Polyteknisk Boghandel

A complete, self-taught course in analysis. and mathematics that enables you to. improve your math skills. "Calculus Know-It-ALL" uses a reader-friendly. tone and slow-paced presentation to teach all aspects. of calculus. Featuring the proven pedagogy that has. made Stan Gibiliscos McGraw-Hill titles so successful, . the book presents easy-to-understand concepts, extensively. explained exercises, multiple-choice questions And. answers, and abundant self-test questions.. Filled with over 250 illustrations, this great educational. resource takes you step-by-step through the. concept of a set and its relevance to mathematics, set. notation and operations, the difference between a. rational number and a real number, imaginary and. complex numbers, and proving theorems by mathematical. induction. You will also learn how to add, . subtract, and multiply complex numbers, add finite and. infinite series, master techniques of differentiation and. integration, and 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