Calculus I

Calculus I

Let's face it: most students don't take calculus because they find it intellectually stimulating. It's not ... at least for those who come up on the wrong side of the bell curve! There they are, minding their own business, working toward some non-science related degree, when ... BLAM!...

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Detalles Bibliográficos
Otros Autores: Kelley, W. Michael, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Indianapolis, Indiana : Alpha, a member of Penguin Random House LLC 2016.
Edición:First American edition
Colección:Idiot's guides.
Materias:
Calculus.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630168406719
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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