|Content- Chapter evaluation.||Single Variable Calculus 4th Edition James Stewart||Calculus Concepts and Contexts 2nd Edition James Stewart||The Sensible Calculus Book|
|A Preview of Calculus.|
|Pre-Calculus Main Text Materials.||1. Functions and Models. This is a standard treatment of functions, tables, graphs.The algebra of functions not connected to graphs or tables. The review and interpretation of linear functions is inadequate- especially with regard to the point slope formula and its connection to rates.[The review of lines appears in an appendix].||1. Functions and Models. Similar to the 4th Edition.||Introduction of multiple visual and numerical approaches to understanding functions.|
|Introduction to the Derivative.||2. Limits and Rates of Change. The initial motivation for limits is
followed by much space devoted to limit algebra. Continuity properties
(IVT) are mixed in with the algebra for continuity. The derivative is presented
as a number and a function. A separate section is provided on general rate
interpretations with delta notation after the calculus but before trigonometry.
The Leibniz notation is used extensively with delta notation.
|2.Limits and Derivatives.||The derivative is the focus of attention, first through models, then developed to its mathematical definition. Limit concepts are developed slowly with notation for limits developed first as a short hand for concepts related to the derivative. The treatment is balanced between models, mathematics, and interpretations for the mathematics.|
|Derivative Calculus||3. Derivatives.||3. Differentiation Rules.||The calculus is presented as a systematic approach to finding f '(x).
This is based on the connection of a function to other core or known functions
with arithmetic or composition.
Core function derivatives are examined analytically, graphically, and numerically, providing a solid web of understanding for further development. Transcendental functions are given brief but adequate initial treatments that allow their use for further explorations in depth later in the book.
|Applications of Differentiation||4. Applications of Differentiation. It is not clear what contitutes an application. Linearization, the differential, and Newtons' Method are not connected to graphical applications. Related Rates and implicit differentiation are not connected or treated as "applications". Continuity issues are not distinguished from calculus procedures in the analysis of intervals. One section is provided for both 1st and 2nd derivative graphing analysis. Very little connection is made with models/interpretations in the graphical analysis. There is a separate section on economics but no discussion of elasticity.||4. Applications of Differentiation.|
|Introduction to Integration||5. Integrals. 8. Techniques of Integration..||5. Integrals
G: Integration of Rational Functions by Partial Fractions
|Applications of Integration||6. Applications of Integration. 9. Further Applications of Integration.||6. Applications of Integration.|
|Transcendental functions and DE's||7. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric
10. Differential Equations.
|7. Differential Equations.|
|Infinite Series and Taylor Theory||8. Infinite Sequences and Series.||12. Infinite Sequences and Series.|
|Proof and Theory||Appendices.
F. Proofs of Theorems
F: Sigma Notation.
|Appendixes.D: Precise Definitions of Limits.
E: A Few Proofs.
|11. Parametric Equations and Polar Coordinates.|
"Stewart's CALCULUS, FOURTH EDITION
emphasize conceptual understanding.
from the most unprepared to the most mathematically gifted, Stewart writes to a range of students -
adding the explanations that make ideas come alive
problems that challenge.
heuristic examples reveal calculus to students.
His examples : not just models for problem solving or a means of demonstrating techniques
encourage students to develop an analytic view of the subject. "
|Selected Features||Calculus Concepts and Contexts 2nd Edition James Stewart||Single Variable Calculus 4th Edition James Stewart||The Sensible Calculus|
|Use of Transformation Figures|
|Introduction of Deivative Concepts|
|Early DE's with symbolic, graphic and numeric (SGN) approaches.|
|Definite Integral concepts connected to DE's with SGN approaches.|
|Taylor Theory motivates series.|
|Series concepts developed with SGN approaches.|
|Applications of integration connected to DE's.|