Calculus I /

"Let's face it: the thought of Calculus I can be daunting. But it needn't be. in this helpful guide, the fundamentals of Calculus I are taught in easy-to-understand terms, with lots of explanatory graphs and illustrations and over 150 practice problems that feature simple, step-by-ste...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kelley, W. Michael (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Indianapolis, Indiana : Alpha, a member of Penguin Random House LLC, 2016.
Edición:First American edition.
Colección:Idiot's guides.
Temas:
Calculus.
Calcul infinitésimal.
calculus.
MATHEMATICS / Calculus
Calculus
Acceso en línea:Texto completo (Requiere registro previo con correo institucional)
Tabla de Contenidos:
  • Intro
  • Contents iii
  • Part 1: The Roots of Calculus 1
  • 1 What Is Calculus, Anyway? 3
  • What's the Purpose of Calculus? 4
  • Finding the Slopes of Curves 4
  • Calculating the Area of Bizarre Shapes 4
  • Justifying Old Formulas 5
  • Calculating Complicated x-Intercepts 5
  • Visualizing Graphs 5
  • Finding the Average Value of a Function 6
  • Calculating Optimal Values 6
  • Who's Responsible for This? 7
  • Ancient Influences 7
  • Newton vs Leibniz 9
  • I Ever Learn This? 11
  • 2 Polish Up Your Algebra Skills 13
  • Walk the Line: Linear Equations 14
  • Common Forms of Linear Equations 14
  • Calculating Slope 16
  • Interpreting Linear Graphs 18
  • You've Got the Power: Exponential Rules 21
  • Breaking Up Is Hard to Do: Factoring Polynomials 22
  • Greatest Common Factor 23
  • Special Factoring Patterns 23
  • Solving Quadratic Equations 24
  • Method One: Factoring 25
  • Method Two: Completing the Square 25
  • Method Three: The Quadratic Formula 26
  • Synthesizing the Quadratic Solution Methods 27
  • 3 Equations, Relations, and Functions 31
  • What Makes a Function Tick? 31
  • Working with Graphs of Functions 36
  • Functional Symmetry 39
  • Graphs to Know by Heart 43
  • Constructing an Inverse Function 45
  • Parametric Equations 47
  • What's a Parameter? 47
  • Converting to Rectangular Form 48
  • 4 Trigonometry: Last Stop Before Calculus 51
  • Getting Repetitive: Periodic Functions 51
  • Introducing the Trigonometric Functions 53
  • Sine (Written as y = sin x) 54
  • Cosine (Written as y = cos x) 54
  • Tangent (Written as y = tan x) 55
  • Cotangent (Written as y = cot x) 56
  • Secant (Written as y = sec x) 57
  • Cosecant (Written as y = csc x) 57
  • What's Your Sine: The Unit Circle 59
  • Incredibly Important Identities 61
  • Pythagorean Identities 62
  • Double-Angle Formulas 63
  • Solving Trigonometric Equations 64.
  • Part 2: Laying the Foundation for Calculus 67
  • 5 Take It to the Limit 69
  • What Is a Limit? 70
  • Can Something Be Nothing? 71
  • One-Sided Limits 74
  • When Does a Limit Exist? 78
  • When Does a Limit Not Exist? 79
  • 6 Evaluating Limits Numerically 85
  • The Major Methods 86
  • Substitution Method 86
  • Factoring Method 87
  • Conjugate Method 88
  • What If Nothing Works? 90
  • Limits and Infinity 90
  • Vertical Asymptotes 90
  • Horizontal Asymptotes 92
  • Special Limit Theorems 96
  • Evaluating Limits Graphically 97
  • Technology Focus: Calculating Limits 99
  • 7 Continuity 103
  • What Does Continuity Look Like? 104
  • The Mathematical Definition of Continuity 104
  • Types of Discontinuity 109
  • Jump Discontinuity 109
  • Point Discontinuity 113
  • Infinite/Essential Discontinuity 114
  • Removable vs Nonremovable Discontinuity 117
  • The Intermediate Value Theorem 118
  • 8 The Difference Quotient 121
  • When a Secant Becomes a Tangent 122
  • Honey, I Shrunk the x 123
  • Applying the Difference Quotient 127
  • The Alternate Difference Quotient 129
  • Part 3: The Derivative 131
  • 9 Laying Down the Law for Derivatives 133
  • When Does a Derivative Exist? 134
  • Discontinuity 134
  • Sharp Point in the Graph 134
  • Vertical Tangent Line 135
  • Basic Derivative Techniques 136
  • The Power Rule 136
  • The Product Rule 138
  • The Quotient Rule 139
  • The Chain Rule 140
  • Rates of Change 141
  • Trigonometric Derivatives 144
  • Tabular and Graphical Derivatives 145
  • Technology Focus: Calculating Derivatives 150
  • 10 Common Differentiation Tasks 155
  • Finding Equations of Tangent Lines 156
  • Implicit Differentiation 159
  • Differentiating an Inverse Function 161
  • Parametric Derivatives 164
  • Technology Focus: Solving Gross Equations 166
  • Using the Built-In Equation Solver 166
  • The Equation-Function Connection 170.
  • 11 Using Derivatives to Graph 173
  • Relative Extrema 174
  • Finding Critical Numbers 175
  • Classifying Extrema 176
  • The Wiggle Graph 178
  • The Extreme Value Theorem 180
  • Determining Concavity 182
  • Another Wiggle Graph 183
  • The Second Derivative Test 184
  • 12 Derivatives and Motion 187
  • The Position Equation 188
  • Velocity 190
  • Acceleration 191
  • Vertical Projectile Motion 193
  • 13 Common Derivative Applications 195
  • Newton's Method 196
  • Evaluating Limits: L'Hôpital's Rule 199
  • More Existence Theorems 200
  • The Mean Value Theorem 201
  • Rolle's Theorem 203
  • Related Rates 204
  • Optimization 208
  • Part 4: The Integral 215
  • 14 Approximating Area 217
  • Riemann Sums 218
  • Right and Left Sums 219
  • Midpoint Sums 221
  • The Trapezoidal Rule 222
  • Simpson's Rule 225
  • 15 Antiderivatives 227
  • The Power Rule for Integration 228
  • Integrating Trigonometric Functions 230
  • Separation 232
  • The Fundamental Theorem of Calculus 233
  • Part One: Areas and Integrals Are Related 233
  • Part Two: Derivatives and Integrals Are Opposites 235
  • u-Substitution 236
  • Tricky u-Substitution and Long Division 237
  • Technology Focus: Definite and Indefinite Integrals 239
  • 16 Applications of the Fundamental Theorem 245
  • Calculating Area Between Two Curves 246
  • The Mean Value Theorem for Integration 249
  • A Geometric Interpretation 249
  • The Average Value Theorem 251
  • Finding Distance Traveled 253
  • Accumulation Functions 255
  • Arc Length 256
  • Rectangular Equations 256
  • Parametric Equations 257
  • Part 5: Differential Equations and More 259
  • 17 Differential Equations 261
  • Separation of Variables 262
  • Types of Solutions 263
  • Family of Solutions 264
  • Specific Solutions 266
  • Exponential Growth and Decay 267
  • 18 Visualizing Differential Equations 275
  • Linear Approximation 276
  • Slope Fields 277.
  • Euler's Method 281
  • Technology Focus: Slope Fields 285
  • 19 Final Exam 289
  • A Solutions to "You've Got Problems" 301
  • B Glossary 317
  • Index 323.

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