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Schaum's Outline of Calculus, Seventh Edition
1 online resource (560 pages) : 382 illustrations.
Study smarter and stay on top of your calculus course with the bestselling Schaum's Outline-now with the new Schaum's app and website!. Schaum's Outline of Calculus, Seventh Edition is the go-to study guide for hundreds of thousands of high school and college students enrolled in calculus courses-including Calculus I, Calculus II, Calculus III, AP Calculus, and Precalculus. With an outline format that facilitates quick and easy review, Schaum's Outline of Calculus, Seventh Edition helps you understand basic concepts and get the extra practice you need to excel in these courses. Chapters include Linear Coordinate Systems, Functions, Limits, Rules for Differentiating Functions, Law of the Mean, Inverse Trigonometric Functions, The Definite Integral, Space Vectors, Directional Derivatives, and much, much more.
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1 Linear Coordinate Systems. Absolute Value. Inequalities. -- Linear Coordinate System -- Finite Intervals -- Infinite Intervals -- Inequalities -- Solved Problems -- Supplementary Problems -- Chapter 2 Rectangular Coordinate Systems -- Coordinate Axes -- Coordinates -- Quadrants -- The Distance Formula -- The Midpoint Formulas -- Proofs of Geometric Theorems -- Solved Problems -- Supplementary Problems -- Chapter 3 Lines -- The Steepness of a Line -- The Sign of the Slope -- Slope and Steepness -- Equations of Lines -- A Point-Slope Equation -- Slope-Intercept Equation -- Parallel Lines -- Perpendicular Lines -- Solved Problems -- Supplementary Problems -- Chapter 4 Circles -- Equations of Circles -- The Standard Equation of a Circle -- Solved Problems -- Supplementary Problems -- Chapter 5 Equations and Their Graphs -- The Graph of an Equation -- Parabolas -- Ellipses -- Hyperbolas -- Conic Sections -- Solved Problems -- Supplementary Problems -- Chapter 6 Functions -- Solved Problems -- Supplementary Problems -- Chapter 7 Limits -- Limit of a Function -- Right and Left Limits -- Theorems on Limits -- Infinity -- Solved Problems -- Supplementary Problems -- Chapter 8 Continuity -- Continuous Function -- Solved Problems -- Supplementary Problems -- Chapter 9 The Derivative -- Delta Notation -- The Derivative -- Notation for Derivatives -- Differentiability -- Solved Problems -- Supplementary Problems -- Chapter 10 Rules for Differentiating Functions -- Differentiation -- Composite Functions. The Chain Rule. -- Chain Rule -- Alternative Formulation of the Chain Rule -- Inverse Functions -- Higher Derivatives -- Solved Problems -- Supplementary Problems -- Chapter 11 Implicit Differentiation -- Implicit Functions -- Derivatives of Higher Order -- Solved Problems -- Supplementary Problems -- Chapter 12 Tangent and Normal Lines -- The Angles of Intersection -- Solved Problems -- Supplementary Problems -- Chapter 13 Law of the Mean. Increasing and Decreasing Functions. -- Relative Maximum and Minimum -- Increasing and Decreasing Functions -- Solved Problems -- Supplementary Problems -- Chapter 14 Maximum and Minimum Values -- Critical Numbers -- Second Derivative Test for Relative Extrema -- First Derivative Test -- Absolute Maximum and Minimum -- Tabular Method for Finding the Absolute Maximum and Minimum -- Solved Problems -- Supplementary Problems -- Chapter 15 Curve Sketching. Concavity. Symmetry. -- Concavity -- Points of Inflection -- Vertical Asymptotes -- Horizontal Asymptotes -- Symmetry -- Inverse Functions and Symmetry -- Even and Odd Functions -- Hints for Sketching the Graph G of y = f(x) -- Solved Problems -- Supplementary Problems -- Chapter 16 Review of Trigonometry -- Angle Measure -- Directed Angles -- Sine and Cosine Functions -- Solved Problems -- Supplementary Problems.
Chapter 17 Differentiation of Trigonometric Functions -- Continuity of cos x and sin x -- Graph of sin x -- Graph of cos x -- Other Trigonometric Functions -- Derivatives -- Other Relationships -- Graph of y = tan x -- Graph of y = sec x -- Angles Between Curves -- Solved Problems -- Supplementary Problems -- Chapter 18 Inverse Trigonometric Functions -- The Derivative of sin-1 x -- The Inverse Cosine Function -- The Inverse Tangent Function -- Solved Problems -- Supplementary Problems -- Chapter 19 Rectilinear and Circular Motion -- Rectilinear Motion -- Motion Under the Influence of Gravity -- Circular Motion -- Solved Problems -- Supplementary Problems -- Chapter 20 Related Rates -- Solved Problems -- Supplementary Problems -- Chapter 21 Differentials. Newton's Method. -- The Differential -- Definition -- Newton's Method -- Solved Problems -- Supplementary Problems -- Chapter 22 Antiderivatives -- Laws for Antiderivatives -- Solved Problems -- Supplementary Problems -- Chapter 23 The Definite Integral. Area Under a Curve. -- Sigma Notation -- Area Under a Curve -- Properties of the Definite Integral -- Solved Problems -- Supplementary Problems -- Chapter 24 The Fundamental Theorem of Calculus -- Mean Value Theorem for Integrals -- Average Value of a Function on a Closed Interval -- Fundamental Theorem of Calculus -- Change of Variable in a Definite Integral -- Solved Problems -- Supplementary Problems -- Chapter 25 The Natural Logarithm -- The Natural Logarithm -- Definition -- Properties of the Natural Logarithm -- Solved Problems -- Supplementary Problems -- Chapter 26 Exponential and Logarithmic Functions -- Definition -- Properties of ex -- The General Exponential Function -- General Logarithmic Functions -- Solved Problems -- Supplementary Problems -- Chapter 27 L'H?pital's Rule -- L'H?pital's Rule -- Indeterminate Type 0 ? 8 -- Indeterminate Type 8 - 8 -- Indeterminate Types 00, 80, and 18 -- Solved Problems -- Supplementary Problems -- Chapter 28 Exponential Growth and Decay -- Half-Life -- Solved Problems -- Supplementary Problems -- Chapter 29 Applications of Integration I: Area and Arc Length -- Area Between a Curve and the Y-Axis -- Areas Between Curves -- Arc Length -- Solved Problems -- Supplementary Problems -- Chapter 30 Applications of Integration II: Volume -- Disk Formula -- Washer Method -- Cylindrical Shell Method -- Difference of Shells Formula -- Cross-Section Formula (Slicing Formula) -- Solved Problems -- Supplementary Problems -- Chapter 31 Techniques of Integration I: Integration by Parts -- Solved Problems -- Supplementary Problems -- Chapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions -- Trigonometric Integrands -- Trigonometric Substitutions -- Solved Problems -- Supplementary Problems.
Chapter 33 Techniques of Integration III: Integration by Partial Fractions -- Method of Partial Fractions -- Solved Problems -- Supplementary Problems -- Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions -- Solved Problems -- Supplementary Problems -- Chapter 35 Improper Integrals -- Infinite Limits of Integration -- Discontinuities of the Integrand -- Solved Problems -- Supplementary Problems -- Chapter 36 Applications of Integration III: Area of a Surface of Revolution -- Solved Problems -- Supplementary Problems -- Chapter 37 Parametric Representation of Curves -- Parametric Equations -- Arc Length for a Parametric Curve -- Solved Problems -- Supplementary Problems -- Chapter 38 Curvature -- Derivative of Arc Length -- Curvature -- The Radius of Curvature -- The Circle of Curvature -- The Center of Curvature -- The Evolute -- Solved Problems -- Supplementary Problems -- Chapter 39 Plane Vectors -- Scalars and Vectors -- Sum and Difference of Two Vectors -- Components of a Vector -- Scalar Product (or Dot Product) -- Scalar and Vector Projections -- Differentiation of Vector Functions -- Solved Problems -- Supplementary Problems -- Chapter 40 Curvilinear Motion -- Velocity in Curvilinear Motion -- Acceleration in Curvilinear Motion -- Tangential and Normal Components of Acceleration -- Solved Problems -- Supplementary Problems -- Chapter 41 Polar Coordinates -- Polar and Rectangular Coordinates -- Some Typical Polar Curves -- Angle of Inclination -- Points of Intersection -- Angle of Intersection -- The Derivative of the Arc Length -- Curvature -- Solved Problems -- Supplementary Problems -- Chapter 42 Infinite Sequences -- Infinite Sequences -- Limit of a Sequence -- Monotonic Sequences -- Solved Problems -- Supplementary Problems -- Chapter 43 Infinite Series -- Geometric Series -- Solved Problems -- Supplementary Problems -- Chapter 44 Series with Positive Terms. The Integral Test. Comparison Tests. -- Series of Positive Terms -- Solved Problems -- Supplementary Problems -- Chapter 45 Alternating Series. Absolute and Conditional Convergence. The Ratio Test. -- Alternating Series -- Definition -- Solved Problems -- Supplementary Problems -- Chapter 46 Power Series -- Power Series -- Uniform Convergence -- Solved Problems -- Supplementary Problems -- Chapter 47 Taylor and Maclaurin Series. Taylor's Formula with Remainder. -- Taylor and Maclaurin Series -- Applications of Taylor's Formula with Remainder -- Solved Problems -- Supplementary Problems -- Chapter 48 Partial Derivatives -- Functions of Several Variables -- Limits -- Continuity -- Partial Derivatives -- Partial Derivatives of Higher Order -- Solved Problems -- Supplementary Problems.
Chapter 49 Total Differential. Differentiability. Chain Rules. -- Total Differential -- Differentiability -- Chain Rules -- Chain Rule (2 ? 1) -- Chain Rule (2 ? 2) -- Implicit Differentiation -- Solved Problems -- Supplementary Problems -- Chapter 50 Space Vectors -- Vectors in Space -- Direction Cosines of a Vector -- Determinants -- Vector Perpendicular to Two Vectors -- Vector Product of Two Vectors -- Triple Scalar Product -- The Straight Line -- The Plane -- Solved Problems -- Supplementary Problems -- Chapter 51 Surfaces and Curves in Space -- Planes -- Spheres -- Cylindrical Surfaces -- Ellipsoid -- Elliptic Paraboloid -- Elliptic Cone -- Hyperbolic Paraboloid -- Hyperboloid of One Sheet -- Hyperboloid of Two Sheets -- Tangent Line and Normal Plane to a Space Curve -- Tangent Plane and Normal Line to a Surface -- Surface of Revolution -- Solved Problems -- Supplementary Problems -- Chapter 52 Directional Derivatives. Maximum and Minimum Values. -- Directional Derivatives -- Relative Maximum and Minimum Values -- Absolute Maximum and Minimum Values -- Solved Problems -- Supplementary Problems -- Chapter 53 Vector Differentiation and Integration -- Vector Differentiation -- Space Curves -- Surfaces -- The Operation ? -- Divergence and Curl -- Integration -- Line Integrals -- Solved Problems -- Supplementary Problems -- Chapter 54 Double and Iterated Integrals -- The Double Integral -- The Iterated Integral -- Solved Problems -- Supplementary Problems -- Chapter 55 Centroids and Moments of Inertia of Plane Areas -- Plane Area by Double Integration -- Centroids -- Moments of Inertia -- Solved Problems -- Supplementary Problems -- Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface -- Solved Problems -- Supplementary Problems -- Chapter 57 Triple Integrals -- Cylindrical and Spherical Coordinates -- The Triple Integral -- Evaluation of Triple Integrals -- Centroids and Moments of Inertia -- Solved Problems -- Supplementary Problems -- Chapter 58 Masses of Variable Density -- Solved Problems -- Supplementary Problems -- Chapter 59 Differential Equations of First and Second Order -- Separable Differential Equations -- Homogeneous Functions -- Integrating Factors -- Second-Order Equations -- Solved Problems -- Supplementary Problems -- Appendix A Trigonometric Formulas -- Appendix B Geometric Formulas -- Index.
Electronic reproduction. New York, N.Y. : McGraw Hill, 2022. Mode of access: World Wide Web. System requirements: Web browser. Access may be restricted to users at subscribing institutions.
Mode of access: Internet via World Wide Web.
Includes bibliographical references and index.
New York, N.Y. : McGraw-Hill Education, 2022