## CALCULUS (3)

#### Department of Mathematics Kwok-Wing Tsoi (蔡國榮)

### 課程簡介

**中文課程名稱：**微積分3

**英文課程名稱：**CALCULUS (3)

**授課教師：**Kwok-Wing Tsoi (蔡國榮)

**學分數：**2 學分

**開課單位：**Department of Mathematics

**建立日期：**2023 年 2 月

### 課程概述

Having discussed Calculus on functions of a single (real) variable in MATH4006-7, this course turns to an introduction (and applications) of multivariable (mainly 2- and 3-variable) Calculus, which is the foundation for various disciplines in Science and Engineering.

Topics to be discussed include :

- Partial derivatives,

- Continuous and differentiable functions in multivariables,

- Chain rule and directional derivatives,

- Second derivative test for two-variable functions and the method of Lagrange multipliers,

- Double and triple integrations.

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.

### 課程目標

On successful completion of this module students should be able to:

- Compute partial derivatives and understand their geometric meaning

- Determine whether a multivariable function is continuous and/or differentiable

- Apply the chain rule to compute derivatives of composed functions in multivariables & directional derivatives

- Determine local extrema of a given two-variable function

- Use Lagrange multiplier to resolve constrained optimization problems

- Compute multiple integrations by Fubini's Theorem and/or change of variables

- Understand the geometric and physical meanings of multiple integrations

### 課程要求

Assumed knowledge :

- MATH4006-7,

- Basic trigonometry, vector geometry,

- Determinants of 2x2 and 3x3 matrices (knowledge in linear algebra will be useful but not necessary)