## 基本素養 Basic Literacy

Ethics and humanities

Integrity and pragmatic literacy

Environmental and social care

Possessing the ability of global view

## 核心能力 Competence

Apply knowledge of mathematics, science & engineering.

Design & operation of experiments, analysis and interpretation of data.

Necessary Technology, skill & modern tool usage for naval or mechatronic engineering.

Design systems, components or processes for naval or mechatronic engineering.

Project Management, effective Communication, and multidisciplinary teamwork.

Identify, formulate & solve engineering problems using reasoning of naval or mechatronic engineering.

Interested in global current issues, understand the impact of engineering techniques in societal, environmental and global contexts, and develop habit of life-long learning.

Respect for multi-perspective, understand professional ethics & recognize social responsibilities of engineers.

## 課程概述 Course Description

This class is a continuation of Calculus (1) , we will mainly discuss the differentiation and integration of functions in hyperspace. We will discuss vector-valued functions and functions of several variables.

## 課程學習目標 Course Objectives

• multivariate derivations
• multiple integrals
• sequence and series
• ## 課程進度 Progress Description

進度說明 Progress Description
1series, sequences, integral test, comparison test (11.1~11.4)
2alternating series, absolute convergence, ratio/root test, power series (11.5,11.6,11.8)
3representations of functions as power series, Taylor and Maclaurin series (11.9~11.10)
4calculus with parametric curves, polar coordinates (10.1~10.3)
5areas and lengths in polar coordinates, 3D spaces, vectors (10.4, 12.1~12.2)
6dot products, cross products (12.3~12.4), holiday (April 1)
7holiday (April 5), , equations of lines and planes (12.5),
8cylinders and quadric surfaces (12.6), functions of several variables, limits and continuity (14.1~14.2)
9partial derivatives, tangent planes and linear approximations (14.3~14.4), MIDTERM EXAM (April 22)
10chain rule, directional derivatives and gradient vector (14.5~14.6)
11maximum and minimum values, Lagrange multipliers (14.7~14.8)
12double integrals, iterated integrals (15.1~15.3)
13double integrals in polar coordinates, surface area (15.4,15.6)
14triple integrals in Cartesian and cylindrical coordinates (15.7~15.8)
15triple integrals in spherical coordinates (15.9), change of variables in multiple integrals (15.10)
16overview of vector functions (chap 13), holiday (June 10)
17overview of vector calculus (chap 16)
18FINAL EXAM (June 21)
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

## 有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No