\nChapter 13: Derivatives and Function Graphs 187\n Critical Numbers 188\n Signs of the First Derivative 191\n Signs of the Second Derivative 197\n Function and Derivative Graphs 202\nChapter 14: Basic Applications of Differentiation 205\n Equations of Tangent Lines 206\n The Extreme Value Theorem 211\n Newton’s Method 214\n L’Hôpital’s Rule 218\nChapter 15: Advanced Applications of Differentiation 223\n The Mean Value and Rolle’s Theorems 224\n Rectilinear Motion 229\n Related Rates 233\n Optimization 240\nChapter 16: Additional Differentiation Techniques 247\n Implicit Differentiation 248\n Logarithmic Differentiation 255\n Differentiating Inverse Trigonometric Functions 260\n Differentiating Inverse Functions 262\nChapter 17: Approximating Area 269\n Informal Riemann Sums 270\n Trapezoidal Rule 281\n Simpson’s Rule 289\n Formal Riemann Sums 291\nChapter 18: Integration 297\n Power Rule for Integration 298\n Integrating Trigonometric and Exponential Functions 301\n The Fundamental Theorem of Calculus 303\n Substitution of Variables 313\nChapter 19: Applications of the Fundamental Theorem 319\n Calculating the Area Between Two Curves 320\n The Mean Value Theorem for Integration 326\n Accumulation Functions and Accumulated Change 334\nChapter 20: Integrating Rational Expressions 343\n Separation 344\n Long Division 347\n Applying Inverse Trigonometric Functions 350\n Completing the Square 353\n Partial Fractions 357\nChapter 21: Advanced Integration Techniques 363\n Integration by Parts 364\n Trigonometric Substitution 368\n Improper Integrals 383\nChapter 22: Cross-Sectional and Rotational Volume 389\n Volume of a Solid with Known Cross-Sections 390\n Disc Method 397\n Washer Method 406\n Shell Method 417\nChapter 23: Advanced Applications of Definite Integrals 423\n Arc Length 424\n Surface Area 427\n Centroids 432\nChapter 24: Parametric and Polar Equations 443\n Parametric Equations 444\n Polar Coordinates 448\n Graphing Polar Curves 451\n Applications of Parametric and Polar Differentiation 456\n Applications of Parametric and Polar Integration 462\nChapter 25: Differential Equations 467\n Separation of Variables 468\n Exponential Growth and Decay 473\n Linear Approximations 480\n Slope Fields 482\n Euler’s Method 488\nChapter 26: Basic Sequences and Series 495\n Sequences and Convergence 496\n Series and Basic Convergence Tests 498\n Telescoping Series and p-Series 502\n Geometric Series 505\n The Integral Test 507\nChapter 27: Additional Infinite Series Convergence Tests 511\n Comparison Test 512\n Limit Comparison Test 514\n Ratio Test 517\n Root Test 520\n Alternating Series Test and Absolute Convergence 524\nChapter 28: Advanced Infinite Series 529\n Power Series 530\n Taylor and Maclaurin Series 538\nAppendix A: Impo rtant Graphs to memorize and Graph Transformations 545\nAppendix B: The Unit Circle 551\nAppendix C: Trigonometric Identities 553\nAppendix D: Derivative Fo rmulas 555\nAppendix E: Anti-Derivative Formulas 557\nIndex 559