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Teaching/FN6801

FN6801 / FE8506 · Previously taught postgraduate course

Calculus & Linear Algebra

MSc in Financial Engineering, Nanyang Business School

Fall, 2019–2025Back to teaching history

I taught FN6801/FE8506 from 2019 to 2025. Current syllabus, assessment and course materials are provided by Nanyang Business School and through NTULearn.

Overview

This course review important concepts and methods in linear algebra, before moving on to introduce multivariate calculus, culminating in the solution of ordinary and partial differential equations. In particular, we will understand their implications in finance with concrete examples.

By the end of this course, you should be able to:
1. Solve linear systems, change the bases of vector spaces, compute and operate matrices, and diagonalize and decompose matrices with their eigenvalues and eigenvectors.
2. Compute the partial and total derivatives as well as multiple integrals of functions and leverage on them to optimize and approximate functions.
3. Solve the first-order and second-order ordinary differential equations as well as the Black-Scholes-type parabolic partial differential equations.

Assessment Scheme

  • 3 Take-home Assignments (20%)
  • 3 In-class Quizzes (20%)
  • Final Examination (60%)

Topics

  1. [3.5hrs] Linear Algebra I - Linear Systems and Vector Spaces;
  2. [3.5hrs] Linear Algebra II - Eigenvalues and Eigenvectors;
  3. [3.5hrs] Multivariate Calculus I - Differentiation and Optimization;
  4. [3.5hrs] Multivariate Calculus II - Approximation and Integration;
  5. [3.5hrs] Differential Equation I - Ordinary Differential Equations;
  6. [3.5hrs] Differential Equation II - Partial Differential Equations.

References