Calculus of multivariable functions together with its profound applications in various subject areas are introduced in this half-semester course. Especially, topics about differentiation include limits, partial derivatives, directional derivatives, tangent planes, linear approximations, and the chain rule. Also, applications such as finding extreme values and methods of Lagrange multipliers are discussed. Topics about integration involve definitions of multiple integrals and iterated integrals, Fubini’s theorem, change of variables, and how multiple integrals are used in probability.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course
also provides discussion sessions in which students are able to improve their skills in handling calculations in Calculus and complete small projects under the guidance of our teaching assistants.