The course introduces concepts and skills of calculus of functions of several variables and the basic theory of differential equations, as well as Fourier analysis and calculus of variations that are useful to understand other mathematical techniques applied to modelling in the financial markets. The emphasis will be on the basic understanding of the concepts, techniques and applications.

CILO-1: Develop an understanding of partial derivative and its geometric meaning, and compute derivatives using appropriate rules of differentiation. CILO-2: Apply differential calculus to calculate rates of change, locate local extrema and approximate functional change by means of the total differential. CILO-3: Apply the idea of Lagrange Multiplier to constrained optimization problems. CILO-4: Use differential equations to model basic problems in economics and finance. CILO-5: Acquire the techniques for solving certain classes of first and second order linear partial differential equations using Fourier Series. CILO-6: Acquire a basic knowledge of calculus of variations, and aware of its applications in economics and finance. CILO-7: Demonstrate the ability to evaluate and differentiate multiple integrals. CILO-8: Develop better problem solving skill.