Calculus

<h1>Calculus: Early Transcendental Functions</h1><h3>Chapter 0: Preliminaries</h3><h4>0.1, "The Real Numbers and the Cartesian Plane"</h4><h4>0.2, "Lines and Functions"</h4><h4>0.3, "Graphing Calculators and Computer Algebra Systems"</h4><h4>0.4, "Trigonometric Functions"</h4><h4>0.5, "Transformations of Functions"</h4><h3>Chapter 1: Limits and Continuity</h3><h4>1.1, "A Brief Preview of Calculus: Tangent Lines and the Length of a Curve</h4><h4>1.2, "The Concept of Limit"</h4><h4>1.3, "Computation of Limits"</h4><h4>1.4, "Continuity and Its Consequences"</h4><h4>1.5, "Limits Involving Infinity; Asymptotes"</h4><h4>1.6, "Formal Definition of the Limit"</h4><h4>1.7, "Limits and Loss-of-Significance Errors"</h4><h3>Chapter 2: Differentiation</h3><h4>2.1, "Tangent Lines and Velocity"</h4><h4>2.2, "The Derivative"</h4><h4>2.3, "Computation of Derivatives: The Power Rule"</h4><h4>2.4, "The Product and Quotient Rules"</h4><h4>2.5, "The Chain Rule"</h4><h4>2.6, "Derivatives of Trigonometric Functions"</h4><h4>2.7, "Implicit Differentiation"</h4><h4>2.8, "The Mean Value Theorem"</h4><h3>Chapter 3: Applications of the Derivative</h3><h4>3.1, "Linear Approximations and Newton's Method""</h4><h4>3.2, "Maximum and Minimum Values"</h4><h4>3.3, "Increasing and Decreasing Functions"</h4><h4>3.4, "Concavity and the Second Derivative Test"</h4><h4>3.5, "Overview of Curve Sketching"</h4><h4>3.6, "Optimization"</h4><h4>3.7, "Related Rates"</h4><h4>3.8, "Rates of Change in Economics and the Sciences"</h4><h3>Chapter 4: Integration</h3><h4>4.1, "Antiderivatives"</h4><h4>4.2, "Sums and Sigma Notation"</h4><h4>4.3, "Area"</h4><h4>4.4, "The Definite Integral"</h4><h4>4.5, "The Fundamental Theorem of Calculus"</h4><h4>4.6, "Integration by Substitution"</h4><h4>4.7, "Numerical Integration"</h4><h3>Chapter 5: Applications of the Definite Integral</h3><h4>5.1, "Area Between Curves"</h4><h4>5.2, "Volume: Slicing, Disks and Washers"</h4><h4>5.3, "Volumes by Cylindrical Shells"</h4><h4>5.4, "Arc Length and Surface Area"</h4><h4>5.5, "Projectile Motion"</h4><h4>5.6, "Applications of Integration to Physics and Engineering"</h4><h3>Chapter 6: Exponentials, Logarithms and Other Transcendental Functions</h3><h4>6.1, "The Natural Logarithm"</h4><h4>6.2, "Inverse Functions"</h4><h4>6.3, "The Exponential Function"</h4><h4>6.4, "The Inverse Trigonometric Functions"</h4><h4>6.5, "The Calculus of the Inverse Trigonometric Functions"</h4><h4>6.6, "The Hyperbolic Functions"</h4><h3>Chapter 7: Integration Techniques</h3><h4>7.1, "Review of Formulas and Techniques"</h4><h4>7.2, "Integration by Parts"</h4><h4>7.3, "Trigonometric Techniques of Integration"</h4><h4>7.4, "Integration of Rational Functions Using Partial Fractions"</h4><h4>7.5, "Integration Tables and Computer Algebra Systems"</h4><h4>7.6, "Indeterminate Forms and L'Hopital's Rule" </h4><h4>7.7, "Improper Integrals"</h4><h4>7.8, "Probability"</h4><h3>Chapter 8: First-Order Differential Equations</h3><h4>8.1, "Modeling with Differential Equations"</h4><h4>8.2, "Separable Differential Equations"</h4><h4>8.3, "Direction Fields and Euler's Method"</h4><h4>8.4, "Systems of First-Order Differential Equations"</h4><h3>Chapter 9: Infinite Series</h3><h4>9.1, "Sequences of Real Numbers"</h4><h4>9.2, "Infinite Series"</h4><h4>9.3, "The Integral and Comparison Tests"</h4><h4>9.4, "Alternating Series"</h4><h4>9.5, "Absolute Convergence and the Ratio Test"</h4><h4>9.6, "Power Series"</h4><h4>9.7, "Taylor Series"</h4><h4>9.8, "Applications of Taylor Series"</h4><h4>9.9, "Fourier Series"</h4><h3>Chapter 10: Parametric Equations and Polar Coordinates</h3><h4>10.1, "Plane curves and Parametric Equations"</h4><h4>10.2, "Calculus and Parametric Equations"</h4><h4>10.3, "Arc Length and Surface Area in Parametric Equations"</h4><h4>10.4, "Polar Coordinates"</h4><h4>10.5, "Calculus and Polar Coordinates"</h4><h4>10.6, "Conic Sections"</h4><h4>10.7, "Conic Sections in Polar Coordinates"</h4><h3>Chapter 11: Vectors and the Geometry of Space</h3><h4>11.1, "Vectors in the Plane"</h4><h4>11.2, "Vectors in Space"</h4><h4>11.3, "The Dot Product"</h4><h4>11.4, "The Cross Product"</h4><h4>11.5, "Lines and Planes in Space"</h4><h4>11.6, "Surfaces in Space"</h4><h3>Chapter 12: Vector-Valued Functions</h3><h4>12.1, "Vector-Valued Functions"</h4><h4>12.2, "The Calculus of Vector-Valued Functions"</h4><h4>12.3, "Motion in Space"</h4><h4>12.4, "Curvature"</h4><h4>12.5, "Tangent and Normal Vectors"</h4><h4>12.6, "Parametric Surfaces"</h4><h3>Chapter 13: Functions of Several Variables and Partial Differentiation</h3><h4>13.1, "Functions of Several Variables"</h4><h4>13.2, "Limits and Continuity"</h4><h4>13.3, "Partial Derivatives"</h4><h4>13.4, "Tangent Planes and Linear Approximations"</h4><h4>13.5, "The Chain Rule"</h4><h4>13.6, "The Gradient and Directional Derivatives"</h4><h4>13.7, "Extrema of Functions of Several Variables"</h4><h4>13.8, "Constrained Optimization and and Lagrange Multipliers"</h4><h3>Chapter 14: Multiple Integrals</h3><h4>14.1, "Double Integrals"</h4><h4>14.2, "Area, Volume and Center of Mass"</h4><h4>14.3, "Double Integrals in Polar Coordinates"</h4><h4>14.4, "Surface Area"</h4><h4>14.5, "Triple Integrals"</h4><h4>14.6, "Cylindrical Coordinates"</h4><h4>14.7, "Spherical Coordinates"</h4><h4>14.8, "Change of Variables in Multiple Integrals"</h4><h3>Chapter 15: Vector Calculus</h3><h4>15.1, "Vector Fields"</h4><h4>15.2, "Line Integrals"</h4><h4>15.3, "Independence of Path and Conservative Vector Fields"</h4><h4>15.4, "Green's Theorem"</h4><h4>15.5, "Curl and Divergence"</h4><h4>15.6, "Surface Integrals"</h4><h4>15.7, "The Divergence Theorem"</h4><h4>15.8, "Stokes' Theorem"</h4><h4>15.9, "Applications of Vector Calculus"</h4><h3>Chapter 16: Second Order Differential Equations</h3><h4>16.1, Second-Order Equations With Constant Coefficients"</h4><h4>16.2, "Nonhomogeneous Equations: Undetermined Coefficients"</h4><h4>16.3, "Applications of Second-Order Equations"</h4><h4>16.4, "Power Series Solutions of Differential Equations"</h4><h4>Appendix A: Proofs of Selected Theorems</h4><h4>Appendix B: Answers to Odd-Numbered Exercises</h4>