Book

Ayres, Frank, 1901-1994.

Schaum's outlines calculus / Frank Ayres, Jr., PhD, Former Professor and Head of the Department of Mathematics, Dickinson College, Elliot Mendelson, PhD, Professor of Mathematics, Queens College.

Sixth edition.

New York : McGraw-Hill, [2013]

xii, 534 pages : illustrations ; 28 cm.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

Schaum's outlines

Schaum's outline series.

Calculus -- Outlines, syllabi, etc.

Calculus -- Problems, exercises, etc.

Calculus.

Outlines and syllabi.

Problems and exercises.

Outlines and syllabi.

Problems and exercises.

Mendelson, Elliott.

Schaum's outline of theory and problems of differential and integral calculus

Calculus

Revision of: Schaum's outline of theory and problems of differential and integral calculus. 3rd ed. c1990.

Includes index.

Linear Coordinate Systems. Absolute Value. Inequalities -- Linear Coordinate System -- Finite Intervals -- Infinite Intervals -- Inequalities -- Rectangular Coordinate Systems -- Coordinate Axes -- Coordinates -- Quadrants -- The Distance Formula -- The Midpoint Formulas -- Proofs of Geometric Theorems -- 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 -- Circles -- Equations of Circles -- The Standard Equation of a Circle -- Equations and Their Graphs -- The Graph of an Equation -- Parabolas -- Ellipses -- Hyperbolas -- Conic Sections -- Functions -- Limits -- Limit of a Function -- Right and Left Limits -- Theorems on Limits -- Infinity -- Continuity -- Continuous Function -- The Derivative -- Delta Notation -- The Derivative -- Notation for Derivatives -- Differentiability -- Rules for Differentiating Functions -- Differentiation -- Composite Functions -- The Chain Rule -- Alternative Formulation of the Chain Rule -- Inverse Functions -- Higher Derivatives -- Implicit Differentiation -- Implicit Functions -- Derivatives of Higher Order -- Tangent and Normal Lines -- The Angles of Intersection -- Law of the Mean. Increasing and Decreasing Functions -- Relative Maximum and Minimum -- Increasing and Decreasing Functions -- 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 -- 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 of y=f(x) -- Review of Trigonometry -- Angle Measure -- Directed Angles -- Sine and Cosine Functions -- 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 -- Inverse Trigonometric Functions -- The Derivative of sin-1 x -- The Inverse Cosine Function -- The Inverse Tangent Function -- Rectilinear and Circular Motion -- Rectilinear -- Motion Motion Under the Influence of Gravity -- Circular Motion -- Related Rates -- Differentials. Newton's Method -- The Differential -- Newton's Method -- Antiderivatives -- Laws for Antiderivatives -- The Definite Integral. Area Under a Curve -- Sigma Notation -- Area Under a Curve -- Properties of the Definite Integral -- 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 -- The Natural Logarithm -- The Natural Logarithm -- Properties of the Natural Logarithm -- Exponential and Logarithmic Functions -- Properties of ex -- The General Exponential Function -- General Logarithmic Functions -- L'Hopital's Rule -- L'Hopital's Rule -- Indeterminate Type 0-[∞] -- Indeterminate Type [∞]- [∞] -- Indeterminate Types 0°, [∞]0, and 1[∞] -- Exponential Growth and Decay -- Half-Life -- Applications of Integration I: Area and Arc Length -- Area Between a Curve and the y Axis -- Areas Between Curves -- Arc Length -- Applications of Integration II: Volume -- Disk Formula -- Washer Method -- Cylindrical Shell Method -- Difference of Shells Formula -- Cross-Section Formula (Slicing Formula) -- Techniques of Integration I: Integration by Parts -- Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions -- Trigonometric Integrands -- Trigonometric Substitutions -- Techniques of Integration III: Integration by Partial Fractions -- Method of Partial Fractions -- Techniques of Integration IV: Miscellaneous Substitutions -- Improper Integrals -- Infinite Limits of Integration -- Discontinuities of the Integrand -- Applications of Integration III: Area of a Surface of Revolution -- Parametric Representation of Curves -- Parametric Equations -- Arc Length for a Parametric Curve -- Curvature -- Derivative of Arc Length -- Curvature -- The Radius of Curvature -- The Circle of Curvature -- The Center of Curvature -- The Evolute -- 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 -- Curvilinear Motion -- Velocity in Curvilinear Motion -- Acceleration in Curvilinear Motion -- Tangential and Normal Components of Acceleration -- Polar Coordinates -- Polar and Rectangular Coordinates -- Some Topical Polar Curves -- Angle of Inclination -- Points of Intersection -- Angle of Intersection -- The Derivative of the Arc Length -- Curvature -- Infinite Sequences -- Infinite Sequences -- Limit of a Sequence -- Monotonic Sequences -- Infinite Series -- Geometric Series -- Series with Positive Terms. The Integral Test. Comparison Tests -- Series of Positive Terms -- Alternating Series. Absolute and Conditional Convergence. The Ratio Test -- Alternating Series -- Power Series -- Power Series -- Uniform Convergence -- Taylor and Maclaurin Series. Taylor's Formula with Remainder -- Taylor and Maclaurin Series -- Applications of Taylor's Formula with Remainder -- Partial Derivatives -- Functions of Several Variables -- Limits -- Continuity -- Partial Derivatives -- Partial Derivatives of Higher Order -- Total Differential. Differentiability. Chain Rules -- Total Differential -- Differentiability -- Chain Rules -- Implicit Differentiation -- Space Vectors -- Vectors in Space -- Direction Cosines of a Vector -- Determinants -- Vector -- Perpendicular to Two Vectors -- Vector Product of Two Vectors -- Triple Scalar Product -- Triple Vector Product -- The Straight Line -- The Plane -- 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 -- Directional Derivatives. Maximum and Minimum Values -- Directional Derivatives -- Relative Maximum and Minimum Values -- Absolute Maximum and Minimum Values -- Vector Differentiation and Integration -- Vector Differentiation -- Space Curves -- Surfaces -- The Operation Δ Divergence and Curl -- Integration -- Line Integrals -- Double and Iterated Integrals -- The Double Integral -- The Iterated Integral -- Centroids and Moments of Inertia of Plane Areas -- Plane Area by Double Integration -- Centroids -- Moments of Inertia -- Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface -- Triple Integrals -- Cylindrical and Spherical Coordinates -- The Triple Integral -- Evaluation of Triple Integrals -- Centroids and Moments of Inertia -- Masses of Variable Density -- Differential Equations of First and Second Order -- Separable Differential Equations -- Homogeneous Functions -- Integrating Factors -- Second-Order Equations.

2012948439

9780071795531

0071795537

* 9780071795548

* 9780071813839

809082704

1

1

1

1

0