Student Solutions Manual for Calculus

Häftad, Engelska, 2006

Av Dale Varberg, Edwin Purcell, Steve Rigdon

1 279 kr

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Fully worked solutions to odd-numbered exercises.

Produktinformation

Utgivningsdatum2006-12-20
Mått10 x 10 x 10 mm
Vikt1 111 g
SpråkEngelska
Antal sidor496
Upplaga9
FörlagPearson Education
EAN9780131469662

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0 PRELIMINARIES0.1 Real Numbers, Logic and Estimation0.2 Inequalities and Absolute Values0.3 The Rectangular Coordinate System0.4 Graphs of Equations0.5 Functions and Their Graphs0.6 Operations on Functions0.7 The Trigonometric Functions 1 LIMITS1.1 Introduction to Limits1.2 Rigorous Study of Limits1.3 Limit Theorems1.4 Limits Involving Trigonometric Functions1.5 Limits at Infinity, Infinite Limits1.6 Continuity of Functions1.7 Chapter Review 2 THE DERIVATIVE2.1 Two Problems with One Theme2.2 The Derivative2.3 Rules for Finding Derivatives2.4 Derivatives of Trigonometric Functions2.5 The Chain Rule2.6 Higher-Order Derivatives2.7 Implicit Differentiation2.8 Related Rates2.9 Differentials and Approximations2.10 Chapter Review 3 APPLICATIONS OF THE DERIVATIVE3.1 Maxima and Minima3.2 Monotonicity and Concavity3.3 Local Extrema and Extrema on Open Intervals3.4 Graphing Functions Using Calculus3.6 The Mean Value Theorem for Derivatives3.7 Solving Equations Numerically3.8 Antiderivatives3.9 Introduction to Differential Equations 4 THE DEFINITE INTEGRAL4.1 Introduction to Area4.2 The Definite Integral4.3 The 1st Fundamental Theorem of Calculus4.4 The 2nd Fundamental Theorem of Calculusand the Method of Substitution4.5 The Mean Value Theorem for Integrals & the Use of Symmetry4.6 Numerical Integration4.7 Chapter Review 5 APPLICATIONS OF THE INTEGRAL5.1 The Area of a Plane Region5.2 Volumes of Solids: Slabs, Disks, Washers5.3 Volumes of Solids of Revolution: Shells5.4 Length of a Plane Curve5.5 Work and Fluid Pressure5.6 Moments, Center of Mass5.7 Probability and Random Variables5.8 Chapter Review 6 TRANSCENDENTAL FUNCTIONS6.1 The Natural Logarithm Function6.2 Inverse Functions and Their Derivatives6.3 The Natural Exponential Function6.4 General Exponential & Logarithmic Functions6.5 Exponential Growth and Decay6.6 First-Order Linear Differential Equations6.7 Approximations for Differential Equations6.8 Inverse Trig Functions & Their Derivatives6.9 The Hyperbolic Functions & Their Inverses6.10 Chapter Review 7 TECHNIQUES OF INTEGRATION7.1 Basic Integration Rules7.2 Integration by Parts7.3 Some Trigonometric Integrals7.4 Rationalizing Substitutions7.5 The Method of Partial Fractions7.6 Strategies for Integration7.7 Chapter Review 8 INDETERMINATE FORMS & IMPROPER INTEGRALS8.1 Indeterminate Forms of Type 0/08.2 Other Indeterminate Forms8.3 Improper Integrals: Infinite Limits of Integration8.4 Improper Integrals: Infinite Integrands8.5 Chapter Review 9 INFINITE SERIES9.1 Infinite Sequences9.2 Infinite Series9.3 Positive Series: The Integral Test9.4 Positive Series: Other Tests9.5 Alternating Series, Absolute Convergence,and Conditional Convergence9.6 Power Series9.7 Operations on Power Series9.8 Taylor and Maclaurin Series9.9 The Taylor Approximation to a Function9.10 Chapter Review 10 CONICS AND POLAR COORDINATES10.1 The Parabola10.2 Ellipses and Hyperbolas10.3 Translation and Rotation of Axes10.4 Parametric Representation of Curves10.5 The Polar Coordinate System10.6 Graphs of Polar Equations10.7 Calculus in Polar Coordinates10.8 Chapter Review 11 GEOMETRY IN SPACE, VECTORS11.1 Cartesian Coordinates in Three-Space11.2 Vectors11.3 The Dot Product11.4 The Cross Product11.5 Vector Valued Functions & Curvilinear Motion11.6 Lines in Three-Space11.7 Curvature and Components of Acceleration11.8 Surfaces in Three Space11.9 Cylindrical and Spherical Coordinates11.10 Chapter Review 12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES12.1 Functions of Two or More Variables12.2 Partial Derivatives12.3 Limits and Continuity12.4 Differentiability12.5 Directional Derivatives and Gradients12.6 The Chain Rule12.7 Tangent Planes, Approximations12.8 Maxima and Minima12.9 Lagrange Multipliers12.10 Chapter Review 13 MULTIPLE INTEGRATION13.1 Double Integrals over Rectangles13.2 Iterated Integrals13.3 Double Integrals over Nonrectangular Regions13.4 Double Integrals in Polar Coordinates13.5 Applications of Double Integrals13.6 Surface Area13.7 Triple Integrals (Cartesian Coordinates)13.8 Triple Integrals (Cyl & Sph Coordinates)13.9 Change of Variables in Multiple Integrals13.1 Chapter Review 14 VECTOR CALCULUS14.1 Vector Fields14.2 Line Integrals14.3 Independence of Path14.4 Green's Theorem in the Plane14.5 Surface Integrals14.6 Gauss's Divergence Theorem14.7 Stokes's Theorem14.8 Chapter Review APPENDIXA.1 Mathematical InductionA.2 Proofs of Several TheoremsA.3 A Backward Look