Course Objectives
Learning purposes :
Students will acquire the mathematical knowledge, calculation techniques, and applied abilities necessary to solve basic engineering problems through Laplace transform, vector analysis, Fourier series, and Fourier transform.
Course Objectives :
1. To understand the concepts of the Laplace transform and apply them to the solution of differential equations.
2. To understand the concepts of Fourier series and Fourier transform, and be able to find the Fourier transform of basic functions.
3. To understand the basic concepts of vector analysis such as gradient, divergence, rotation, line integral, and surface integral, and be able to solve problems related to them.
Rubric
| Excellent | Good | Acceptable | Not acceptable |
| Achievement 1 | The student can solve applied problems related to Laplace transform | The student an solve about 70% of the basic problems related to Laplace transform. | The student can solve about 60% of the basic problems related to Laplace transform. | The student can not solve about 60% of the basic problems related to Laplace transform. |
| Achievement 2 | The student can solve applied problems related to Fourier series and Fourier transform. | The student can solve about 70% of basic problems related to Fourier series and Fourier transform | The student can solve about 60% of basic problems related to Fourier series and Fourier transform. | The student can not solve about 60% of basic problems related to Fourier series and Fourier transform. |
| Achievement 3 | The student can solve applied problems related to vector analysis. | The student can solve about 70% of basic problems related to vector analysis. | The student can solve about 60% of basic problems related to vector analysis. | The student can not solve about 60% of basic problems related to vector analysis. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : General
Field of learning : Natural sciences, Common and basic
Required, Elective, etc. : Must complete subjects
Foundational academic disciplines：
Mathematical science / mathematics / analysis basics
Relationship with Educational Objectives :
This class is equivalent to "(2) Acquire basic science and technical knowledge".
Relationship with JABEE programs :
The main goal of learning / education in this class are "(A), and A-1".
Course outline :
The 1st semester deals with Laplace transform, Fourier series, and Fourier transform. The 2nd semester deals with vector analysis.
Style:
Course method :
The course is based on lectures with exercises given to further deepen understanding.
Grade evaluation method :
Exams [60%] + Others (exercises, reports, etc.)[40%].
Regular examinations will be conducted a total of 4 times, and the evaluation ratios will be the same. Additional assignments may be given depending on grades. Re-examinations, in principle, will not be conducted.
Notice:
Precautions on the enrollment :
Students must take courses to complete the course of the academic year (the number of absence hours must be less than one-third of the class hours).
Course advice :
Review and confirm the contents of mathematics up to the third grade, especially trigonometric functions, space vectors, determinants, differential calculus (including partial derivatives), and integral calculus (including multiple integrals). As a preparatory study, review the integration by parts in Differential and Integral I.
Foundational subjects :
Fundamental mathematics (1st year), Fundamental Linear Algebra (2nd), Differential and Integral I, II (2nd, 3rd), Fundamental Differential Equations (3rd)
Related subjects :
Physics after 4th year, specialized subjects
Attendance advice :
Students who join the class after the attendance verification are marked as tardy. Three tardy arrivals count as one absence.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Guidance, Laplace transform |
Students can find the Laplace transform of basic functions.
|
| 2nd |
Inverse Laplace transform |
Students can find the inverse Laplace transform of the basic function.
|
| 3rd |
Differentiation formulas and solutions for differential equations |
Students can use the Laplace transform to solve basic differential equations.
|
| 4th |
Exercise |
Confirm basic matters
|
| 5th |
Unit step function and delta function |
Students can find the Laplace transform of the unit step function and the delta function.
|
| 6th |
Convolution |
Students can calculate the convolution of basic functions.
|
| 7th |
Linear system |
For linear systems, students can find the response to the basic input.
|
| 8th |
1st semester mid-term exam |
|
| 2nd Quarter |
| 9th |
Return and commentary of exam answers, periodic function |
Students can find the integral of the period of the periodic function and the basic trigonometric function.
|
| 10th |
Fourier series |
Students can find the Fourier series of the basic periodic function.
|
| 11th |
Complex Fourier series |
Students can find the complex Fourier series of the basic periodic functions.
|
| 12th |
Fourier transform |
Students can find the Fourier transform of the basic function.
|
| 13th |
Fourier integral theorem |
Students can solve problems that apply the Fourier integral theorem.
|
| 14th |
Exercise |
Confirm basic matters
|
| 15th |
1st semester final exam |
|
| 16th |
Return and commentary of exam answers |
Confirm basic matters
|
| 2nd Semester |
| 3rd Quarter |
| 1st |
Guidance, Vector and its dot product |
Students can calculate the dot product of vectors.
|
| 2nd |
Vector cross product |
Students can calculate the cross product of vectors.
|
| 3rd |
Scalar field and vector field, gradient |
Studentsan find the gradient of the scalar field.
|
| 4th |
Divergence |
Students can find the divergence of the scalar field.
|
| 5th |
Rotation |
Students can find the rotation of the vector field.
|
| 6th |
Curve, scalar field line integral |
Students can find the line integral of the scalar field.
|
| 7th |
Line integral of vector field |
Students can find the line integral of the vector field.
|
| 8th |
2nd semester final exam |
|
| 4th Quarter |
| 9th |
Return and commentary of exam answers, Surface parameter display, curved surface tangent vector and normal vector |
Students can find the parametric representation of the surface, the tangent vector and the normal vector of the surface.
|
| 10th |
Surface integral of scalar field |
Students can find the surface integral of the scalar field.
|
| 11th |
Surface integral of vector field |
Students can find the surface integral of the vector field.
|
| 12th |
Exercise |
Confirm basic matters
|
| 13th |
Gauss's divergence theorem, Green's theorem |
Students can use Gauss's divergence theorem to find the surface integral on the surface of solids.
|
| 14th |
Stokes' theorem |
Using Stokes' theorem, students can find the line integral along the boundary of a curved surface.
|
| 15th |
2nd semester final exam |
|
| 16th |
Return and commentary of exam answers |
Confirm basic matters
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 60 | 0 | 0 | 0 | 0 | 40 | 100 |
| Basic Proficiency | 60 | 0 | 0 | 0 | 0 | 40 | 100 |
| Specialized Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |