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ISBN10: 0071549315 | ISBN13: 9780071549318
ISBN10: 0071549315
ISBN13: 9780071549318
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Master calculus from the comfort of home! Want to "know it ALL" when it comes to calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace. Train your brain with ease! Calculus Know-It-ALL features: Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mind Stan's expert guidance gives you the know-how to: Understand mappings, relations, and functions Calculate limits and determine continuity Differentiate and integrate functions Analyze graphs using first and second derivatives Define and evaluate inverse functions Use specialized integration techniques Determine arc lengths, surface areas, and solid volumes Work with multivariable functions Take college entrance examinations with confidence And much more!
Part I: Differentiation in One Variable
Chapter 1. Single-Variable Functions
Chapter 2. Limits and Continuity
Chapter 3. What's a Derivative?
Chapter 4. Derivatives Don't Always Exist
Chapter 5. Differentiating Polynomial Functions
Chapter 6. More Rules for Differentiation
Chapter 7. A Few More Derivatives
Chapter 8. Higher Derivatives
Chapter 9. Analyzing Groups with Derivatives
Chapter 10. Review Questions and Answers
Part II: Integration in One Variable
Chapter 11. What's an Integral?
Chapter 12. Derivatives in Reverse
Chapter 13. Three Rules for Integration
Chapter 14. Improper Integrals
Chapter 15. Integrating Polynomial Functions
Chapter 16. Areas between Graphs
Chapter 17. A Few More Integrals
Chapter 18. How Long Is the Arc?
Chapter 19. Special Integration Tricks
Chapter 20. Review Questions and Answers
Part III: Advanced Topics
Chapter 21. Differentiating Inverse Functions
Chapter 22. Implicit Differentiation
Chapter 23. The L'Hopital Principles
Chapter 24. Partial Derivatives
Chapter 25. Second Partial Derivatives
Chapter 26. Surface-Area and Volume Integrals
Chapter 27. Repeated, Double, and Iterated Integrals
Chapter 28. More Volume Integrals
Chapter 29. What's a Differential Equation?
Chapter 30. Review Questions and Answers
Final Exam
Appendix A: Worked-Out Solutions to Exercises: Chapter 1 - 9
Appendix B: Worked-Out Solutions to Exercises: Chapters 11 - 19
Appendix C: Worked-Out Solutions to Exercises: Chapters 21 - 29
Appendix D: Answers to Final Exam Questions
Appendix E: Special Characters in Order of Appearance
Appendix F: Table of Derivatives
Appendix G: Table of Integrals
Suggested Additional Reading
Index
Chapter 1. Single-Variable Functions
Chapter 2. Limits and Continuity
Chapter 3. What's a Derivative?
Chapter 4. Derivatives Don't Always Exist
Chapter 5. Differentiating Polynomial Functions
Chapter 6. More Rules for Differentiation
Chapter 7. A Few More Derivatives
Chapter 8. Higher Derivatives
Chapter 9. Analyzing Groups with Derivatives
Chapter 10. Review Questions and Answers
Part II: Integration in One Variable
Chapter 11. What's an Integral?
Chapter 12. Derivatives in Reverse
Chapter 13. Three Rules for Integration
Chapter 14. Improper Integrals
Chapter 15. Integrating Polynomial Functions
Chapter 16. Areas between Graphs
Chapter 17. A Few More Integrals
Chapter 18. How Long Is the Arc?
Chapter 19. Special Integration Tricks
Chapter 20. Review Questions and Answers
Part III: Advanced Topics
Chapter 21. Differentiating Inverse Functions
Chapter 22. Implicit Differentiation
Chapter 23. The L'Hopital Principles
Chapter 24. Partial Derivatives
Chapter 25. Second Partial Derivatives
Chapter 26. Surface-Area and Volume Integrals
Chapter 27. Repeated, Double, and Iterated Integrals
Chapter 28. More Volume Integrals
Chapter 29. What's a Differential Equation?
Chapter 30. Review Questions and Answers
Final Exam
Appendix A: Worked-Out Solutions to Exercises: Chapter 1 - 9
Appendix B: Worked-Out Solutions to Exercises: Chapters 11 - 19
Appendix C: Worked-Out Solutions to Exercises: Chapters 21 - 29
Appendix D: Answers to Final Exam Questions
Appendix E: Special Characters in Order of Appearance
Appendix F: Table of Derivatives
Appendix G: Table of Integrals
Suggested Additional Reading
Index
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