Elliott Mendelson

Schaum's Outline of Calculus, Seventh Edition

• Broschiertes Buch

Produktbeschreibung

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, 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. Features: * NEW to this edition: the new Schaum's app and website! * 1,105 problems solved step by step * 30 problem-solving videos online * Outline format supplies a concise guide to the standard college course in calculus * Clear, concise explanations covers all course fundamentals * Hundreds of additional practice problems * Supports the major leading textbooks in calculus * Appropriate for the following courses: Calculus I, Calculus II, Calculus III, AP Calculus, Precalculus

Produktdetails

• Verlag: McGraw-Hill Education
• 7 ed
• Erscheinungstermin: 22. Oktober 2021
• Englisch
• Abmessung: 274mm x 208mm x 30mm
• Gewicht: 1138g
• ISBN-13: 9781264258338
• ISBN-10: 126425833X
• Artikelnr.: 61681255

Autorenporträt

McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide

Inhaltsangabe

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'Hôpital's Rule    L'Hôpital'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    Supplem entary 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