Larson book

Chapter 1: Limits and Their Properties

• • 1.1: A Preview of Calculus 42

  • 1.2: Finding Limits Graphically and Numerically 48

  • 1.3: Evaluating Limits Analytically 59

  • 1.4: Continuity and One-Sided Limits 70

  • 1.5: Infinite Limits 83

  • 1: Review Exercises 91

  • 1: Problem Solving

Chapter 2: Differentiation

• • 2.1: The Derivative and the Tangent Line Problem 96

  • 2.2: Basic Differentiation Rules and Rates of Change 106

  • 2.3: Product and Quotient Rules and Higher-Order Derivatives 118

  • 2.4: The Chain Rule 129

  • 2.5: Implicit Differentiation 140

  • 2.6: Related Rates 148

  • 2: Review Exercises 157

  • 2: Problem Solving

Chapter 3: Applications of Differentiation

• • 3.1: Extrema on an Interval 162

  • 3.2: Rolle's Theorem and the Mean Value Theorem 170

  • 3.3: Increasing and Decreasing Functions and the First Derivative Test 177

  • 3.4: Concavity and the Second Derivative Test 187

  • 3.5: Limits at Infinity 195

  • 3.6: A Summary of Curve Sketching 206

  • 3.7: Optimization Problems 215

  • 3.8: Newton's Method 225

  • 3.9: Differentials 231

  • 3: Review Exercises 238

  • 3: Problem Solving

Chapter 4: Integration

• • 4.1: Antiderivatives and Indefinite Integration 244

  • 4.2: Area 254

  • 4.3: Riemann Sums and Definite Integrals 266

  • 4.4: The Fundamental Theorem of Calculus 277

  • 4.5: Integration by Substitution 292

  • 4.6: Numerical Integration 305

  • 4: Review Exercises 312

  • 4: Problem Solving

Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions

• • 5.1: The Natural Logarithmic Function: Differentiation 318

  • 5.2: The Natural Logarithmic Function: Integration 328

  • 5.3: Inverse Functions 337

  • 5.4: Exponential Functions: Differentiation and Integration 346

  • 5.5: Bases Other than e and Applications 356

  • 5.6: Inverse Trigonometric Functions: Differentiation 366

  • 5.7: Inverse Trigonometric Functions: Integration 375

  • 5.8: Hyperbolic Functions 383

  • 5: Review Exercises 393

  • 5: Problem Solving

Chapter 6: Differential Equations

• • 6.1: Slope Fields and Euler's Method 398

  • 6.2: Differential Equations: Growth and Decay 407

  • 6.3: Separation of Variables and the Logistic Equation 415

  • 6.4: First-Order Linear Differential Equations 424

  • 6: Review Exercises 431

  • 6: Problem Solving

Chapter 7: Applications of Integration

• • 7.1: Area of a Region Between Two Curves 436

  • 7.2: Volume: The Disk Method 446

  • 7.3: Volume: The Shell Method 457

  • 7.4: Arc Length and Surfaces of Revolution 466

  • 7.5: Work 477

  • 7.6: Moments, Centers of Mass, and Centroids 486

  • 7.7: Fluid Pressure and Fluid Force 497

  • 7: Review Exercises 503

  • 7: Problem Solving

Chapter 8: Integration Techniques, L'Hopital's Rule, and Improper Integrals

• • 8.1: Basic Integration Rules 508

  • 8.2: Integration by Parts 515

  • 8.3: Trigonometric Integrals 524

  • 8.4: Trigonometric Substitution 533

  • 8.5: Partial Fractions 542

  • 8.6: Integration by Tables and Other Integration Techniques 561

  • 8.7: Indeterminate Forms and L'Hopital's Rule 557

  • 8.8: Improper Integrals 568

  • 8: Review Exercises 579

  • 8: Problem Solving

Chapter 9: Infinite Series

• • 9.1: Sequences 584

  • 9.2: Series and Convergence 595

  • 9.3: The Integral Test and p-Series 605

  • 9.4: Comparisons of Series 612

  • 9.5: Alternating Series 619

  • 9.6: The Ratio and Root Tests 627

  • 9.7: Taylor Polynomials and Approximations 636

  • 9.8: Power Series 647

  • 9.9: Representation of Functions by Power Series 657

  • 9.10: Taylor and Maclaurin Series 664

  • 9: Review Exercises 676

  • 9: Problem Solving

Chapter 10: Conics, Parametric Equations, and Polar Coordinates

• • 10.1: Conics and Calculus 682

  • 10.2: Plane Curves and Parametric Equations 696

  • 10.3: Parametric Equations and Calculus 706

  • 10.4: Polar Coordinates and Polar Graphs 715

  • 10.5: Area and Arc Length in Polar Coordinates 725

  • 10.6: Polar Equations of Conics and Kepler's Laws 734

  • 10: Review Exercises 742

  • 10: Problem Solving