Striking a balance between concepts, modeling, and skills, this highly acclaimed book arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material.
Table of Contents
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. Series. 10. Approximating Functions. 11. Differential Equations. 12. Functions of Several Variables. 13. A Fundamental Tool: Vectors. 14. Differentiating Functions of Many Variables. 15. Optimization: Local and Global Extrema. 16. Integrating Functions of Many Variables. 17. Parameterized Curves and Vector Fields. 18. Line Integrals. 19. Flux Integrals. 20. Calculus of Vector Fields. Appendix A: Roots, Accuracy, and Bounds. Appendix B: Complex Numbers. Appendix C: Newton's Method. Appendix D: Determinants. Ready Reference. Answers to Odd Numbered Problems. Index.