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Table of Content
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 Optimizations II
20. Homogenous and Homothetic 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