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

Includes index.

1: Linear Coordinate Systems: Absolute Value: Inequalities -- Linear coordinate system -- Finite intervals -- Infinite intervals -- Inequalities -- 2: Rectangular Coordinate Systems -- Coordinate axes -- Coordinates -- Quadrants -- Distance formula -- Midpoint formulas -- Proofs of geometric theorems -- 3: Lines -- Steepness of a line -- Sign of the slope -- Slope and steepness -- Equations of lines -- Point-slope equation -- Slope-intercept equation -- Parallel lines -- Perpendicular lines -- 4: Circles -- Equations of circles -- Standard equation of a circle -- 5: Equations And Their Graphs -- Graph of an equation -- Parabolas -- Ellipses -- Hyperbolas -- Conic sections -- 6: Functions -- 7: Limits -- Limit of a function -- Right and left limits -- Theorems on limits -- Infinity -- 8: Continuity -- Continuous function -- 9: Derivative -- Delta notation -- Derivative -- Notation for derivatives -- Differentiability -- 10: Rules For Differentiating Functions -- Differentiation -- Composite functions-the chain rule -- Alternative formulation of the chain rule -- Inverse functions -- Higher derivatives -- 11: Implicit Differentiation -- Implicit functions -- Derivatives of higher order -- 12: Tangent And Normal Lines -- Angles of intersection -- 13: Law Of The Mean: Increasing And Decreasing Functions -- Relative maximum and minimum -- Increasing and decreasing functions -- 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 --

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 of y=f(x) -- 16: Review Of Trigonometry -- Angle measure -- Directed angles -- Sine and cosine functions -- 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 -- 18: Inverse Trigonometric Functions -- Derivative of sin-1 x -- Inverse cosine function -- Inverse tangent function -- 19: Rectilinear And Circular Motion -- Rectilinear motion -- Motion under the influence of gravity -- Circular motion -- 20: Related Rates -- 21: Differentials: Newton's Method -- Differential -- Newton's method -- 22: Antiderivatives -- Laws for antiderivatives -- 23: Definite Integral: Area Under A Curve -- Sigma notation -- Area under a curve -- Properties of the definite integral -- 24: 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 -- 25: Natural Logarithm -- Natural logarithm -- Properties of the natural logarithm -- 26: Exponential And Logarithmic Functions -- Properties of e to the power of x -- General exponential function -- General logarithmic functions --

27: L'Hopital's Rule -- L'Hospital's Rule -- Indeterminate type 0-oo -- Indeterminate type oo-oo -- Indeterminate types 0, oo, and 1 -- 28: Exponential Growth And Decay -- Half-life -- 29: Applications Of Integration I: Area And Arc Length -- Area between a curve and the y axis -- Areas between curves -- Arc length -- 30: Applications Of Integration II: Volume -- Disk formula -- Washer method -- Cylindrical shell method -- Difference of shells formula -- Cross-section formula (slicing formula) -- 31: Techniques Of Integration I: Integration By Parts -- 32: Techniques Of Integration II: Trigonometric Integrands And Trigonometric Substitutions -- Trigonometric integrands -- Trigonometric substitutions -- 33: Techniques Of Integration III: Integration By Partial Fractions -- Method of partial fractions -- 34: Techniques Of Integration IV: Miscellaneous Substitutions -- 35: Improper Integrals -- Infinite limits of integration -- Discontinuities of the integrand -- 36: Applications Of Integration III: Area Of A Surface Of Revolution -- 37: Parametric Representation Of Curves -- Parametric equations -- Arc length for a parametric curve -- 38: Curvature -- Derivative of arc length -- Curvature -- Radius of curvature -- Circle of curvature -- Center of curvature -- Evolute -- 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 -- 40: Curvilinear Motion -- Velocity in curvilinear motion -- Acceleration in curvilinear motion -- Tangential and normal components of acceleration -- 41: Polar Coordinates -- Polar and rectangular coordinates -- Some typical polar curves -- Angle of inclination -- Points of intersection -- Angle of intersection -- Derivative of the arc length -- Curvature -- 42: Infinite Sequences -- Infinite sequences -- Limit of a sequence -- Monotonic sequences -- 43: Infinite Series -- Geometric series --

44: Series With Positive Terms: The Integral Test: Comparison Tests -- Series of positive terms -- 45: Alternating Series: Absolute And Conditional Convergence: The Ratio Test -- Alternating series -- 46: Power Series -- Power series -- Uniform convergence -- 47: Taylor And Maclaurin Series: Taylor's Formula With Remainder -- Taylor and Maclaurin series -- Applications of Taylor's formula with remainder -- 48: Partial Derivatives -- Functions of several variables -- Limits -- Continuity -- Partial derivatives -- Partial derivatives of higher order -- 49: Total Differential: Differentiability: Chain Rules -- Total differential -- Differentiability -- Chain rules -- Implicit differentiation -- 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 -- Triple vector product -- Straight line -- Plane -- 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 -- 52: Directional Derivatives: Maximum And Minimum Values -- Directional derivatives -- Relative maximum and minimum values -- Absolute maximum and minimum values -- 53: Vector Differentiation And Integration -- Vector differentiation -- Space curves -- Surfaces -- Operation V -- Divergence and curl -- Integration -- Line integrals -- 54: Double And Iterated Integrals -- Double integral -- Iterated integral -- 55: Centroids And Moments Of Inertia Of Plane Areas -- Plane area by double integration -- Centroids -- Moments of inertia -- 56: Double Integration Applied To Volume Under A Surface And The Area Of A Curved Surface -- 57: Triple Integrals -- Cylindrical and spherical coordinates -- Triple integral -- Evaluation of triple integrals -- Centroids and moments of inertia -- 58: Masses Of Variable Density -- 59: Differential Equations Of First And Second Order -- Separable differential equations -- Homogeneous functions -- Integrating factors -- Second-order equations -- Appendix A -- Appendix B -- Index.