Course Objectives
(1) Can make a deductive inference based on basic matters, including reading and writing logical sentences containing mathematical formulae.
(2) Can perform basic calculations in vector calculus and apply them to engineering and physics on a basic level.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
Achievement 1 | Can accurately make a deductive inference based on basic matters. | Can make a deductive inference based on basic matters. | Cannot make a deductive inference based on basic matters. |
Achievement 2 | Can fully perform basic calculations in vector calculus and fully apply them to engineering and physics on a basic level. | Can perform basic calculations in vector calculus and apply them to engineering and physics on a basic level. | Cannot perform basic calculations in vector calculus and apply them to engineering and physics on a basic level. |
Assigned Department Objectives
Teaching Method
Outline:
In this course, we will learn the basics of vector calculus (including topics on complex functions of one variable) based on the calculus and linear algebra learned so far. This is also applied to engineering and physics, so this class will also cover them, including basic applications.
Style:
Classes will be taught in a lecture style, and there will also be exercises and quizzes.
Notice:
Instead of memorizing theorems and formulae individually, carefully follow the development of discussions and the proof of theorems given in each lecture, so that you can understand it yourself. In problem exercises, do not try to remember the steps to solve a problem, but rather try to solve it yourself based on definitions and basic theorem and ideas. Also, if necessary, review the content learned during the previous years.
The schedule of the midterm exam may be changed.
Students who miss 1/3 or more of classes will not be eligible for evaluation.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
2nd Semester |
3rd Quarter |
1st |
Review and supplementary lesson on vector calculations |
Can handle the basic matters of vector calculations that's necessary for future learning.
|
2nd |
Curves
|
Can handle curves using parameters.
|
3rd |
Curves |
Can handle curves using the arc length parameter.
|
4th |
Line integrals |
Can calculate and discuss based on the basic matters of line integrals.
|
5th |
Line integrals Gradient |
Can perform calculations and discussions related to Green's theorem. Can calculate and discuss based on the basic matters of the gradient vector.
|
6th |
Gradient |
Can perform calculations and discussions related to exact differential equations.
|
7th |
Conservative forces and potential energy Surfaces and surface integrals |
Can handle conservative forces and potential energy based on the methods of vector calculus. Can handle surfaces using parameters.
|
8th |
Surfaces and surface integrals Midterm exam
|
Can perform calculations and discussions related to tangent planes.
|
4th Quarter |
9th |
Surfaces and surface integrals |
Can calculate and discuss based on the basic matters of surface integrals.
|
10th |
Derivative of vector fields and integral theorem |
Can calculate and discuss based on the basic matters of volume integrals.
|
11th |
Derivative of vector fields and integral theorem |
Can calculate and discuss based on the basic matters of the divergence of a vector field and Gauss's theorem.
|
12th |
Derivative of vector fields and integral theorem Overview of the theory of functions of a complex variable |
Can calculate and discuss based on the basic matters of the rotation of a vector field and Stokes's theorem. Can calculate and discuss based on the basic matters of the functions of a complex variable.
|
13th |
Overview of the theory of functions of a complex variable |
Can calculate and discuss based on the basic matters of complex integrals.
|
14th |
Overview of the theory of functions of a complex variable |
Can calculate and discuss based on the basic matters of singular points.
|
15th |
Application to electromagnetism |
Can handle the basic matters of electromagnetism based on the methods of vector calculus.
|
16th |
Final exam
|
|
Evaluation Method and Weight (%)
| Examinations | Exercises / Quizzes | Attendance / Behavior | Total |
Subtotal | 40 | 30 | 30 | 100 |
Basic Proficiency | 40 | 30 | 30 | 100 |
Specialized Proficiency | 0 | 0 | 0 | 0 |
Cross Area Proficiency | 0 | 0 | 0 | 0 |