Test Bank for Multivariable Calculus 10th Edition by Ron Larson, Bruce Edwards – Ebook PDF Instant Download/Delivery: 1285060296, 978-1285060293
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ISBN 10: 1285060296
ISBN 13: 978-1285060293
Author: Ron Larson, Bruce Edwards
The Larson Calculus program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
Multivariable Calculus 10th Table of contents:
Chapter 1. Limits and Their Properties
1.1. A Preview of Calculus
1.1a. What Is Calculus? Remark Item note As you progress through this course, remember that learning calculus is just one of your goals. Your most important goal is to learn how to use calculus to model and solve real-life problems. Here are a few problem-solving strategies that may help you. Be sure you understand the question. What is given? What are you asked to find? Outline a plan. There are many approaches you could use: look for a pattern, solve a simpler problem, work backwards, draw a diagram, use technology, or any of many other approaches. Complete your plan. Be sure to answer the question. Verbalize your answer. For example, rather than writing the answer as x = 4.6 , it would be better to write the answer as, “The area of the region is as 4.6 square meters .” Look back at your work. Does your answer make sense? Is there a way you can check the reasonableness of your answer?
1.1b. The Tangent Line Problem
1.1c. The Area Problem
1.1d. Exercises
1.2. Finding Limits Graphically and Numerically
1.2a. An Introduction to Limits
1.2b. Limits that Fail to Exist
1.2c. A Formal Definition of Limit
1.2d. Exercises
1.3. Evaluating Limits Analytically
1.3a. Properties of Limits
1.3b. A Strategy for Finding Limits
1.3c. Dividing Out Technique
1.3d. Rationalizing Technique
1.3e. The Squeeze Theorem
1.3f. Exercises
1.4. Continuity and One-Sided Limits
1.4a. Continuity at a Point and on an Open Interval
1.4b. One-Sided Limits and Continuity on a Closed Interval
1.4c. Properties of Continuity
1.4d. The Intermediate Value Theorem
1.4e. Exercises
1.5. Infinite Limits
1.5a. Infinite Limits
1.5b. Vertical Asymptotes
1.5c. Exercises
1.5d. Section Project
Review Exercises
P.S. Problem Solving
Chapter 2. Differentiation
2.1. The Derivative and the Tangent Line Problem
2.1a. The Tangent Line Problem
2.1b. The Derivative of a Function
2.1c. Differentiability and Continuity
2.1d. Exercises
2.2. Basic Differentiation Rules and Rates of Change
2.2a. The Constant Rule
2.2b. The Power Rule
2.2c. The Constant Multiple Rule
2.2d. The Sum and Difference Rules
2.2e. Derivatives of the Sine and Cosine Functions
2.2f. Rates of Change
2.2g. Exercises
2.3. Product and Quotient Rules and Higher-Order Derivatives
2.3a. The Product Rule
2.3b. The Quotient Rule
2.3c. Derivatives of Trigonometric Functions
2.3d. Higher-Order Derivatives
2.3e. Exercises
2.4. The Chain Rule
2.4a. The Chain Rule
2.4b. The General Power Rule
2.4c. Simplifying Derivatives
2.4d. Trigonometric Functions and the Chain Rule
2.4e. Exercises
2.5. Implicit Differentiation
2.5a. Implicit and Explicit Functions
2.5b. Implicit Differentiation
2.5c. Exercises
2.5d. Section Project
2.6. Related Rates
2.6a. Finding Related Rates
2.6b. Problem Solving with Related Rates
2.6c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 3. Applications of Differentiation
3.1. Extrema on an Interval
3.1a. Extrema of a Function
3.1b. Relative Extrema and Critical Numbers
3.1c. Finding Extrema on a Closed Interval
3.1d. Exercises
3.2. Rolle’s Theorem and the Mean Value Theorem
3.2a. Rolle’s Theorem
3.2b. The Mean Value Theorem
3.2c. Exercises
3.3. Increasing and Decreasing Functions and the First Derivative Test
3.3a. Increasing and Decreasing Functions
3.3b. The First Derivative Test
3.3c. Exercises
3.3d. Section Project
3.4. Concavity and the Second Derivative Test
3.4a. Concavity
3.4b. Points of Inflection
3.4c. The Second Derivative Test
3.4d. Exercises
3.5. Limits at Infinity
3.5a. Limits at Infinity
3.5b. Horizontal Asymptotes
3.5c. Infinite Limits at Infinity
3.5d. Exercises
3.6. A Summary of Curve Sketching
3.6a. Analyzing the Graph of a Function
3.6b. Exercises
3.7. Optimization Problems
3.7a. Applied Minimum and Maximum Problems
3.7b. Exercises
3.7c. Section Project
3.8. Newton’s Method
3.8a. Newton’s Method
3.8b. Exercises
3.9. Differentials
3.9a. Tangent Line Approximations
3.9b. Differentials
3.9c. Error Propagation
3.9d. Calculating Differentials
3.9e. Exercises
Review Exercises
P.S. Problem Solving
Chapter 4. Integration
4.1. Antiderivatives and Indefinite Integration
4.1a. Antiderivatives
4.1b. Basic Integration Rules
4.1c. Initial Conditions and Particular Solutions
4.1d. Exercises
4.2. Area
4.2a. Sigma Notation
4.2b. Area
4.2c. The Area of a Plane Region
4.2d. Upper and Lower Sums
4.2e. Exercises
4.3. Riemann Sums and Definite Integrals
4.3a. Riemann Sums
4.3b. Definite Integrals
4.3c. Properties of Definite Integrals
4.3d. Exercises
4.4. The Fundamental Theorem of Calculus
4.4a. The Fundamental Theorem of Calculus
4.4b. The Mean Value Theorem for Integrals
4.4c. Average Value of a Function
4.4d. The Second Fundamental Theorem of Calculus
4.4e. Net Change Theorem
4.4f. Exercises
4.4g. Section Project: Demonstrating the Fundamental Theorem
4.5. Integration by Substitution
4.5a. Pattern Recognition
4.5b. Change of Variables
4.5c. The General Power Rule for Integration
4.5c. Change of Variables for Definite Integrals
4.5e. Integration of Even and Odd Functions
4.5f. Exercises
4.6. Numerical Integration
4.6a. The Trapezoidal Rule
4.6b. Simpson’s Rule
4.6c. Error Analysis
4.6d. Exercises
Review Exercises
P.S. Problem Solving
Chapter 5. Logarithmic, Exponential, and Other Transcendental Functions
5.1. The Natural Logarithmic Function: Differentiation
5.1a. The Natural Logarithmic Function
5.1b. The Number e
5.1c. The Derivative of the Natural Logarithmic Function
5.1d. Exercises
5.2. The Natural Logarithmic Function: Integration
5.2a. Log Rule for Integration
5.2b. Integrals of Trigonometric Functions
5.2c. Exercises
5.3. Inverse Functions
5.3a. Inverse Functions
5.3b. Existence of an Inverse Function
5.3c. Derivative of an Inverse Function
5.3d. Exercises
5.4. Exponential Functions: Differentiation and Integration
5.4a. The Natural Exponential Function
5.4b. Derivatives of Exponential Functions
5.4c. Integrals of Exponential Functions
5.4d. Exercises
5.5. Bases Other than e and Applications
5.5a. Bases Other than e
5.5b. Differentiation and Integration
5.5c. Applications of Exponential Functions
5.5d. Exercises
5.5e. Section Project
5.6. Inverse Trigonometric Functions: Differentiation
5.6a. Inverse Trigonometric Functions
5.6b. Derivatives of Inverse Trigonometric Functions
5.6c. Review of Basic Differentiation Rules
5.6d. Exercises
5.7. Inverse Trigonometric Functions: Integration
5.7a. Integrals Involving Inverse Trigonometric Functions
5.7b. Completing the Square
5.7c. Review of Basic Integration Rules
5.7d. Exercises
5.8. Hyperbolic Functions
5.8a. Hyperbolic Functions
5.8b. Differentiation and Integration of Hyperbolic Functions
5.8c. Inverse Hyperbolic Functions
5.8d. Inverse Hyperbolic Functions: Differentiation and Integration
5.8e. Exercises
5.8f. Section Project
Review Exercises
P.S. Problem Solving
Chapter 6. Differential Equations
6.1. Slope Fields and Euler’s Method
6.1a. General and Particular Solutions
6.1b. Slope Fields
6.1c. Euler’s Method
6.1d. Exercises
6.2. Differential Equations: Growth and Decay
6.2a. Differential Equations
6.2b. Growth and Decay Models
6.2c. Exercises
6.3. Separation of Variables and the Logistic Equation
6.3a. Separation of Variables
6.3b. Applications
6.3c. Logistic Differential Equation
6.3d. Exercises
6.4. First-Order Linear Differential Equations
6.4a. First-Order Linear Differential Equations
6.4b. Exercises
6.4c. Section Project: Weight Loss
Review Exercises
P.S. Problem Solving
Chapter 7. Applications of Integration
7.1. Area of a Region Between Two Curves
7.1a. Area of a Region Between Two Curves
7.1b. Area of a Region Between Intersecting Curves
7.1c. Integration as an Accumulation Process
7.1d. Exercises
7.2. Volume: The Disk Method
7.2a. The Disk Method
7.2b. The Washer Method
7.2c. Solids with Known Cross Sections
7.2d. Exercises
7.3. Volume: The Shell Method
7.3a. The Shell Method
7.3b. Comparison of Disk and Shell Methods
7.3c. Exercises
7.3d. Section Project: Saturn
7.4. Arc Length and Surfaces of Revolution
7.4a. Arc Length
7.4b. Area of a Surface of Revolution
7.4c. Exercises
7.5. Work
7.5a. Work Done by a Constant Force
7.5b. Work Done by a Variable Force
7.5c. Exercises
7.5d. Section Project: Tidal Energy
7.6. Moments, Centers of Mass, and Centroids
7.6a. Mass
7.6b. Center of Mass in a One-Dimensional System
7.6c. Center of Mass in a Two-Dimensional System
7.6d. Center of Mass of a Planar Lamina
7.6e. Theorem of Pappus
7.6f. Exercises
7.7. Fluid Pressure and Fluid Force
7.7a. Fluid Pressure And Fluid Force
7.7b. Exercises
Review Exercises
P.S. Problem Solving
Chapter 8. Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.1. Basic Integration Rules
8.1a. Fitting Integrands to Basic Integration Rules
8.1b. Exercises
8.2. Integration by Parts
8.2a. Integration by Parts
8.2b. Exercises
8.3. Trigonometric Integrals
8.3a. Integrals Involving Powers of Sine and Cosine
8.3b. Integrals Involving Powers of Secant and Tangent
8.3c. Integrals Involving Sine-Cosine Products with Different Angles
8.3d. Exercises
8.3e. Section Project
8.4. Trigonometric Substitution
8.4a. Trigonometric Substitution
8.4b. Applications
8.4c. Exercises
8.5. Partial Fractions
8.5a. Partial Fractions
8.5b. Linear Factors
8.5c. Quadratic Factors
8.5d. Exercises
8.6. Integration by Tables and Other Integration Techniques
8.6a. Integration by Tables
8.6b. Reduction Formulas
8.6c. Rational Functions of Sine and Cosine
8.6d. Exercises
8.7. Indeterminate Forms and L’Hôpital’s Rule
8.7a. Indeterminate Forms
8.7b. L’Hôpital’s Rule
8.7c. Exercises
8.8. Improper Integrals
8.8a. Improper Integrals with Infinite Limits of Integration
8.8b. Improper Integrals with Infinite Discontinuities
8.8c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 9. Infinite Series
9.1. Sequences
9.1a. Sequences
9.1b. Limit of a Sequence
9.1c. Pattern Recognition for Sequences
9.1d. Monotonic Sequences and Bounded Sequences
9.1e. Exercises
9.2. Series and Convergence
9.2a. Infinite Series
9.2b. Geometric Series
9.2c. n th-Term Test for Divergence
9.2d. Exercises
9.2e. Section Project: Cantor’S Disappearing Table
9.3. The Integral Test and p -Series
9.3a. The Integral Test
9.3b. p -Series and Harmonic Series
9.3c. Exercises
9.3d. Section Project: The Harmonic Series
9.4. Comparisons of Series
9.4a. Direct Comparison Test
9.4b. Limit Comparison Test
9.4c. Exercises
9.4d. Section Project: Solera Method
9.5. Alternating Series
9.5a. Alternating Series
9.5b. Alternating Series Remainder
9.5c. Absolute and Conditional Convergence
9.5d. Rearrangement of Series
9.5e. Exercises
9.6. The Ratio and Root Tests
9.6a. The Ratio Test
9.6b. The Root Test
9.6c. Strategies for Testing Series
9.6d. Exercises
9.7. Taylor Polynomials and Approximations
9.7a. Polynomial Approximations of Elementary Functions
9.7b. Taylor and Maclaurin Polynomials
9.7c. Remainder of a Taylor Polynomial
9.7d. Exercises
9.8. Power Series
9.8a. Power Series
9.8b. Radius and Interval of Convergence
9.8c. Endpoint Convergence
9.8d. Differentiation and Integration of Power Series
9.8e. Exercises
9.9. Representation of Functions by Power Series
9.9a. Geometric Power Series
9.9b. Operations with Power Series
9.9c. Exercises
9.10. Taylor and Maclaurin Series
9.10a. Taylor Series and Maclaurin Series
9.10b. Binomial Series
9.10c. Deriving Taylor Series from a Basic List
9.10d. Exercises
Review Exercises
P.S. Problem Solving
Chapter 10. Conics, Parametric Equations, and Polar Coordinates
10.1. Conics and Calculus
10.1a. Conic Sections
10.1b. Parabolas
10.1c. Ellipses
10.1d. Hyperbolas
10.1e. Exercises
10.2. Plane Curves and Parametric Equations
10.2a. Plane Curves and Parametric Equations
10.2b. Eliminating the Parameter
10.2c. Finding Parametric Equations
10.2d. The Tautochrone and Brachistochrone Problems
10.2e. Exercises
10.2f. Section Project: Cycloids
10.3. Parametric Equations and Calculus
10.3a. Slope and Tangent Lines
10.3b. Arc Length
10.3c. Area of a Surface of Revolution
10.3d. Exercises
10.4. Polar Coordinates and Polar Graphs
10.4a. Polar Coordinates
10.4b. Coordinate Conversion
10.4c. Polar Graphs
10.4d. Slope and Tangent Lines
10.4e. Special Polar Graphs
10.4f. Exercises
10.4g. Section Project
10.5. Area and Arc Length in Polar Coordinates
10.5a. Area of a Polar Region
10.5b. Points of Intersection of Polar Graphs
10.5c. Arc Length in Polar form
10.5d. Area of a Surface of Revolution
10.5e. Exercises
10.6. Polar Equations of Conics and Kepler’s Laws
10.6a. Polar Equations of Conics
10.6b. Kepler’s Laws
10.6c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 11. Vectors and the Geometry of Space
11.1. Vectors in the Plane
11.1a. Component Form of a Vector
11.1b. Vector Operations
11.1c. Standard Unit Vectors
11.1d. Exercises
11.2. Space Coordinates and Vectors in Space
11.2a. Coordinates in Space
11.2b. Vectors in Space
11.2c. Exercises
11.3. The Dot Product of Two Vectors
11.3a. The Dot Product
11.3b. Angle Between Two Vectors
11.3c. Direction Cosines
11.3d. Projections and Vector Components
11.3e. Work
11.3f. Exercises
11.4. The Cross Product of Two Vectors in Space
11.4a. The Cross Product
11.4b. The Triple Scalar Product
11.4c. Exercises
11.5. Lines and Planes in Space
11.5a. Lines in Space
11.5b. Planes in Space
11.5c. Sketching Planes in Space
11.5d. Distances Between Points, Planes, and Lines
11.5e. Exercises
11.5f. Section Project
11.6. Surfaces in Space
11.6a. Cylindrical Surfaces
11.6b. Quadric Surfaces
11.6c. Surfaces of Revolution
11.6d. Exercises
11.7. Cylindrical and Spherical Coordinates
11.7a. Cylindrical Coordinates
11.7b. Spherical Coordinates
11.7c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 12. Vector-Valued Functions
12.1. Vector-Valued Functions
12.1a. Space Curves and Vector-Valued Functions
12.1b. Limits and Continuity
12.1c. Exercises
12.1d. Section Project: Witch of Agnesi
12.2. Differentiation and Integration of Vector-Valued Functions
12.2a. Differentiation of Vector-Valued Functions
12.2b. Integration of Vector-Valued Functions
12.2c. Exercises
12.3. Velocity and Acceleration
12.3a. Velocity and Acceleration
12.3b. Projectile Motion
12.3c. Exercises
12.4. Tangent Vectors and Normal Vectors
12.4a. Tangent Vectors and Normal Vectors
12.4b. Tangential and Normal Components of Acceleration
12.4c. Exercises
12.5. Arc Length and Curvature
12.5a. Arc Length
12.5b. Arc Length Parameter
12.5c. Curvature
12.5d. Application
12.5e. Exercises
Review Exercises
P.S. Problem Solving
Chapter 13. Functions of Several Variables
13.1. Introduction to Functions of Several Variables
13.1a. Functions of Several Variables
13.1b. The Graph of a Function of Two Variables
13.1c. Level Curves
13.1d. Level Surfaces
13.1e. Computer Graphics
13.1f. Exercises
13.2. Limits and Continuity
13.2a. Neighborhoods in the Plane
13.2b. Limit of a Function of Two Variables
13.2c. Continuity of a Function of Two Variables
13.2d. Continuity of a Function of Three Variables
13.2e. Exercises
13.3. Partial Derivatives
13.3a. Partial Derivatives of a Function of Two Variables
13.3b. Partial Derivatives of a Function of Three or More Variables
13.3c. Higher-Order Partial Derivatives
13.3d. Exercises
13.3e. Section Project: Moiré Fringes
13.4. Differentials
13.4a. Increments and Differentials
13.4b. Differentiability
13.4c. Approximation by Differentials
13.4d. Exercises
13.5. Chain Rules for Functions of Several Variables
13.5a. Chain Rules for Functions of Several Variables
13.5b. Implicit Partial Differentiation
13.5c. Exercises
13.6. Directional Derivatives and Gradients
13.6a. Directional Derivative
13.6b. The Gradient of a Function of Two Variables
13.6c. Applications of the Gradient
13.6d. Functions of Three Variables
13.6e. Exercises
13.7. Tangent Planes and Normal Lines
13.7a. Tangent Plane and Normal Line To a Surface
13.7b. The Angle of Inclination of a Plane
13.7c. A Comparison of the Gradients ∇ f ( x , y ) and ∇ F ( x , y , z )
13.7d. Exercises
13.7e. Section Project: Wildflowers
13.8. Extrema of Functions of Two Variables
13.8a. Absolute Extrema and Relative Extrema
13.8b. The Second Partials Test
13.8c. Exercises
13.9. Applications of Extrema
13.9a. Applied Optimization Problems
13.9b. The Method of Least Squares
13.9c. Exercises
13.9d. Section Project
13.10. Lagrange Multipliers
13.10a. Lagrange Multipliers
13.10b. Constrained Optimization Problems
13.10c. The Method of Lagrange Multipliers with Two Constraints
13.10d. Exercises
Review Exercises
P.S. Problem Solving
Chapter 14. Multiple Integration
14.1. Iterated Integrals and Area in the Plane
14.1a. Iterated Integrals
14.1b. Area of a Plane Region
14.1c. Exercises
14.2. Double Integrals and Volume
14.2a. Double Integrals and Volume of a Solid Region
14.2b. Evaluation of Double Integrals
14.2c. Average Value of a Function
14.2d. Exercises
14.3. Change of Variables: Polar Coordinates
14.3a. Double Integrals in Polar Coordinates
14.3b. Exercises
14.4. Center of Mass and Moments of Inertia
14.4a. Mass
14.4b. Moments and Center of Mass
14.4c. Moments of Inertia
14.4d. Exercises
14.4e. Section Project: Center of Pressure on a Sail
14.5. Surface Area
14.5a. Surface Area
14.5b. Exercises
14.5c. Section Project: Capillary Action
14.6. Triple Integrals and Applications
14.6a. Triple Integrals
14.6b. Center of Mass and Moments of Inertia
14.6c. Exercises
14.7. Triple Integrals in Other Coordinates
14.7a. Triple Integrals in Cylindrical Coordinates
14.7b. Triple Integrals in Spherical Coordinates
14.7c. Exercises
14.7d. Section Project: Wrinkled and Bumpy Spheres
14.8. Change of Variables: Jacobians
14.8a. Jacobians
14.8b. Change of Variables for Double Integrals
14.8c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 15. Vector Analysis
15.1. Vector Fields
15.1a. Vector Fields
15.1b. Conservative Vector Fields
15.1c. Curl of a Vector Field
15.1d. Divergence of a Vector Field
15.1e. Exercises
15.2. Line Integrals
15.2a. Piecewise Smooth Curves
15.2b. Line Integrals
15.2c. Line Integrals of Vector Fields
15.2d. Line Integrals in Differential Form
15.2e. Exercises
15.3. Conservative Vector Fields and Independence of Path
15.3a. Fundamental Theorem of Line Integrals
15.3b. Independence of Path
15.3c. Conservation of Energy
15.3d. Exercises
15.4. Green’s Theorem
15.4a. Green’s Theorem
15.4b. Alternative Forms of Green’s Theorem
15.4c. Exercises
15.4d. Section Project: Hyperbolic and Trigonometric Functions
15.5. Parametric Surfaces
15.5a. Parametric Surfaces
15.5b. Finding Parametric Equations for Surfaces
15.5c. Normal Vectors and Tangent Planes
15.5d. Area of a Parametric Surface
15.5e. Exercises
15.6. Surface Integrals
15.6a. Surface Integrals
15.6b. Parametric Surfaces and Surface Integrals
15.6c. Orientation of a Surface
15.6d. Flux Integrals
15.6e. Exercises
15.6f. Section Project: Hyperboloid of One Sheet
15.7. Divergence Theorem
15.7a. Divergence Theorem
15.7b. Flux and the Divergence Theorem
15.7c. Exercises
15.8. Stokes’s Theorem
15.8a. Stokes’s Theorem
15.8b. Physical Interpretation of Curl
15.8c. Exercises
Review Exercises
P.S. Problem Solving
Chapter 16. Additional Topics in Differential Equations
16.1. Exact First-Order Equations
16.1a. Exact Differential Equations
16.1b. Integrating Factors
16.1c. Exercises
16.2. Second-Order Homogeneous Linear Equations
16.2a. Second-Order Linear Differential Equations
16.2b. Higher-Order Linear Differential Equations
16.2c. Application
16.2d. Exercises
16.3. Second-Order Nonhomogeneous Linear Equations
16.3a. Nonhomogeneous Equations
16.3b. Method of Undetermined Coefficients
16.3c. Variation of Parameters
16.3d. Exercises
16.3e. Section Project: Parachute Jump
16.4. Series Solutions of Differential Equations
16.4a. Power Series Solution of a Differential Equation
16.4b. Approximation by Taylor Series
16.4c. Exercises
Review Exercises
P.S. Problem Solving
Appendix A. Proofs of Selected Theorems
Appendix B. Integration Tables
Formula Cards
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