As a continuation of the course MATH1201 Calculus A, in which Calculus on functions of a single variable is discussed, this course turns to the introduction and applications of multivariable (mainly 2- and 3-variable) Calculus, which is the foundation of most of the practical use of Calculus in real life. Topics to be highlighted include definitions of partial derivatives and double/triple/line/surface integrals together with their geometric meanings, method of Lagrange Multipliers for solving extreme-value problems with constraints, and Green's/Stokes'/Divergence Theorem (multivariable version of the Fundamental Theorem of Calculus).

For the completeness of the discussion on limits of a function or a sum of functions in the course of the study of Calculus, the definitions of limits of sequences and series are also introduced, which provide the theoretical basis of the introduction of power series. Power series is a generalisation of polynomials and can be used to represent elementary as well as more general functions, which paves the way for more advanced analysis of functions, necessary in practical applications in the non-idealistic world.

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 sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.