Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students.
1 A LIBRARY OF FUNCTIONS.
2 KEY CONCEPT: THE DERIVATIVE.
3 SHORT-CUTS TO DIFFERENTIATION.
4 USING THE DERIVATIVE.
5 KEY CONCEPT: THE DEFINITE INTEGRAL.
6 CONSTRUCTING ANTIDERIVATIVES.
7 INTEGRATION.
8 USING THE DEFINITE INTEGRAL.
9 SEQUENCES AND SERIES.
10 APPROXIMATING FUNCTIONS USING SERIES.
11 DIFFERENTIAL EQUATIONS.
12 FUNCTIONS OF SEVERAL VARIABLES.
13 A FUNDAMENTAL TOOL: VECTORS.
14 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES.
15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA.
16 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES.
17 PARAMETERIZATION AND VECTOR FIELDS.
18 LINE INTEGRALS.
19 FLUX INTEGRALS.
20 CALCULUS OF VECTOR FIELDS.
Appendix.
A Roots, Accuracy, and Bounds.
B Complex Numbers.
C Newtons's Method.
D Vectors in the Plane.
E Determinants.