Schaum's Outline of Calculus, 5ed : Schaum's Outline of Calc, 5ed

Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. 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. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! An enhanced ebook is now available with 30 videos of professors showing you exactly how to solve calculus problems! Select the Kindle Edition with Audio/Video from the available formats. Schaum's Outlines-Problem Solved. From The Publisher: Schaum's Has Satisfied Students For 50 Years. Now Schaum's Biggest Sellers Are In New Editions! For Half A Century, More Than 40 Million Students Have Trusted Schaum's To Help Them Study Faster, Learn Better, And Get Top Grades. Now Schaum's Celebrates Its 50th Birthday With A Brand-new Look, A New Format With Hundreds Of Practice Problems, And Completely Updated Information To Conform To The Latest Developments In Every Field Of Study. Schaum's Outlines-problem Solved. More Than 1.3 Million Sold! This Review Of Standard College Courses In Calculus Has Been Updated To Reflect The Latest Course Scope And Sequences. The New Edition Includes Green's And Stokes' Theorems, As Well As Explanations Of Tough Topics Such As Delta-epsilon Proofs And Riemann Integrals. 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. Frank Ayres, Jr., Elliot Mendelson. Rev. Ed. Of: Schaum's Outline Of Theory And Problems Of Differential And Integral Calculus. 3rd Ed. C1990. Includes Index. Contents......Page 9 Linear Coordinate System......Page 15 Finite Intervals......Page 16 Inequalities......Page 17 Coordinates......Page 23 Quadrants......Page 24 The Distance Formula......Page 25 The Midpoint Formulas......Page 26 Proofs of Geometric Theorems......Page 27 The Sign of the Slope......Page 32 Slope and Steepness......Page 33 Equations of Lines......Page 34 Parallel Lines......Page 35 Perpendicular Lines......Page 36 The Standard Equation of a Circle......Page 43 Parabolas......Page 51 Hyperbolas......Page 52 Conic Sections......Page 53 Chapter 6 Functions......Page 63 Limit of a Function......Page 70 Infinity......Page 71 Continuous Function......Page 80 Notation for Derivatives......Page 87 Differentiability......Page 88 Differentiation......Page 93 Alternative Formulation of the Chain Rule......Page 94 Inverse Functions......Page 95 Higher Derivatives......Page 96 Derivatives of Higher Order......Page 104 Chapter 12 Tangent and Normal Lines......Page 107 The Angles of Intersection......Page 108 Relative Maximum and Minimum......Page 112 Increasing and Decreasing Functions......Page 114 Second Derivative Test for Relative Extrema......Page 119 First Derivative Test......Page 120 Tabular Method for Finding the Absolute Maximum and Minimum......Page 121 Concavity......Page 133 Symmetry......Page 134 Hints for Sketching the Graph of y = f (x)......Page 136 Angle Measure......Page 144 Sine and Cosine Functions......Page 145 Continuity of cos x and sin x......Page 153 Graph of cos x......Page 154 Other Relationships......Page 156 Graph of y = tan x......Page 157 Angles Between Curves......Page 158 The Derivative of sin[sup(-1)] x......Page 166 The Inverse Tangent Function......Page 167 Rectilinear Motion......Page 175 Motion Under the Influence of Gravity......Page 176 Circular Motion......Page 177 Chapter 20 Related Rates......Page 181 Chapter 21 Differentials. Newton’s Method......Page 187 The Differential......Page 188 Newton’s Method......Page 189 Laws for Antiderivatives......Page 195 Area Under a Curve......Page 204 Properties of the Definite Integral......Page 207 Average Value of a Function on a Closed Interval......Page 212 Change of Variable in a Definite Integral......Page 213 The Natural Logarithm......Page 220 Properties of the Natural Logarithm......Page 221 Properties of e[sup(x)]......Page 228 The General Exponential Function......Page 230 General Logarithmic Functions......Page 231 L’Hôpital’s Rule......Page 236 Indeterminate Types 0[sup(0)], ∞[sup(0)], and 1[sup(∞)]......Page 237 Half-Life......Page 244 Area Between a Curve and the y Axis......Page 249 Areas Between Curves......Page 250 Arc Length......Page 251 Disk Formula......Page 258 Washer Method......Page 260 Difference of Shells Formula......Page 261 Cross-Section Formula (Slicing Formula)......Page 262 Chapter 31 Techniques of Integration I: Integration by Parts......Page 273 Trigonometric Integrands......Page 280 Trigonometric Substitutions......Page 282 Chapter 33 Techniques of Integration III: Integration by Partial Fractions......Page 293 Method of Partial Fractions......Page 294 Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions......Page 302 Discontinuities of the Integrand......Page 307 Chapter 36 Applications of Integration III: Area of a Surface of Revolution......Page 315 Parametric Equations......Page 321 Arc Length for a Parametric Curve......Page 322 Derivative of Arc Length......Page 326 The Circle of Curvature......Page 327 The Evolute......Page 328 Sum and Difference of Two Vectors......Page 335 Components of a Vector......Page 336 Scalar Product (or Dot Product)......Page 337 Differentiation of Vector Functions......Page 338 Acceleration in Curvilinear Motion......Page 346 Tangential and Normal Components of Acceleration......Page 347 Chapter 41 Polar Coordinates......Page 353 Some Typical Polar Curves......Page 354 Points of Intersection......Page 355 Angle of Intersection......Page 356 Curvature......Page 357 Limit of a Sequence......Page 366 Monotonic Sequences......Page 368 Geometric Series......Page 374 Series of Positive Terms......Page 380 Alternating Series......Page 389 Power Series......Page 397 Uniform Convergence......Page 399 Taylor and Maclaurin Series......Page 410 Applications of Taylor’s Formula with Remainder......Page 412 Limits......Page 419 Partial Derivatives......Page 420 Partial Derivatives of Higher Order......Page 421 Total Differential......Page 428 Chain Rules......Page 429 Implicit Differentiation......Page 431 Vectors in Space......Page 440 Direction Cosines of a Vector......Page 441 Vector Product of Two Vectors......Page 442 Triple Scalar Product......Page 444 The Straight Line......Page 445 The Plane......Page 446 Cylindrical Surfaces......Page 455 Elliptic Paraboloid......Page 456 Hyperboloid of One Sheet......Page 457 Hyperboloid of Two Sheets......Page 458 Tangent Plane and Normal Line to a Surface......Page 459 Surface of Revolution......Page 460 Directional Derivatives......Page 466 Absolute Maximum and Minimum Values......Page 467 Vector Differentiation......Page 474 Space Curves......Page 475 Surfaces......Page 476 The Operation ∇......Page 477 Divergence and Curl......Page 478 Line Integrals......Page 479 The Double Integral......Page 488 The Iterated Integral......Page 489 Centroids......Page 495 Moments of Inertia......Page 496 Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface......Page 503 Cylindrical and Spherical Coordinates......Page 512 Evaluation of Triple Integrals......Page 513 Centroids and Moments of Inertia......Page 514 Chapter 58 Masses of Variable Density......Page 524 Integrating Factors......Page 530 Second-Order Equations......Page 531 Appendix A......Page 541 Appendix B......Page 542 C......Page 543 F......Page 544 L......Page 545 Q......Page 546 V......Page 547 Z......Page 548 Confusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. 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.This Schaum's Outline gives you: Practice problems with full explanations that reinforce knowledge; Coverage of the most up-to-date developments in your course field; In-depth review of practices and applications.Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time - and get your best test scores!Schaum's Outlines - Problem Solved. Provides an overview of the fundamentals of calculus and includes 1,105 example problems with step-by-step solutions and explanations of calculator use for solving problems