Comparison of The Sensible Calculus Book ( First Year)

with Stewart Concepts and Contexts

and Stewart  Single Variable Calculus

Draft: Work in progress. 
Not to be used in any publication review without permission.

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 Functions. 
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.   
Statements from Stewart's self-description:
"James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS,
reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement.
This new edition continues to offer the balanced approach along with
Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems.
includes a free CD-ROM for students that contains animations, activities, and homework hints.
The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept.
emphasizes conceptual understanding -
motivating students with real world applications and
stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations.
All concepts are presented: with simplicity, character, and attention to detail.
clear exposition,
well thought-out problems and exercises.
The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills. "

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. "

Topical comparison of features of Sensible Calculus with Stewart Texts
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.
Probability models.
Economic models.
Taylor Theory motivates series.
Series concepts developed with SGN approaches.
Applications of integration connected to DE's.