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Calculus 4th Edition Smith Test Bank
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Calculus 4th Edition Smith Test Bank.
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Product Details:
- ISBN-10 : 0073383112
- ISBN-13 : 978-0073383118
- Author;
Now in its 4th edition, Smith/Minton, Calculus offers students and instructors a mathematically sound text, robust exercise sets and elegant presentation of calculus concepts. When packaged with ALEKS Prep for Calculus, the most effective remediation tool on the market, Smith/Minton offers a complete package to ensure students success in calculus.The new edition has been updated with a reorganization of the exercise sets, making the range of exercises more transparent. Additionally, over 1,000 new classic calculus problems were added.
Table of Content:
- CHAPTER 0 Preliminaries
- 0.1 The Real Numbers and the Cartesian Plane
- The Real Number System and Inequalities
- The Cartesian Plane
- 0.2 Lines and Functions
- Equations of Lines
- Functions
- 0.3 Graphing Calculators and Computer Algebra Systems
- 0.4 Trigonometric Functions
- 0.5 Transformations of Functions
- CHAPTER 1 Limits and Continuity
- 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
- 1.2 The Concept of Limit
- 1.3 Computation of Limits
- 1.4 Continuity and Its Consequences
- The Method of Bisections
- 1.5 Limits Involving Infinity; Asymptotes
- Limits at Infinity
- 1.6 Formal Definition of the Limit
- Exploring the Definition of Limit Graphically
- Limits Involving Infinity
- 1.7 Limits and Loss-of-Significance Errors
- Computer Representation of Real Numbers
- CHAPTER 2 Differentiation
- 2.1 Tangent Lines and Velocity
- The General Case
- Velocity
- 2.2 The Derivative
- Alternative Derivative Notations
- Numerical Differentiation
- 2.3 Computation of Derivatives: The Power Rule
- The Power Rule
- General Derivative Rules
- Higher Order Derivatives
- Acceleration
- 2.4 The Product and Quotient Rules
- Product Rule
- Quotient Rule
- Applications
- 2.5 The Chain Rule
- 2.6 Derivatives of Trigonometric Functions
- Applications
- 2.7 Implicit Differentiation
- 2.8 The Mean Value Theorem
- CHAPTER 3 Applications of Differentiation
- 3.1 Linear Approximations and Newton’s Method
- Linear Approximations
- Newton’s Method
- 3.2 Maximum and Minimum Values
- 3.3 Increasing and Decreasing Functions
- What You See May Not Be What You Get
- 3.4 Concavity and the Second Derivative Test
- 3.5 Overview of Curve Sketching
- 3.6 Optimization
- 3.7 Related Rates
- 3.8 Rates of Change in Economics and the Sciences
- CHAPTER 4 Integration
- 4.1 Antiderivatives
- 4.2 Sums and Sigma Notation
- Principle of Mathematical Induction
- 4.3 Area
- 4.4 The Definite Integral
- Average Value of a Function
- 4.5 The Fundamental Theorem of Calculus
- 4.6 Integration by Substitution
- Substitution in Definite Integrals
- 4.7 Numerical Integration
- Simpson’s Rule
- Error Bounds for Numerical Integration
- CHAPTER 5 Applications of the Definite Integral
- 5.1 Area Between Curves
- 5.2 Volume: Slicing, Disks and Washers
- Volumes by Slicing
- The Method of Disks
- The Method of Washers
- 5.3 Volumes by Cylindrical Shells
- 5.4 Arc Length and Surface Area
- Arc Length
- Surface Area
- 5.5 Projectile Motion
- 5.6 Applications of Integration to Physics and Engineering
- CHAPTER 6 Exponentials, Logarithms and Other Transcendental Functions
- 6.1 The Natural Logarithm
- Logarithmic Differentiation
- 6.2 Inverse Functions
- 6.3 The Exponential Function
- Derivative of the Exponential Function
- 6.4 The Inverse Trigonometric Functions
- 6.5 The Calculus of the Inverse Trigonometric Functions
- Integrals Involving the Inverse Trigonometric Functions
- 6.6 The Hyperbolic Functions
- The Inverse Hyperbolic Functions
- Derivation of the Catenary
- CHAPTER 7 Integration Techniques
- 7.1 Review of Formulas and Techniques
- 7.2 Integration by Parts
- 7.3 Trigonometric Techniques of Integration
- Integrals Involving Powers of Trigonometric Functions
- Trigonometric Substitution
- 7.4 Integration of Rational Functions Using Partial Fractions
- Brief Summary of Integration Techniques
- 7.5 Integration Tables and Computer Algebra Systems
- Using Tables of Integrals
- Integration Using a Computer Algebra System
- 7.6 Indeterminate Forms and L‘Hôpital’s Rule
- Other Indeterminate Forms
- 7.7 Improper Integrals
- Improper Integrals with a Discontinuous Integrand
- Improper Integrals with an Infinite Limit of Integration
- A Comparison Test
- 7.8 Probability
- CHAPTER 8 First-Order Differential Equations
- 8.1 Modeling with Differential Equations
- Growth and Decay Problems
- Compound Interest
- 8.2 Separable Differential Equations
- Logistic Growth
- 8.3 Direction Fields and Euler’s Method
- 8.4 Systems of First-Order Differential Equations
- Predator-Prey Systems
- CHAPTER 9 Infinite Series
- 9.1 Sequences of Real Numbers
- 9.2 Infinite Series
- 9.3 The Integral Test and Comparison Tests
- Comparison Tests
- 9.4 Alternating Series
- Estimating the Sum of an Alternating Series
- 9.5 Absolute Convergence and the Ratio Test
- The Ratio Test
- The Root Test
- Summary of Convergence Tests
- 9.6 Power Series
- 9.7 Taylor Series
- Representation of Functions as Power Series
- Proof of Taylor’s Theorem
- 9.8 Applications of Taylor Series
- The Binomial Series
- 9.9 Fourier Series
- Functions of Period Other Than 2π
- Fourier Series and Music Synthesizers
- CHAPTER 10 Parametric Equations and Polar Coordinates
- 10.1 Plane Curves and Parametric Equations
- 10.2 Calculus and Parametric Equations
- 10.3 Arc Length and Surface Area in Parametric Equations
- 10.4 Polar Coordinates
- 10.5 Calculus and Polar Coordinates
- 10.6 Conic Sections
- Parabolas
- Ellipses
- Hyperbolas
- 10.7 Conic Sections in Polar Coordinates
- CHAPTER 11 Vectors and the Geometry of Space
- 11.1 Vectors in the Plane
- 11.2 Vectors in Space
- Vectors in R3
- 11.3 The Dot Product
- Components and Projections
- 11.4 The Cross Product
- 11.5 Lines and Planes in Space
- Planes in R3
- 11.6 Surfaces in Space
- Cylindrical Surfaces
- Quadric Surfaces
- An Application
- CHAPTER 12 Vector-Valued Functions
- 12.1 Vector-Valued Functions
- Arc Length in R3
- 12.2 The Calculus of Vector-Valued Functions
- 12.3 Motion in Space
- Equations of Motion
- 12.4 Curvature
- 12.5 Tangent and Normal Vectors
- Tangential and Normal Components of Acceleration
- Kepler’s Laws
- 12.6 Parametric Surfaces
- CHAPTER 13 Functions of Several Variables and Partial Differentiation
- 13.1 Functions of Several Variables
- 13.2 Limits and Continuity
- 13.3 Partial Derivatives
- 13.4 Tangent Planes and Linear Approximations
- Increments and Differentials
- 13.5 The Chain Rule
- Implicit Differentiation
- 13.6 The Gradient and Directional Derivatives
- 13.7 Extrema of Functions of Several Variables
- Proof of the Second Derivatives Test
- 13.8 Constrained Optimization and Lagrange Multipliers
- CHAPTER 14 Multiple Integrals
- 14.1 Double Integrals
- Double Integrals over a Rectangle
- Double Integrals over General Regions
- 14.2 Area, Volume and Center of Mass
- Moments and Center of Mass
- 14.3 Double Integrals in Polar Coordinates
- 14.4 Surface Area
- 14.5 Triple Integrals
- Mass and Center of Mass
- 14.6 Cylindrical Coordinates
- 14.7 Spherical Coordinates
- Triple Integrals in Spherical Coordinates
- 14.8 Change of Variables in Multiple Integrals
- CHAPTER 15 Vector Calculus
- 15.1 Vector Fields
- 15.2 Line Integrals
- 15.3 Independence of Path and Conservative Vector Fields
- 15.4 Green’s Theorem
- 15.5 Curl and Divergence
- 15.6 Surface Integrals
- Parametric Representation of Surfaces
- 15.7 The Divergence Theorem
- 15.8 Stokes’ Theorem
- 15.9 Applications of Vector Calculus
- CHAPTER 16 Second-Order Differential Equations
- 16.1 Second-Order Equations with Constant Coefficients
- 16.2 Nonhomogeneous Equations: Undetermined Coefficients
- 16.3 Applications of Second-Order Equations
- 16.4 Power Series Solutions of Differential Equations
- Appendix A: Proofs of Selected Theorems
- Appendix B: Answers to Odd-Numbered Exercises
- Credits
- Subject Index
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