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The Ellis/Gulick Calculus is an honest approach to calculus that does not burden the student with theory. The definitions and theorems are well-motivated and clearly stated, and supplemented with plenty of examples, exercises and applications, as well as some historical remarks and mini-projects.
- An additional appendix entitled "Concepts Exercises in Calculus" was added to the text. The exercises in "Concept Exercises for Calculus" are designed to enhance the understanding of the concepts, definitions and theorems that are basic to calculus.
- The authors have assembled 20 problems from each of Chapters 2-10 that together focus on the core of calculus of one variable. They should be considered as being supplemental to the regular exercises in the text, rather than an alternative to them.
- As requested by previous uses of the text, a new section on parametrized surfaces (Sections 14.9 and 15.5) has been included in the several variable portion of the book.
- The concepts presented in an honest but accessible manner, because students need to be able to grasp both the concepts and the applications.
- Mathematically accurate, yet accessible and readable, with geometric motivation or interpretation where appropriate.
- Emphasis on graphical and numerical aspects, as well as the analytical aspects of calculus.
- More exercises requiring written responses, and more numerical examples and exercises are included; also the tables of integrals were eliminated. Each of these features is a result of the present-day teaching techniques, in which students are asked to contemplate the concepts more, and use technology where applicable.
- A greater focus on the fundamental limits that give rise to derivatives was included in Chapter 2, Limits and Continuity.
- A brief discussion of 2nd degree Taylor polynomials now accompanies coverage of the tangent-line approximation (within Chapter 3, Derivatives).
- In the motivation of the notion of integral, (Chapter 5) the text not only uses area but also the problem of calculating distance from velocity. The integral is also defined by means of Riemann sums (rather than by lower and upper sums).
- The chapter on applications of the integral (Chapter 6) now appears before the chapter on techniques of integration (Chapter 8). This change reflects the general availability of software packages such as Mathematica, MATLB, Maple, and Derive that perform symbolic integration.
- In response to requests of many physicists, there is a brief introduction to complex numbers in a project within Chapter 10, Curves in the Plane.
2. Limits and Continuity.
4. Applications of Derivative.
5. The Integral.
6. Applications of the Integral.
7. Inverse Functions, L'Hopital's Rule, and Differential Equations.
8. Techniques of Integration.
9. Sequences and Series.
10. Curves in the Plane.
11. Vectors, Lines and Planes.
12. Vector-Valued Functions and Curves in Space.
13. Partial Derivatives.
14. Multiple Integrals.
15. Calculus of Vector Fields.
16. Appendices and Indexes.
17. Concept Exercises in Calculus.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Student Solutions Manual for Ellis' Calculus
Contains worked-out solutions for all odd-numbered exercises in the text.