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| 1709 | 20.1 >>> The Divergence of a Vector Field |
1709 | 20.1 >>> The Divergence of a Vector Field |
| 1710 | 20.2 >>> The Divergence Theorem |
1710 | 20.2 >>> The Divergence Theorem |
| 1711 | 20.3 >>> The Curl of a Vector Field |
1711 | 20.3 >>> The Curl of a Vector Field |
| 1712 | 20.4 >>> Stokes' Theorem |
1712 | 20.4 >>> Stokes' Theorem |
| 1713 | 20.5 >>> The Three Fundamental Theorems |
1713 | 20.5 >>> The Three Fundamental Theorems |
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1714 | |
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1715 | TitleText('Calculus: Early Transcendentals') |
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1716 | EditionText('1') |
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1717 | AuthorText('Rogawski') |
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1718 | |
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1719 | 1 >>> Precalculus Review |
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1720 | 1.1 >>> Real Numbers Functions, Equations and Graphs |
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1721 | 1.2 >>> Linear and Quadratic Functions |
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1722 | 1.3 >>> The Basic Classes of Functions |
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1723 | 1.4 >>> Trigonometric Functions |
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1724 | 1.5 >>> Inverse Functions |
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1725 | 1.6 >>> Exponential and Logarithmic Functions |
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1726 | 1.7 >>> Technology: Calculators and Computers |
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1727 | 2 >>> Limits |
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1728 | 2.1 >>> Limits, Rates of Change, and Tangent Lines |
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1729 | 2.2 >>> Limits: A Numerical and Graphical Approach |
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1730 | 2.3 >>> Basic Limit Laws |
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1731 | 2.4 >>> Limits and Continuity |
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1732 | 2.5 >>> Evaluating Limits Algebraically |
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1733 | 2.6 >>> Trigonometric Limits |
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1734 | 2.7 >>> Intermediate Value Theorem |
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1735 | 2.8 >>> The Formal Definition of a Limit |
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1736 | 3 >>> Differentiation |
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1737 | 3.1 >>> Definition of the Derivative |
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1738 | 3.2 >>> The Derivative as a Function |
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1739 | 3.3 >>> Product and Quotient Rules |
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1740 | 3.4 >>> Rates of Change |
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1741 | 3.5 >>> Higher Derivatives |
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1742 | 3.6 >>> Derivatives of Trigonometric Functions |
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1743 | 3.7 >>> The Chain Rule |
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1744 | 3.8 >>> Implicit Differentiation |
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1745 | 3.9 >>> Derivatives of Inverse Functions |
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1746 | 3.10 >>> Derivatives of Logarithmic Functions |
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1747 | 3.11 >>> Related Rates |
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1748 | 4 >>> Applications of the Derivative |
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1749 | 4.1 >>> Linear Approximation and Applications |
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1750 | 4.2 >>> Extreme Values |
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1751 | 4.3 >>> The Mean Value Theorem and Monotonicity |
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1752 | 4.4 >>> The Shape of a Graph |
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1753 | 4.5 >>> Graph Sketching and Asymptotes |
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1754 | 4.6 >>> Applied Optimization |
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1755 | 4.7 >>> L'Hopital's Rule |
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1756 | 4.8 >>> Newton's Method |
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1757 | 4.9 >>> Antiderivatives |
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1758 | 5 >>> The Integral |
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1759 | 5.1 >>> Approximating and Computing Area |
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1760 | 5.2 >>> The Definite Integral |
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1761 | 5.3 >>> The Fundamental Theorem of Calculus, Part I |
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1762 | 5.4 >>> The Fundamental Theorem of Calculus, Part II |
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1763 | 5.5 >>> Net or Total Change as the Integral of a Rate |
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1764 | 5.6 >>> Substitution Method |
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1765 | 5.7 >>> Integrals of Exponential and Logarithmic Functions |
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1766 | 5.8 >>> Exponential Growth and Decay |
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1767 | 6 >>> Applications of the Integral |
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1768 | 6.1 >>> Area Between Two Curves |
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1769 | 6.2 >>> Setting Up Integrals: Volumes, Density, Average Value |
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1770 | 6.3 >>> Volumes of Revolution |
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1771 | 6.4 >>> The Method of Cylindrical Shells |
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1772 | 6.5 >>> Work and Energy |
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1773 | 7 >>> Techniques of Integration |
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1774 | 7.1 >>> Numerical Integration |
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1775 | 7.2 >>> Integration by Parts |
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1776 | 7.3 >>> Trigonometric Integrals |
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1777 | 7.4 >>> Trigonometric Substitution |
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1778 | 7.5 >>> Integrals of Hyperbolic and Inverse Hyperbolic Functions |
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1779 | 7.6 >>> The Method of Partial Fractions |
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1780 | 7.7 >>> Improper Integrals |
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1781 | 8 >>> Further Applications of the Integral and Taylor Polynomials |
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1782 | 8.1 >>> Arc Length and Surface Area |
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1783 | 8.2 >>> Fluid Pressure and Force |
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1784 | 8.3 >>> Center of Mass |
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1785 | 8.4 >>> Taylor Polynomials |
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1786 | 9 >>> Introduction to Differential Equations |
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1787 | 9.1 >>> Separable Equations |
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1788 | 9. 2 Models Involving y' = k(y-b) |
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1789 | 9. 3 Graphical and Numerical Methods |
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1790 | 9.4 >>> The Logistic Equation |
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1791 | 9. 5 First-Order Linear Equations |
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1792 | 10 >>> Infinite Series |
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1793 | 10.1 >>> Sequences |
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1794 | 10.2 >>> Summing an Infinite Series |
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1795 | 10.3 >>> Convergence of Series with Positive Terms |
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1796 | 10.4 >>> Absolute and Conditional Convergence |
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1797 | 10.5 >>> The Ratio and Root Tests |
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1798 | 10.6 >>> Power Series |
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1799 | 10.7 >>> Taylor Series |
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1800 | 11 >>> Parametric Equations, Polar Coordinates, and Conic Sections |
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1801 | 11.1 >>> Parametric Equations |
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1802 | 11.2 >>> Arc Length and Speed |
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1803 | 11.3 >>> Polar Coordinates |
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1804 | 11.4 >>> Area and Arc Length in Polar Coordinates |
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1805 | 11.5 >>> Conic Sections |
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1806 | 12 >>> Vector Geometry |
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1807 | 12.1 >>> Vectors in the Plane |
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1808 | 12.2 >>> Vectors in Three Dimensions |
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1809 | 12.3 >>> Dot Product and the Angle Between Two Vectors |
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1810 | 12.4 >>> The Cross Product |
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1811 | 12.5 >>> Planes in Three-Space |
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1812 | 12.6 >>> Survey of Quadric Surfaces |
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1813 | 12.7 >>> Cylindrical and Spherical Coordinates |
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1814 | 13 >>> Calculus of Vector-Valued Functions |
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1815 | 13.1 >>> Vector-Valued Functions |
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1816 | 13.2 >>> Calculus of Vector-Valued Functions |
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1817 | 13.3 >>> Arc Length and Speed |
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1818 | 13.4 >>> Curvature |
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1819 | 13.5 >>> Motion in Three-Space |
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1820 | 13.6 >>> Planetary Motion According to Kepler and Newton |
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1821 | 14 >>> Differentiation in Several Variables |
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1822 | 14.1 >>> Functions in Two or More Variables |
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1823 | 14.2 >>> Limits and Continuity in Several Variables |
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1824 | 14.3 >>> Partial Derivatives |
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1825 | 14.4 >>> Linear Approximation, Differentiability, and Tangent Planes |
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1826 | 14.5 >>> The Gradient and Directional Derivatives |
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1827 | 14.6 >>> The Chain Rule |
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1828 | 14.7 >>> Optimization in Several Variables |
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1829 | 14.8 >>> Lagrange Multipliers: Optimizing with a Constraint |
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1830 | 15 >>> Multiple Integration |
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1831 | 15.1 >>> Integrals in Several Variables |
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1832 | 15.2 >>> Double Integrals over More General Regions |
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1833 | 15.3 >>> Triple Integrals |
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1834 | 15.4 >>> Integration in Polar, Cylindrical, and Spherical Coordinates |
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1835 | 15.5 >>> Change of Variables |
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1836 | 16 >>> Line and Surface Integrals |
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1837 | 16.1 >>> Vector Fields |
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1838 | 16.2 >>> Line Integrals |
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1839 | 16.3 >>> Conservative Vector Fields |
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1840 | 16.4 >>> Parametrized Surfaces and Surface Integrals |
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1841 | 16.5 >>> Integrals of Vector Fields |
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1842 | 17 >>> Fundamental Theorems of Vector Analysis |
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1843 | 17.1 >>> Green's Theorem |
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1844 | 17.2 >>> Stokes' Theorem |
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1845 | 17.3 >>> Divergence Theorem |
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