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The success of this work has led the author to add a considerable number of worked examples and exercises. Advantage has also been taken to enlarge certain parts where experience showed that further explanations would be useful. The author acknowledges with gratitude many valuable suggestions and letters received, students and critics.

Contents: 1. To deliver you from the preliminary terrors 1. 2. On different degrees of smallness. 3. On relative growings. 4. Simplest cases. 5. Next stage. What to do with constants 6. Sums, differences, products and quotients. 7. Successive differentiation. 8. When time varies. 9. Introducing a useful dodge. 10. Geometrical meaning of differentiation. 11. Maxima and minima. 12. Curvature of curves. 13. Other useful dodges. 14. On true compound interest and the law of organic growth. 15. How to deal with sines and cosines. 16. Partial differentiation. 17. Integration. 18. Integrating as the reverse of differentiating. 19. On finding areas by integrating. 20. Dodges, pitfalls and triumphs. 21. Finding some solutions.