Part I Introduction:
1. Introduction -
2. One-Variable Calculus: Foundations -
3. One-Variable Calculus: Applications –
4. One-Variable Calculus: Chain Rule –
5. Exponents and Logarithms –
Part II Linear Algebra:
6. Introduction to Linear Algebra –
7. Systems of Linear Equations –
8. Matrix Algebra –
9. Determinants: An Overview –
10. Euclidean Spaces –
11. Linear Independence –
Part III Calculus of Several Variables:
12. Limits and Open Sets –
13. Functions of Several Variables –
14. Calculus of Several Variables –
15. Implicit Functions and their Derivatives –
Part IV Optimization:
16. Quadratic forms and Definite Matrices –
17. Unconstrained Optimization –
18. Constrained Optimization I: First Order Conditions -
19. Constrained Optimization II –
20. Homogeneous and Omothetic Functions –
21. Concave and Quasiconcave Functions –
22. Economic Applications –
Part V Eigenvalues and Dynamics:
23. Eigenvalues and Eigenvectors –
24. Ordinary Differential Equations: Scalar Equations –
25. Ordinary Differential Equations: Systems of Equations ?
Part VI Advanced Linear Algebra:
26. Determinants : the Details –
27. Subspaces Attached to a Matrix –
28. Applications of Linear Independence –
Part VII: Advanced Analysis:
29. Limits and Compact Sets –
30. Calculus of Several Variables II –
Part VIII Appendices:
A1. Sets, Numbers, and Proofs –
A2. Trigonometric Functions –
A3. Complex Numbers –
A4. Integral Calculus –
A5. Introduction to Probability -
A6. Selected Answers -
Index.

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