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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