The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.
Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.
The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.
1. Cover image - p. Cover 2. Title page - p. Cover 3. Table of Contents - p. Cover 4. Copyright - p. Cover 5. Preface to the Third Edition - p. iv 6. Notation - p. x 7. Chapter 1: Preliminaries - p. xii 8. Chapter 2: Functions and Inverse Functions - p. 27 9. Chapter 3: Polynomials and Rational Functions - p. 49 10. Chapter 4: Induction and the Binomial Theorem - p. 70 11. Chapter 5: Trigonometry - p. 87 12. Chapter 6: Complex Numbers - p. 111 13. Chapter 7: Limits and Continuity - p. 141 14. Chapter 8: Differentiation—Fundamentals - p. 165 15. Chapter 9: Differentiation—Applications - p. 185 16. Chapter 10: Curve Sketching - p. 188 17. Chapter 11: Matrices and Linear Equations - p. 239 18. Chapter 12: Vectors and Three Dimensional Geometry - p. 274 19. Chapter 13: Products of Vectors - p. 298 20. Chapter 14: Integration—Fundamentals - p. 327 21. Chapter 15: Logarithms and Exponentials - p. 351 22. Chapter 16: Integration—Methods and Applications - p. 380 23. Chapter 17: Ordinary Differential Equations - p. 409 24. Chapter 18: Sequences and Series - p. 431 25. Chapter 19: Numerical Methods - p. 466 26. Appendix A: Answers to Exercises - p. 488 27. Appendix B: Solutions to Problems - p. 509 28. Appendix C: Limits and Continuity—A Rigorous Approach - p. 525 29. Appendix D: Properties of Trigonometric Functions - p. 538 30. Appendix E: Table of Integrals - p. 540 31. Appendix F: Which Test for Convergence? - p. 542 32. Appendix G: Standard Maclaurin Series - p. 543 33. Index - p. 544
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.
Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.
The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.
1. Cover image - p. Cover 2. Title page - p. Cover 3. Table of Contents - p. Cover 4. Copyright - p. Cover 5. Preface to the Third Edition - p. iv 6. Notation - p. x 7. Chapter 1: Preliminaries - p. xii 8. Chapter 2: Functions and Inverse Functions - p. 27 9. Chapter 3: Polynomials and Rational Functions - p. 49 10. Chapter 4: Induction and the Binomial Theorem - p. 70 11. Chapter 5: Trigonometry - p. 87 12. Chapter 6: Complex Numbers - p. 111 13. Chapter 7: Limits and Continuity - p. 141 14. Chapter 8: Differentiation—Fundamentals - p. 165 15. Chapter 9: Differentiation—Applications - p. 185 16. Chapter 10: Curve Sketching - p. 188 17. Chapter 11: Matrices and Linear Equations - p. 239 18. Chapter 12: Vectors and Three Dimensional Geometry - p. 274 19. Chapter 13: Products of Vectors - p. 298 20. Chapter 14: Integration—Fundamentals - p. 327 21. Chapter 15: Logarithms and Exponentials - p. 351 22. Chapter 16: Integration—Methods and Applications - p. 380 23. Chapter 17: Ordinary Differential Equations - p. 409 24. Chapter 18: Sequences and Series - p. 431 25. Chapter 19: Numerical Methods - p. 466 26. Appendix A: Answers to Exercises - p. 488 27. Appendix B: Solutions to Problems - p. 509 28. Appendix C: Limits and Continuity—A Rigorous Approach - p. 525 29. Appendix D: Properties of Trigonometric Functions - p. 538 30. Appendix E: Table of Integrals - p. 540 31. Appendix F: Which Test for Convergence? - p. 542 32. Appendix G: Standard Maclaurin Series - p. 543 33. Index - p. 544
