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E-grāmata: Schaum's Outline of Calculus, Seventh Edition

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  • Formāts: 560 pages
  • Izdošanas datums: 22-Oct-2021
  • Izdevniecība: McGraw-Hill Education
  • Valoda: eng
  • ISBN-13: 9781264258345
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Schaum's Outline of Calculus, Seventh EditionPalielināt
  • Formāts: 560 pages
  • Izdošanas datums: 22-Oct-2021
  • Izdevniecība: McGraw-Hill Education
  • Valoda: eng
  • ISBN-13: 9781264258345
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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


Preface xv
Chapter 1 Linear Coordinate Systems. Absolute Value. Inequalities
1(8)
Linear Coordinate System
1(1)
Finite Intervals
2(1)
Infinite Intervals
3(1)
Inequalities
3(1)
Solved Problems
3(3)
Supplementary Problems
6(3)
Chapter 2 Rectangular Coordinate Systems
9(10)
Coordinate Axes
9(1)
Coordinates
9(1)
Quadrants
10(1)
The Distance Formula
11(1)
The Midpoint Formulas
12(1)
Proofs of Geometric Theorems
13(1)
Solved Problems
13(2)
Supplementary Problems
15(4)
Chapter 3 Lines
19(12)
The Steepness of a Line
19(1)
The Sign of the Slope
19(1)
Slope and Steepness
20(1)
Equations of Lines
21(1)
A Point-Slope Equation
22(1)
Slope-Intercept Equation
22(1)
Parallel Lines
22(1)
Perpendicular Lines
23(1)
Solved Problems
23(4)
Supplementary Problems
27(4)
Chapter 4 Circles
31(8)
Equations of Circles
31(1)
The Standard Equation of a Circle
31(2)
Solved Problems
33(3)
Supplementary Problems
36(3)
Chapter 5 Equations and Their Graphs
39(12)
The Graph of an Equation
39(1)
Parabolas
39(1)
Ellipses
40(1)
Hyperbolas
40(1)
Conic Sections
41(1)
Solved Problems
41(8)
Supplementary Problems
49(2)
Chapter 6 Functions
51(8)
Solved Problems
53(2)
Supplementary Problems
55(4)
Chapter 7 Limits
59(10)
Limit of a Function
59(1)
Right and Left Limits
60(1)
Theorems on Limits
60(1)
Infinity
60(1)
Solved Problems
61(4)
Supplementary Problems
65(4)
Chapter 8 Continuity
69(8)
Continuous Function
69(4)
Solved Problems
73(1)
Supplementary Problems
74(3)
Chapter 9 The Derivative
77(6)
Delta Notation
77(1)
The Derivative
77(1)
Notation for Derivatives
77(1)
Differentiability
78(1)
Solved Problems
78(3)
Supplementary Problems
81(2)
Chapter 10 Rules for Differentiating Functions
83(12)
Differentiation
83(1)
Composite Functions. The Chain Rule
84(1)
Chain Rule
84(1)
Alternative Formulation of the Chain Rule
84(1)
Inverse Functions
85(1)
Notation
85(1)
Higher Derivatives
86(1)
Notation
86(1)
Solved Problems
86(5)
Supplementary Problems
91(4)
Chapter 11 Implicit Differentiation
95(4)
Implicit Functions
95(1)
Derivatives of Higher Order
95(1)
Solved Problems
96(1)
Supplementary Problems
97(2)
Chapter 12 Tangent and Normal Lines
99(6)
The Angles of Intersection
100(1)
Solved Problems
100(2)
Supplementary Problems
102(3)
Chapter 13 Law of the Mean. Increasing and Decreasing Functions
105(8)
Relative Maximum and Minimum
105(2)
Increasing and Decreasing Functions
107(1)
Solved Problems
107(3)
Supplementary Problems
110(3)
Chapter 14 Maximum and Minimum Values
113(14)
Critical Numbers
113(1)
Second Derivative Test for Relative Extrema
113(1)
First Derivative Test
114(1)
Case {+,-}
114(1)
Case {-+}
114(1)
Cases {+,+} and {-,-}
114(1)
Absolute Maximum and Minimum
115(1)
Tabular Method for Finding the Absolute Maximum and Minimum
115(1)
Solved Problems
116(7)
Supplementary Problems
123(4)
Chapter 15 Curve Sketching. Concavity. Symmetry
127(12)
Concavity
127(1)
Points of Inflection
128(1)
Vertical Asymptotes
128(1)
Horizontal Asymptotes
128(1)
Symmetry
128(2)
Inverse Functions and Symmetry
130(1)
Even and Odd Functions
130(1)
Hints for Sketching the Graph G of y =f{x)
130(1)
Solved Problems
131(4)
Supplementary Problems
135(4)
Chapter 16 Review of Trigonometry
139(10)
Angle Measure
139(1)
Directed Angles
140(1)
Sine and Cosine Functions
140(4)
Solved Problems
144(3)
Supplementary Problems
147(2)
Chapter 17 Differentiation of Trigonometric Functions
149(14)
Continuity of cosx and sinjc
149(1)
Graph of sinx
150(1)
Graph of cosjc
150(2)
Other Trigonometric Functions
152(1)
Derivatives
152(1)
Other Relationships
152(1)
Graph of y = tan x
153(1)
Graph of y = sec x
154(1)
Angles Between Curves
154(1)
Solved Problems
155(4)
Supplementary Problems
159(4)
Chapter 18 Inverse Trigonometric Functions
163(10)
The Derivative of sin-1 x
163(1)
The Inverse Cosine Function
164(1)
The Inverse Tangent Function
164(3)
Solved Problems
167(2)
Supplementary Problems
169(4)
Chapter 19 Rectilinear and Circular Motion
173(6)
Rectilinear Motion
173(1)
Motion Under the Influence of Gravity
174(1)
Circular Motion
175(1)
Solved Problems
175(2)
Supplementary Problems
177(2)
Chapter 20 Related Rates
179(6)
Solved Problems
180(2)
Supplementary Problems
182(3)
Chapter 21 Differentials. Newton's Method
185(8)
The Differential
186(1)
Definition
186(1)
Newton's Method
187(1)
Solved Problems
188(2)
Supplementary Problems
190(3)
Chapter 22 Antiderivatives
193(10)
Laws for Antiderivatives
193(2)
Solved Problems
195(3)
Supplementary Problems
198(5)
Chapter 23 The Definite Integral. Area Under a Curve
203(8)
Sigma Notation
203(1)
Area Under a Curve
203(3)
Properties of the Definite Integral
206(1)
Solved Problems
207(2)
Supplementary Problems
209(2)
Chapter 24 The Fundamental Theorem of Calculus
211(8)
Mean Value Theorem for Integrals
211(1)
Average Value of a Function on a Closed Interval
211(1)
Fundamental Theorem of Calculus
212(1)
Change of Variable in a Definite Integral
212(1)
Solved Problems
213(2)
Supplementary Problems
215(4)
Chapter 25 The Natural Logarithm
219(8)
The Natural Logarithm
219(1)
Definition
219(1)
Properties of the Natural Logarithm
220(2)
Solved Problems
222(2)
Supplementary Problems
224(3)
Chapter 26 Exponential and Logarithmic Functions
227(8)
Definition
227(1)
Properties of ex
227(2)
Definition
228(1)
The General Exponential Function
229(1)
Definition
229(1)
General Logarithmic Functions
230(1)
Definition
230(1)
Solved Problems
231(1)
Supplementary Problems
232(3)
Chapter 27 L'Hopital's Rule
235(8)
L'Hopital's Rule
235(1)
Indeterminate Type 0 ∞
236(1)
Indeterminate Type ∞- ∞
236(1)
Indeterminate Types 0°, ∞° and 1∞
236(1)
Solved Problems
237(3)
Supplementary Problems
240(3)
Chapter 28 Exponential Growth and Decay
243(6)
Half-Life
243(1)
Solved Problems
244(2)
Supplementary Problems
246(3)
Chapter 29 Applications of Integration I: Area and Arc Length
249(10)
Area Between a Curve and the Y-Axis
249(1)
Areas Between Curves
250(1)
Arc Length
251(2)
Solved Problems
253(3)
Supplementary Problems
256(3)
Chapter 30 Applications of Integration II: Volume
259(16)
Disk Formula
259(2)
Washer Method
261(1)
Cylindrical Shell Method
262(1)
Difference of Shells Formula
262(1)
Cross-Section Formula (Slicing Formula)
263(1)
Solved Problems
264(5)
Supplementary Problems
269(6)
Chapter 31 Techniques of Integration I: Integration by Parts
275(8)
Solved Problems
277(3)
Supplementary Problems
280(3)
Chapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions
283(14)
Trigonometric Integrands
283(2)
Trigonometric Substitutions
285(2)
Solved Problems
287(5)
Supplementary Problems
292(5)
Chapter 33 Techniques of Integration III: Integration by Partial Fractions
297(10)
Method of Partial Fractions
298(4)
Case I
298(1)
Case II
299(2)
Case III
301(1)
Case IV
302(1)
Solved Problems
302(2)
Supplementary Problems
304(3)
Chapter 34 Techniques of Integration IV: Miscellaneous Substitutions
307(6)
Solved Problems
307(3)
Supplementary Problems
310(3)
Chapter 35 Improper Integrals
313(8)
Infinite Limits of Integration
313(1)
Discontinuities of the Integrand
313(1)
Solved Problems
314(4)
Supplementary Problems
318(3)
Chapter 36 Applications of Integration III: Area of a Surface of Revolution
321(6)
Solved Problems
321(4)
Supplementary Problems
325(2)
Chapter 37 Parametric Representation of Curves
327(6)
Parametric Equations
327(1)
(37.1) First Derivative
328(1)
(37.2) Second Derivative
328(1)
Arc Length for a Parametric Curve
328(1)
Solved Problems
328(2)
Supplementary Problems
330(3)
Chapter 38 Curvature
333(10)
Derivative of Arc Length
333(1)
Curvature
334(1)
The Radius of Curvature
334(1)
The Circle of Curvature
334(1)
The Center of Curvature
335(1)
The Evolute
335(1)
Solved Problems
335(5)
Supplementary Problems
340(3)
Chapter 39 Plane Vectors
343(12)
Scalars and Vectors
343(1)
Sum and Difference of Two Vectors
343(1)
Components of a Vector
344(1)
Scalar Product (or Dot Product)
345(1)
Scalar and Vector Projections
346(1)
Differentiation of Vector Functions
346(1)
Solved Problems
347(5)
Supplementary Problems
352(3)
Chapter 40 Curvilinear Motion
355(8)
Velocity in Curvilinear Motion
355(1)
Acceleration in Curvilinear Motion
355(1)
Tangential and Normal Components of Acceleration
356(1)
Solved Problems
357(4)
Supplementary Problems
361(2)
Chapter 41 Polar Coordinates
363(14)
Polar and Rectangular Coordinates
364(1)
Some Typical Polar Curves
364(1)
Angle of Inclination
365(1)
Points of Intersection
365(1)
Angle of Intersection
366(1)
The Derivative of the Arc Length
367(1)
Curvature
367(1)
Solved Problems
367(6)
Supplementary Problems
373(4)
Chapter 42 Infinite Sequences
377(8)
Infinite Sequences
377(1)
Limit of a Sequence
377(2)
Monotonic Sequences
379(1)
Solved Problems
380(2)
Supplementary Problems
382(3)
Chapter 43 Infinite Series
385(6)
Geometric Series
385(2)
Solved Problems
387(2)
Supplementary Problems
389(2)
Chapter 44 Series with Positive Terms. The Integral Test. Comparison Tests
391(10)
Series of Positive Terms
391(2)
Solved Problems
393(3)
Supplementary Problems
396(5)
Chapter 45 Alternating Series. Absolute and Conditional Convergence. The Ratio Test
401(8)
Alternating Series
401(1)
Definition
402(1)
Solved Problems
403(3)
Supplementary Problems
406(3)
Chapter 46 Power Series
409(14)
Power Series
409(2)
Uniform Convergence
411(3)
Solved Problems
414(5)
Supplementary Problems
419(4)
Chapter 47 Taylor and Maclaurin Series. Taylor's Formula with Remainder
423(10)
Taylor and Maclaurin Series
423(2)
Applications of Taylor's Formula with Remainder
425(2)
Solved Problems
427(2)
Supplementary Problems
429(4)
Chapter 48 Partial Derivatives
433(10)
Functions of Several Variables
433(1)
Limits
433(1)
Continuity
434(1)
Partial Derivatives
434(1)
Partial Derivatives of Higher Order
435(1)
Solved Problems
435(4)
Supplementary Problems
439(4)
Chapter 49 Total Differential. Differentiability. Chain Rules
443(12)
Total Differential
443(1)
Differentiability
444(1)
Chain Rules
444(1)
Chain Rule (2 → 1)
444(1)
Chain Rule (2 → 2)
445(1)
Implicit Differentiation
446(1)
Solved Problems
446(5)
Supplementary Problems
451(4)
Chapter 50 Space Vectors
455(16)
Vectors in Space
455(1)
Direction Cosines of a Vector
456(1)
Determinants
457(1)
Vector Perpendicular to Two Vectors
457(1)
Vector Product of Two Vectors
457(2)
Triple Scalar Product
459(1)
Triple Vector Product
460(1)
The Straight Line
460(1)
The Plane
461(1)
Solved Problems
461(6)
Supplementary Problems
467(4)
Chapter 51 Surfaces and Curves in Space
471(12)
Planes
471(1)
Spheres
471(1)
Cylindrical Surfaces
471(1)
Ellipsoid
472(1)
Elliptic Paraboloid
472(1)
Elliptic Cone
473(1)
Hyperbolic Paraboloid
473(1)
Hyperboloid of One Sheet
473(1)
Hyperboloid of Two Sheets
474(1)
Tangent Line and Normal Plane to a Space Curve
475(1)
Tangent Plane and Normal Line to a Surface
475(1)
Surface of Revolution
476(1)
Solved Problems
477(3)
Supplementary Problems
480(3)
Chapter 52 Directional Derivatives. Maximum and Minimum Values
483(8)
Directional Derivatives
483(1)
Relative Maximum and Minimum Values
484(1)
Absolute Maximum and Minimum Values
484(1)
Solved Problems
485(4)
Supplementary Problems
489(2)
Chapter 53 Vector Differentiation and Integration
491(14)
Vector Differentiation
491(1)
Space Curves
492(1)
Surfaces
493(1)
The Operation V
494(1)
Divergence and Curl
495(1)
Integration
496(1)
Line Integrals
496(1)
Solved Problems
497(5)
Supplementary Problems
502(3)
Chapter 54 Double and Iterated Integrals
505(8)
The Double Integral
505(1)
The Iterated Integral
506(1)
Solved Problems
507(4)
Supplementary Problems
511(2)
Chapter 55 Centroids and Moments of Inertia of Plane Areas
513(8)
Plane Area by Double Integration
513(1)
Centroids
513(1)
Moments of Inertia
514(1)
Solved Problems
514(5)
Supplementary Problems
519(2)
Chapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface
521(10)
Solved Problems
521(6)
Supplementary Problems
527(4)
Chapter 57 Triple Integrals
531(12)
Cylindrical and Spherical Coordinates
531(1)
The Triple Integral
532(1)
Evaluation of Triple Integrals
532(1)
Centroids and Moments of Inertia
533(1)
Solved Problems
533(6)
Supplementary Problems
539(4)
Chapter 58 Masses of Variable Density
543(6)
Solved Problems
543(4)
Supplementary Problems
547(2)
Chapter 59 Differential Equations of First and Second Order
549(12)
Separable Differential Equations
549(1)
Homogeneous Functions
549(1)
Integrating Factors
549(1)
Second-Order Equations
550(1)
Solved Problems
550(7)
Supplementary Problems
557(4)
Appendix A Trigonometric Formulas 561(2)
Appendix B Geometric Formulas 563(2)
Index 565
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