Course Objectives
Develop important mathematical thinking and problem solving skills as engineering technicians based on the mathematics learned previously. The goal of this class is for students to acquire the ability to understand more specialized applied mathematics.
(1) First, understand the convergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Then understand the function of two variables as a curved surface in space, and are able to calculate partial differentials and multiple integrals.
(2) Acquire a faithful understanding of theories and the ability to express them theoretically.
(3) Acquire the ability to apply an abstract framework to specific issues.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Fully understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Then fully understand two-variable functions as curved surfaces in space, and sufficiently calculate partial derivatives and multiple integrals. | Understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Understand a two-variable function as a curved surface in space, and can calculate partial differentials and multiple integrals.
| Cannot understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Do not understand a two-variable function as a curved surface in space, and cannot calculate partial differentials or multiple integrals. |
| Achievement 2 | Fully have a good understanding of theories and the ability to express them theoretically. | Have a understanding of theories and the ability to express them in theoretically. | Do not have a understanding of theories and the ability express them theoretically. |
| Achievement 3 | Fully have the ability to apply an abstract framework to specific issues. | Have the ability to apply an abstract framework to specific issues. | Do not have the ability to apply an abstract framework to specific issues. |
Assigned Department Objectives
Teaching Method
Outline:
Students will acquire the basic concepts of differential integration and the various computational methods developed from it, and the necessary resources for analyzing various events in the specialized fields. We will mainly teach the convergence and divergence of a sequence, the convergence and divergence of a series, the evolution of the Maclaurin series, the partial differentiation of a two-variable function and its application, and the application of double integrals.
Style:
During the first half, Classes will assume the pre-study has been done, and follow the textbook accordingly. There will also be problem exercises. Students will be asked questions to check their understanding during classes. In the classes, focus on understanding, and ask questions about things do not understand in the pre-study or class, rather than doing nothing about them. Make an effort to always review the material on the same day, and solve the problems in the textbook and the workbook. Some of the classes will use ICT. Tests will sometimes be held without prior notice to confirm attainment. Consequently, please study properly on a daily basis.
During the second half, students will be asked to prepare for the lesson using videos along the syllabus, and to have them study in groups during the lesson.
Matsumiya is in charge of the first half, and Takata in the second half.
Notice:
Try to understand the material thoroughly during the classes. Make an effort to always ask about things that are unclear, and solve them then and there. Also, always review the material on the same day, and do the problem exercises properly by solving the problems in the textbook and the workbook.
During the first half, quizzes will sometimes be given without prior notice, so study properly on a daily basis. The overall evaluation will be based 50% on exams, 20% on submitted assignments, etc., and 30% on presentations and general effort toward classes. The minimum score for a pass will be 60 marks. However, evaluation scores based on these weightings will be calculated at the end of the first half. The cumulative evaluation up to the first semester midterm be based on interim weightings rather than the ones given above. Students who do well in assignments, presentations, etc. may get them evaluated with a higher weighting.
CBT will be conducted in any week.
Students who miss 1/3 or more of classes will not be eligible for a passing grade.
This course's content will amount to 180 hours of study in total. These hours include the learning time guaranteed in classes and the standard self-study time required for pre-study / review, and completing assignment reports.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Differential Equation
|
Understand the second-order differential equation and solve the problem of a simple second-order differential equation.
|
| 2nd |
Differential Equation |
Various simple second-order differential equations such as constant coefficients non-asymmetric linear differential equations can be solved.
|
| 3rd |
Expansion of functions |
Can calculate an approximation by polynomials. Can calculate the local primary approximation of a simple one-variable function.
|
| 4th |
Expansion of functions |
Can calculate an approximation by polynomials.
|
| 5th |
Expansion of functions |
Can calculate various columns of extremes, including indeterminate shapes.
|
| 6th |
Expansion of functions |
Can investigate and calculate the sum of the convergence and divergence of simple series such as infinite equalization series.
|
| 7th |
Expansion of functions |
Can investigate and calculate the sum of the convergence and divergence of simple series such as infinite equalization series.
|
| 8th |
Expansion of functions
|
Understand the Maclaurin expansion of one-variable functions and can calculate the Maclaurin expansion of basic functions.
|
| 2nd Quarter |
| 9th |
Expansion of functions |
Understand the Taylor expansion of one-variable functions and can calculate the Taylor expansion of basic functions.
|
| 10th |
Partial differentiation method |
Can use the Euler formula to perform simple computation of the exponential function of a complex variable.
|
| 11th |
Partial differentiation method |
Understand two-variable functions and can draw simple curves. Understand the definition area of a two-variable function and can represent it by inequality or graph.
|
| 12th |
Partial differentiation method |
Can calculate partial derivatives.
|
| 13th |
Partial differentiation method |
Understand the total derivative and can calculate the total derivative.
|
| 14th |
Partial differentiation method |
Can calculate the equation of a tangent plane.
|
| 15th |
Partial differentiation method |
Can use the partial derivative of a synthesis function to calculate the partial derivative.
|
| 16th |
Final exam
|
|
| 2nd Semester |
| 3rd Quarter |
| 1st |
Applying the partial differentiation method |
Can calculate the differential calculus of the implicit function.
|
| 2nd |
Applying the partial differentiation method |
Can solve the problem of constrained extrema.
|
| 3rd |
Applying the partial differentiation method |
Can obtain the envelope equation.
|
| 4th |
Summary |
To check was learned so far.
|
| 5th |
Double integrals |
Can understand the definition of double integrals and evaluate simple double integrals.
|
| 6th |
Double integrals |
Can change the order of double integrals.
|
| 7th |
Double integrals |
Can determine the volume of a solid by using double integrals.
|
| 8th |
Variable conversion and multiple integrals
|
Can obtain the double integral by converting to polar coordinates.
|
| 4th Quarter |
| 9th |
Applying the partial differentiation method |
Can calculate the variable transformation of double integrals.
|
| 10th |
Variable conversion and multiple integrals |
Can obtain the improper integral.
|
| 11th |
CBT |
To check was learned so far.
|
| 12th |
Variable conversion and multiple integrals |
Can obtain the improper integral by using double integral.
|
| 13th |
Variable conversion and multiple integrals |
Can calculate the average and center of gravity by using double integrals.
|
| 14th |
Summary |
To check was learned so far.
|
| 15th |
Summary |
Do a total review.
|
| 16th |
Final exam
|
To check was learned so far.
|
Evaluation Method and Weight (%)
| Examination(first half) | Task(first half) | Status of efforts(first half) | Examination(second half) | Comprehension confirmation test(second half) | Review quiz(second half) | Assignments(second half) | Attendance(second half) | Total |
| Subtotal | 25 | 10 | 15 | 13 | 10 | 12 | 8 | 7 | 100 |
| Basic Proficiency | 25 | 10 | 15 | 13 | 10 | 12 | 8 | 7 | 100 |
| Specialized Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |