Course Objectives
At the completion of this course, students will be able to
1) Calculate double integrals, change the order of integration, the volume of solids, double integrals in polar coordinates, change variables in double integrals, and improper integrals.
2) Solve first-order differential equations (separation of variables, first-order linear differential equations, homogeneous form) and second-order differential equations (constant coefficient homogeneous linear differential equations, constant coefficient inhomogeneous linear differential equations, etc.).
Rubric
| Ideal Level of Achievement | Standard Level of Achievement | Unacceptable Level of Achievement) |
| Evaluation 1 | Can calculate double integrals, change the order of integration, the volume of solids, double integrals in polar coordinates, change variables in double integrals, and improper integrals with more than 80% correct answers. | Can calculate double integrals, change the order of integration, the volume of solids, double integrals in polar coordinates, change variables in double integrals, and improper integrals with more than 60% correct answers. | Can't calculate double integrals, change the order of integration, the volume of solids, double integrals in polar coordinates, change variables in double integrals, and improper integrals. |
| Evaluation 2 | Can solve first-order differential equations (separation of variables, first-order linear differential equations, homogeneous form) and second-order differential equations (constant coefficient homogeneous linear differential equations, constant coefficient inhomogeneous linear differential equations, etc.) with more than 80% correct answers. | Can solve first-order differential equations (separation of variables, first-order linear differential equations, homogeneous form) and second-order differential equations (constant coefficient homogeneous linear differential equations, constant coefficient inhomogeneous linear differential equations, etc.) with more than 60% correct answers. | Can't solve first-order differential equations (separation of variables, first-order linear differential equations, homogeneous form) and second-order differential equations (constant coefficient homogeneous linear differential equations, constant coefficient inhomogeneous linear differential equations, etc.). |
Assigned Department Objectives
Diploma policy 3
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Teaching Method
Outline:
In this course, students will learn double integrals, ordinary differential equations, and more.
Exercises will be conducted in parallel with lectures to acquire mathematical and computational techniques required in engineering and other subjects.
Style:
The content of the lectures gradually increases in quantity and quality. We recommend that students prepare for each lecture.
If there is anything you do not understand in the lectures, please review it immediately and try to understand it. Active questions are always recommended.
It is not enough to understand basic contents once. Please train repeatedly.
The lecture plan may be changed according to the student's level of understanding.
Notice:
Mini-exams will be carried out up to several times.
Evaluations will be made comprehensively by written exams (making up about 90% of the grade), by exercises and homework (making up about 10% of the grade).
Can take makeup exam in need aid up to maximum of 60 points.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 2nd Semester |
| 3rd Quarter |
| 1st |
Double integrals (1) |
Review (mini-exam), guidance, definition of double integrals.
Definition of double integrals, calculation of double integrals.
|
| 2nd |
Double integrals (2) |
Calculation of double integrals, change the order of integration.
Change the order of integration, the volume of solids.
|
| 3rd |
Double integrals (3) |
The volume of solids, exercise.
(Mini-exam.)
|
| 4th |
Change of variables and multiple integrals (1) |
Double integrals in polar coordinates.
Change variables in double integrals.
|
| 5th |
Change of variables and multiple integrals (2) |
Change variables in double integrals, improper integrals.
Improper integrals.
|
| 6th |
Change of variables and multiple integrals (3) |
Application of double integrals (the surface area and centroid).
|
| 7th |
Application of multiple integrals
|
Application of double integrals (the surface area and centroid).
Supplementary information up to this lecture, and exercise.
|
| 8th |
Mid-term examination |
|
| 4th Quarter |
| 9th |
First-order differential equations (1) |
Answers and explanations for the mid-term exam, meaning of differential equations.
Solutions of differential equations, separation of variables.
|
| 10th |
First-order differential equations (2)
|
Separation of variables, first-order linear differential equations.
Homogeneous form.
|
| 11th |
First-order differential equations (3) |
Exercise. (Mini-exam.)
Solutions of second-order differential equations.
|
| 12th |
Second-order differential equations (1) |
Second-order linear differential equations.
Constant coefficient homogeneous linear differential equations.
|
| 13th |
Second-order differential equations (2) |
Constant coefficient homogeneous linear differential equations.
Constant coefficient inhomogeneous linear differential equations.
|
| 14th |
Second-order differential equations (3) |
Various linear differential equations.
Supplementary information up to this lecture, and exercise.
|
| 15th |
Final examination |
|
| 16th |
Answers and explanations for the final exam, and class questionnaires |
Answers and explanations for the final exam, and class questionnaires.
Summary of the 2nd semester and advice for spring vacation and the next grade.
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 90 | 0 | 0 | 0 | 0 | 10 | 100 |
| Basic Ability | 90 | 0 | 0 | 0 | 0 | 10 | 100 |
| Technical Ability | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Interdisciplinary Ability | 0 | 0 | 0 | 0 | 0 | 0 | 0 |