Techniques of mathematical analysis

Cover......Page 1
General Editor\'s Foreward......Page 8
Preface......Page 10
Contents......Page 12
Abbreviations of Example and Exercise Sources......Page 15
1. Real Numbers. Fundamental Inequalities. Functions of Real Variables......Page 16
2. Finite Series......Page 37
3. The Convergence of Sequences and Series......Page 54
4. Complex Numbers......Page 90
5. The Theory of Equations......Page 122
6. Analytical Trigonometry......Page 154
7. Determinants......Page 189
8. Functions of a Continuous Variable. General Theorems of the Differential Calculus......Page 222
9. Partial Differentiation......Page 251
10. More Advanced Methods of Integration. Further Theorems in the Integral Calculus......Page 275
11. Some Further Geometrical Applications of the Calculus......Page 318
12. Elementary Differential Equations......Page 364
Answers to the Exercises......Page 394
Index......Page 408