Functions and inverse functions
Limits, derivatives, partial derivatives, and chain rule
Integrals and multiple integrals, changing the order of differentiation and integration
Taylor series approximations
Newton's method
Lagrange multiplier method
Vector and matrix arithmetic, determinants, eigenvalue-eigenvector decomposition, singular value decomposition
Numerical methods for optimization
Upon completion of the course students will know the fundamental mathematical concepts needed to effectively study quantitative finance areas such as fixed income, options and derivatives, portfolio optimization, and quantitative risk management.
Understand the concept of a limit, differentiation, and integration;
Be able to compute partial derivatives and multiple integrals;
Understand the utility of matrix decompositions;
Be able to use Lagrange multipliers to solve constrained optimization problems; and
Apply the above methods to problems arising in finance.

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