Learning purposes : Students will acquire the mathematical knowledge, calculation techniques, and applied abilities necessary to solve basic engineering problems through Laplace transform, Fourier series and Fourier transform, and vector analysis.
Course Objectives :
1. You can apply mathematical methods to solve problems in your area of expertise.
2. To understand the concepts of Laplace transform, Fourier analysis, and vector analysis, and apply them to the solution of differential equations that appear in the field of engineering.
Outline:
General or Specialized : General
Field of learning : Common and basics of natural science
Foundational academic disciplines : Mathematical science / Mathematics / Basic analysis
Relationship with Educational Objectives : This class is equivalent to "(2) Acquire basic science and technical knowledge".
Relationship with JABEE programs : The main goals of learning / education in this class is (A),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 : Format is mainly lectures, but exercises are also given to deepen understanding.
Grade evaluation method : Evaluate based on the total of the results of the four regular exams (60% evaluated equally) and others (40% for exercises / submissions, etc.). Depending on the grades, re-exams and additional report assignments may be imposed.
Notice:
Precautions on the enrollment : Students must take this class (no more than one-third of the required number of class hours missed) in order to complete the 3rd year course.
Course advice : Make sure to check what you have learned in mathematics up to the 3rd year, especially trigonometric functions, spatial vectors, determinants, differential methods (including partial differentials), and integral methods (including multiple integrals) as preparatory learning in advance.
Foundational subjects : Fundamental Mathematics (1st year), Fundamental Mathematics Practice (1st), Differential and Integral Ⅰ (2nd), Fundamental Linear Algebra (2nd), Differential and Integral Ⅱ (3rd), Fundamental Differential Equations(3rd)
Related subjects : 4th year and above physics, specialized subjects
Attendance advice : Late arrivals are handled in 1/4 (= 0.5 hour) of class time (= 2 hour).
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Guidance
Correspondence confirmation about distance learning, trial of Microsoft Teams |
Understand the outline of the lesson and check the environment for distance lessons.
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| 2nd |
Laplace transform |
The Laplace transform of the basic function can be obtained.
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| 3rd |
Inverse Laplace transform |
The inverse Laplace transform of the basic function can be obtained.
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| 4th |
Differentiation formulas and solutions for differential equations |
The Laplace transform can be used to solve basic differential equations.
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| 5th |
Unit step function and delta function |
The Laplace transform of the unit step function and the delta function can be obtained.
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| 6th |
Composition product |
The composition product of basic functions can be calculated.
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| 7th |
Linear system |
For linear systems, the response to basic inputs can be found.
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| 8th |
Exercise |
Confirm basic matters, submit report
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| 2nd Quarter |
| 9th |
Periodic function |
The integral of the period of the periodic function and the basic trigonometric function can be obtained.
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| 10th |
Fourier series |
The Fourier series of the basic periodic function can be obtained.
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| 11th |
Partial differential equations and Fourier series |
Applied problems can be solved using Fourier series.
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| 12th |
Complex Fourier series |
The complex Fourier series of the basic periodic function can be obtained.
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| 13th |
Fourier Transform and Fourier Integral Theorem |
The Fourier transform of the basic function can be obtained. In addition, it is possible to solve a problem applying the Fourier integral theorem.
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| 14th |
Discrete Fourier transform |
The discrete Fourier transform of the basic function can be obtained.
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| 15th |
(1st semester final exam) |
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| 16th |
Return and commentary of exam answers |
Confirm basic matters
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Guidance
Vectors and their dot products |
The vector dot product can be calculated.
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| 2nd |
Vector cross product |
The vector cross product can be calculated.
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| 3rd |
Scalar field and vector field
Gradient |
The gradient of the scalar field can be obtained.
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| 4th |
Divergence |
The divergence of the scalar field can be sought.
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| 5th |
Rotation |
The rotation of the scalar field can be sought.
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| 6th |
Line integral of curve and scalar field |
The line integral of the scalar field can be obtained.
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| 7th |
Line integral of vector field |
The line integral of the vector field can be obtained.
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| 8th |
(2nd semester mid-term exam) |
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| 4th Quarter |
| 9th |
Return and commentary of exam answers
Surface parameter display, curved surface tangent vector and normal vector |
The parameter display of the curved surface and the tangent vector and normal vector of the curved surface can be obtained.
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| 10th |
Surface integral of scalar field |
The surface integral of the scalar field can be obtained.
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| 11th |
Surface integral of vector field |
The surface integral of the vector field can be obtained.
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| 12th |
Exercise |
Confirm basic matters
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| 13th |
Gauss's divergence theorem
Green's theorem |
Gauss's divergence theorem can be used to find the surface integral of a solid surface.
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| 14th |
Stokes' theorem |
Using Stokes' theorem, we can find the line integral along the boundary of a curved surface.
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| 15th |
(2nd semester final exam) |
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| 16th |
Return and commentary of exam answers |
Confirm basic matters
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