Outline:
General or Specialized : General
Field of learning : natural science, common and basics
Required, Elective, etc. : Must complete subjects
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 goal of learning / education in this class are "(A), and A-1".
Course outline :
Start by understanding the concept of series and the power series expansion of functions. Next, we will develop the differentiation and integration of one-variable functions learned in the second grade, and learn about the differentiation of two-variable functions (partial differentiation) and the integration of two-variable functions (double-integral).
Style:
Course method :
Classes centered on board writing, and emphasize intuitive understanding of content without being biased toward rigor as much as possible. In addition, a lot of exercise time will be provided to deepen the understanding.
Grade evaluation method :
Exams [60%] + Others (exercises, reports, lessons, etc.)[40%].
Regular examinations will be conducted a total of 4 times, and the evaluation ratios will be the same. Depending on the grade, the student may be required to retake the exam or submit additional report.
Notice:
Precautions on the enrollment :
It is necessary to take this course in order to complete the course of the academic year.
Course advice :
Classes will be conducted while reviewing, but review mathematics (especially differentiation and integration) up to the 2nd year each time.
Foundational subjects :
Fundamental Mathematics (1st year), Fundamental Mathematics Practice (1st), Differential and Integral I (2nd), Fundamental Linear Algebra (2nd)
Related subjects :
Applied Mathematics I and II (4th year)
Attendance advice :
It is important to understand the content of the lecture well and solve the problem by yourself. It is important for students to find solutions on their own. If you are significantly late for class, treat it as absent. If you are late a lot, you may be treated as absent after giving a warning.
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Theme |
Goals |
1st Semester |
1st Quarter |
1st |
Guidance, Polynomial approximation (1) |
Students can find the linear approximation and the quadratic approximation of functions.
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2nd |
Polynomial approximation (2) |
Students can find the n-th approximation of functions, and can determine the extremal value of functions.
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3rd |
Limit of sequences |
Students can find the limit of various sequences including indeterminate forms.
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4th |
Series |
Students can judge the convergence and the divergence of a series.
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5th |
Power series and McLaughlin expansion |
Students can find the McLaughlin expansion of a function.
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6th |
Euler's formula |
Students can calculate complex numbers using Euler's formula.
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7th |
Function of two variables |
Students can draw a graph of a simple two-variable function.
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8th |
1st semester mid-term exam |
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2nd Quarter |
9th |
Return and commentary of exam answers, partial derivative |
Students can find the partial derivative of two-variable functions.
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10th |
Total differential and tangent plane |
Students can find the tangent plane equation
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11th |
Differential calculus of composite function |
Students can find the partial derivative using the derivative of the composite function.
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12th |
Higher-order partial derivative |
Students can find the higher derivative.
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13th |
Maximal value and minimal value |
Studentscan find maximal values and minimal values of two-variable functions.
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14th |
Exercise |
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15th |
1st semester final exam |
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16th |
Return and commentary of exam answers |
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2nd Semester |
3rd Quarter |
1st |
Guidance, Differential of implicit function |
Students can find the derivative using the differential of implicit function.
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2nd |
Conditional extremum problem |
Students can find conditional extrema.
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3rd |
Envelope |
Students can find the envelope equation.
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4th |
Definition of double integral |
Students can understand the definition of double integrals, and can express the volume of solids using double integrals.
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5th |
Calculation of double integral (1) |
Students can calculate the repeated integral.
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6th |
Calculation of double integral (2) |
Students can calculate the volume of solids using the change of integration order.
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7th |
Exercise |
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8th |
2nd semester mid-term exam |
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4th Quarter |
9th |
Return and commentary of exam answers, Multiple integral in polar coordinates |
Studentscan find the double integral by converting it to polar coordinates.
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10th |
Change of variables and multiple integrals |
Students can calculate the double integral using the general change of variables.
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11th |
Improper integral |
Students can calculate the improper integral.
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12th |
Various applications of double integrals (1) |
Students can find the area of the curved surface.
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13th |
Various applications of double integrals (2) |
Students can find the barycenter of the figure.
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14th |
Exercise |
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15th |
2nd semester final exam |
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16th |
Return and commentary of exam answers |
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