calculus of multivariable functions together with its profound applications are introduced in this half-semester course. specifically, 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, as well as applications such as computing the mass and center of mass of a solid. 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 make their skills in handling calculations in calculus more proficient under the guidance of our teaching assistants.
修完本課程學生能熟悉微積分工具，並應用在各學科。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。|
students would be familiar with calculus as a tool and be able to apply it in various subjects after finishing this course. "calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like engineering mathematics, analysis and differential
students participating in the course should be already skilled in high school mathematics. they are expected to attend and participate actively in lectures as well as discussion sessions.
textbook: james stewart, daniel clegg, and saleem watson, calculus early transcendentals, 9th edition.|