Single Variable Calculus
Paperback Engels 2018 3e druk 9780134769783Samenvatting
For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.
The most successful new calculus text in the last two decades
The much-anticipated 3rd Edition of Briggs’ Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts.
For the 3rd Edition, the authors synthesized feedback on the text and MyLab™ Math content from over 140 instructors and an Engineering Review Panel. This thorough and extensive review process, paired with the authors’ own teaching experiences, helped create a text that was designed for today’s calculus instructors and students.
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If you would like to purchase both the physical text and MyLab Math, search for: 0134996690 / 9780134996691 Single Variable Calculus and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e Package consists of: 0134769783 / 9780134769783 Calculus, Single Variable 013485683X / 9780134856834 MyLab Math with Pearson eText - Standalone Access Card - for Calculus, Single Variable
Specificaties
Lezersrecensies
Inhoudsopgave
1. Functions
- 1.1 Review of Functions
- 1.2 Representing Functions
- 1.3 Inverse, Exponential, and Logarithmic Functions
- 1.4 Trigonometric Functions and Their Inverses
- Review Exercises
2. Limits
- 2.1 The Idea of Limits
- 2.2 Definitions of Limits
- 2.3 Techniques for Computing Limits
- 2.4 Infinite Limits
- 2.5 Limits at Infinity
- 2.6 Continuity
- 2.7 Precise Definitions of Limits
- Review Exercises
3. Derivatives
- 3.1 Introducing the Derivative
- 3.2 The Derivative as a Function
- 3.3 Rules of Differentiation
- 3.4 The Product and Quotient Rules
- 3.5 Derivatives of Trigonometric Functions
- 3.6 Derivatives as Rates of Change
- 3.7 The Chain Rule
- 3.8 Implicit Differentiation
- 3.9 Derivatives of Logarithmic and Exponential Functions
- 3.10 Derivatives of Inverse Trigonometric Functions
- 3.11 Related Rates
- Review Exercises
4. Applications of the Derivative
- 4.1 Maxima and Minima
- 4.2 Mean Value Theorem
- 4.3 What Derivatives Tell Us
- 4.4 Graphing Functions
- 4.5 Optimization Problems
- 4.6 Linear Approximation and Differentials
- 4.7 L'Hôpital's Rule
- 4.8 Newton's Method
- 4.9 Antiderivatives
- Review Exercises
5. Integration
- 5.1 Approximating Areas under Curves
- 5.2 Definite Integrals
- 5.3 Fundamental Theorem of Calculus
- 5.4 Working with Integrals
- 5.5 Substitution Rule
- Review Exercises
6. Applications of Integration
- 6.1 Velocity and Net Change
- 6.2 Regions Between Curves
- 6.3 Volume by Slicing
- 6.4 Volume by Shells
- 6.5 Length of Curves
- 6.6 Surface Area
- 6.7 Physical Applications
- Review Exercises
7. Logarithmic, Exponential, and Hyperbolic Functions
- 7.1 Logarithmic and Exponential Functions Revisited
- 7.2 Exponential Models
- 7.3 Hyperbolic Functions
- Review Exercises
8. Integration Techniques
- 8.1 Basic Approaches
- 8.2 Integration by Parts
- 8.3 Trigonometric Integrals
- 8.4 Trigonometric Substitutions
- 8.5 Partial Fractions
- 8.6 Integration Strategies
- 8.7 Other Methods of Integration
- 8.8 Numerical Integration
- 8.9 Improper Integrals
- Review Exercises
9. Differential Equations
- 9.1 Basic Ideas
- 9.2 Direction Fields and Euler's Method
- 9.3 Separable Differential Equations
- 9.4 Special First-Order Linear Differential Equations
- 9.5 Modeling with Differential Equations
- Review Exercises
10. Sequences and Infinite Series
- 10.1 An Overview
- 10.2 Sequences
- 10.3 Infinite Series
- 10.4 The Divergence and Integral Tests
- 10.5 Comparison Tests
- 10.6 Alternating Series
- 10.7 The Ratio and Root Tests
- 10.8 Choosing a Convergence Test
- Review Exercises
11. Power Series
- 11.1 Approximating Functions with Polynomials
- 11.2 Properties of Power Series
- 11.3 Taylor Series
- 11.4 Working with Taylor Series
- Review Exercises
12. Parametric and Polar Curves
- 12.1 Parametric Equations
- 12.2 Polar Coordinates
- 12.3 Calculus in Polar Coordinates
- 12.4 Conic Sections
- Review Exercises
13. Vectors and the Geometry of Space
- 13.1 Vectors in the Plane
- 13.2 Vectors in Three Dimensions
- 13.3 Dot Products
- 13.4 Cross Products
- 13.5 Lines and Planes in Space
- 13.6 Cylinders and Quadric Surfaces
- Review Exercises
14. Vector-Valued Functions
- 14.1 Vector-Valued Functions
- 14.2 Calculus of Vector-Valued Functions
- 14.3 Motion in Space
- 14.4 Length of Curves
- 14.5 Curvature and Normal Vectors
- Review Exercises
15. Functions of Several Variables
- 15.1 Graphs and Level Curves
- 15.2 Limits and Continuity
- 15.3 Partial Derivatives
- 15.4 The Chain Rule
- 15.5 Directional Derivatives and the Gradient
- 15.6 Tangent Planes and Linear Approximation
- 15.7 Maximum/Minimum Problems
- 15.8 Lagrange Multipliers
- Review Exercises
16. Multiple Integration
- 16.1 Double Integrals over Rectangular Regions
- 16.2 Double Integrals over General Regions
- 16.3 Double Integrals in Polar Coordinates
- 16.4 Triple Integrals
- 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
- 16.6 Integrals for Mass Calculations
- 16.7 Change of Variables in Multiple Integrals
- Review Exercises
17. Vector Calculus
- 17.1 Vector Fields
- 17.2 Line Integrals
- 17.3 Conservative Vector Fields
- 17.4 Green's Theorem
- 17.5 Divergence and Curl
- 17.6 Surface Integrals
- 17.7 Stokes' Theorem
- 17.8 Divergence Theorem
- Review Exercises
D2 Second-Order Differential Equations ONLINE
- D2.1 Basic Ideas
- D2.2 Linear Homogeneous Equations
- D2.3 Linear Nonhomogeneous Equations
- D2.4 Applications
- D2.5 Complex Forcing Functions
- Review Exercises
Appendices
- Proofs of Selected Theorems
- Algebra Review ONLINE
- Complex Numbers ONLINE
Answers
Index
Table of Integrals
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