Student Solutions Manual for Thomas' Calculus Early Transcendentals, Single Variable
Produktdetaljer
Biografisk notat
Joel Hass received his PhD from the University of California Berkeley. He is currently a professor of mathematics at the University of California Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.
Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.
Maurice D. Weir (late) of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas’ Calculus.
1. Functions
1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Graphing with Software
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
2. Limits and Continuity
2.1 Rates of Change and Tangent Lines to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity; Asymptotes of Graphs
3. Derivatives
3.1 Tangent Lines and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 The Derivative as a Rate of Change
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Functions and Logarithms
3.9 Inverse Trigonometric Functions
3.10 Related Rates
3.11 Linearization and Differentials
4. Applications of Derivatives
4.1 Extreme Values of Functions on Closed Intervals
4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test
4.4 Concavity and Curve Sketching
4.5 Indeterminate Forms and L'Hôpital's Rule
4.6 Applied Optimization
4.7 Newton's Method
4.8 Antiderivatives
5. Integrals
5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Method
5.6 Definite Integral Substitutions and the Area Between Curves
6. Applications of Definite Integrals
6.1 Volumes Using Cross-Sections
6.2 Volumes Using Cylindrical Shells
6.3 Arc Length
6.4 Areas of Surfaces of Revolution
6.5 Work and Fluid Forces
6.6 Moments and Centers of Mass
7. Integrals and Transcendental Functions
7.1 The Logarithm Defined as an Integral
7.2 Exponential Change and Separable Differential Equations
7.3 Hyperbolic Functions
7.4 Relative Rates of Growth
8. Techniques of Integration
8.1 Using Basic Integration Formulas
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitutions
8.5 Integration of Rational Functions by Partial Fractions
8.6 Integral Tables and Computer Algebra Systems
8.7 Numerical Integration
8.8 Improper Integrals
8.9 Probability
9. First-Order Differential Equations
9.1 Solutions, Slope Fields, and Euler's Method
9.2 First-Order Linear Equations
9.3 Applications
9.4 Graphical Solutions of Autonomous Equations
9.5 Systems of Equations and Phase Planes
10. Infinite Sequences and Series
10.1 Sequences
10.2 Infinite Series
10.3 The Integral Test
10.4 Comparison Tests
10.5 Absolute Convergence; The Ratio and Root Tests
10.6 Alternating Series and Conditional Convergence
10.7 Power Series
10.8 Taylor and Maclaurin Series
10.9 Convergence of Taylor Series
10.10 Applications of Taylor Series
11. Parametric Equations and Polar Coordinates
11.1 Parametrizations of Plane Curves
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Graphing Polar Coordinate Equations
11.5 Areas and Lengths in Polar Coordinates
11.6 Conic Sections
11.7 Conics in Polar Coordinates
12. Vectors and the Geometry of Space
12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Lines and Planes in Space
12.6 Cylinders and Quadric Surfaces
13. Vector-Valued Functions and Motion in Space
13.1 Curves in Space and Their Tangents
13.2 Integrals of Vector Functions; Projectile Motion
13.3 Arc Length in Space
13.4 Curvature and Normal Vectors of a Curve
13.5 Tangential and Normal Components of Acceleration
13.6 Velocity and Acceleration in Polar Coordinates
14. Partial Derivatives
14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions
14.3 Partial Derivatives
14.4 The Chain Rule
14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
14.7 Extreme Values and Saddle Points
14.8 Lagrange Multipliers
14.9 Taylor's Formula for Two Variables
14.10 Partial Derivatives with Constrained Variables
15. Multiple Integrals
15.1 Double and Iterated Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
15.5 Triple Integrals in Rectangular Coordinates
15.6 Applications
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
15.8 Substitutions in Multiple Integrals
16. Integrals and Vector Fields
16.1 Line Integrals of Scalar Functions
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
16.3 Path Independence, Conservative Fields, and Potential Functions
16.4 Green's Theorem in the Plane
16.5 Surfaces and Area
16.6 Surface Integrals
16.7 Stokes' Theorem
16.8 The Divergence Theorem and a Unified Theory
17. Second-Order Differential Equations (Online at www.goo.gl/MgDXPY)
17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power-Series Solutions
Appendices
1. Real Numbers and the Real Line
2. Mathematical Induction
3. Lines, Circles, and Parabolas
4. Proofs of Limit Theorems
5. Commonly Occurring Limits
6. Theory of the Real Numbers
7. Complex Numbers
8. The Distributive Law for Vector Cross Products
9. The Mixed Derivative Theorem and the Increment Theorem
About the Book
Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors
- New co-author Chris Heil (Georgia Institute of Technology) and co-author Joel Hass continue Thomas’ tradition of developing students’ mathematical maturity and proficiency, going beyond memorizing formulas and routine procedures, and showing students how to generalize key concepts once they are introduced.
- The authors are careful to present key topics, such as the definition of the derivative, both informally and formally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.
- Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text.
- A flexible table of contents divides topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students.
- Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
Assess student understanding of key concepts and skills through a wide range of time-tested exercises
- Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery. In the 14th Edition, the authors added new exercises throughout, many geometric in nature.
- Writing exercises placed throughout the text ask students to explore and explain a variety of calculus concepts and applications. In addition, the end of each chapter contains a list of questions for students to review and summarize what they have learned. Many of these exercises make good writing assignments.
- Technology exercises (marked with a T) are included in each section, asking students to use the calculator or computer when solving the problems. In addition, Computer Explorations give the option of assigning exercises that require a computer algebra system (CAS, such as Maple or Mathematica).
Support a complete understanding of calculus for students at varying levels
- Each major topic is developed with both simple and more advanced examples to give the basic ideas and illustrate deeper concepts.
- UPDATED! Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 14th Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.
- ENHANCED! Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 14th Edition, many more annotations were added.
- End-of-chapter materials include review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises with more challenging or synthesizing problems.
- A complete suite of instructor and student s
New to the Book
Co-authors Joel Hass and Chris Heil reconsidered every word, symbol, and piece of art, motivating students to consider the content from different perspectives and compelling a deeper, geometric understanding.
- Updated graphics emphasize clear visualization and mathematical correctness.
- New examples and figures have been added throughout all chapters, many based on user feedback. See, for instance, Example 3 in Section 9.1, which helps students overcome a conceptual obstacle.
- New types of homework exercises, including many geometric in nature, have been added. The new exercises provide different perspectives and approaches to each topic.
- Short URLs have been added to the historical marginnotes, allowing students to navigate directly to online information.
- New annotations within examples (in blue type) guide the student through the problem solution and emphasize that each step in a mathematical argument is rigorously justified.
- All chapters have been revised for clarity, consistency, conciseness, and comprehension.
Detailed content changes
Chapter 1
- Shortened 1.4 to focus on issues arising in use of mathematical software and potential pitfalls. Removed peripheral material on regression, along with associated exercises.
- Clarified explanation of definition of exponential function in 1.5.
- Replaced sin-1 notation for the inverse sine function with arcsin as default notation in 1.6, and similarly for other trig functions.
- Added new Exercises: 1.1: 59-62, 1.2: 21-22; 1.3: 64-65, 1.6: 61-64, 79cd; PE: 29-32.
Chapter 2
- Added definition of average speed in 2.1.
- Updated definition of limits to allow for arbitrary domains. The definition of limits is now consistent with the definition in multivariable domains later in the text and with more general mathematical usage.
- Reworded limit and continuity definitions to remove implication symbols and improve comprehension.
- Added new Example 7 in 2.4 to illustrate limits of ratios of trig functions.
- Rewrote 2.5 Example 11 to solve the equation by finding a zero, consistent with previous discussion.
- Added new Exercises: 2.1: 15-18; 2.2: 3h-k, 4f-I; 2.4: 19-20, 45-46; 2.5: 31-32; 2.6: 69-74; PE: 57-58; AAE: 35-38.
Chapter 3
- Clarified relation of slope and rate of change.
- Added new Figure 3.9 using the square root function to illustrate vertical tangent lines.
- Added figure of xsin(1x)in 3.2 to illustrate how oscillation can lead to non-existence of a derivative of a continuous function.
- Revised product rule to make order of factors consistent throughout text, including later dot product and cross product formulas.
- Added new Exercises: 3.2: 36, 43-44; 3.3: 65-66; 3.5: 43-44, 61bc; 3.6: 79-80, 111-113; 3.7: 27-28; 3.8: 97-100; 3.9: 43-46; 3.10: 47; AAE: 14-15, 26-27.
Chapter 4
- Added summary to 4.1.
- Added new Example 3 with new Figure 4.27 and Example 12 with new Figure 4.35 to give basic and advanced examples of concavity.
- Added new Exercises: 4.1: 53-56, 67-70; 4.3: 45-46, 67-68; 4.4: 107-112; 4.6: 37-42; 4.7: 7-10; 4.8: 115-118; PE: 1-16, 101-102; AAE: 19-20, 38-39. Moved exercises 4.1: 5
Produktdetaljer
Biografisk notat
Joel Hass received his PhD from the University of California Berkeley. He is currently a professor of mathematics at the University of California Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.
Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.
Maurice D. Weir (late) of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas’ Calculus.