Learning purposes: Familiarize yourself with the concept and handling of differentiation and integration.
Course Objective
1. To can understand the concept of differentiation and find the derivative of a basic function.
2. To can draw the increase / decrease table of the function, find the extremum, and draw the outline of the graph.
3. To can understand the concept of integrals and be able to find indefinite integrals and definite integrals of basic functions.
4. To by applying the integral, the length of the curve and the volume of the solid can be obtained.
Outline:
General or Specialized : General
Field of learning : Natural science common and basic
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 on this class is is "(A)".
Class Outline : The differential calculus, along with the integral method, was discovered by Newton and Leibniz in the 17th century. In the first semester, you will learn to differentiate various functions, and learn how to find tangents and normals, and the limit of indeterminate forms. After it was recognized that the integral calculation was the inverse of the differential calculus, many quadrature problems became easier to calculate. In the second half, you will learn about the integration method and how to find the area of figures, the length of curves, and the volume of solids.
Style:
Course method : Classes will be centered on board writing, but at the same time, as much exercise time as possible will be provided so that students can understand the content of the lecture more deeply and acquire the ability to solve problems on their own.
Grade evaluation method : Evaluate the total of 4 regular exams (60% evaluated equally) and other exams, exercises, reports, and lesson approaches (40%). Depending on the grades, etc., a retaking exams may be conducted (report submission is required). Textbooks, notebooks, etc. are not allowed for the exam.
Notice:
Precautions on the enrollment : Students must take this class(no more than one-third of the required number of class hours missed) are required to complete the course of the academic year.
Course advice : It is important to make sure to prepare and review, and to understand the lecture contents more deeply by solving the exercises on your own.
Foundational subjects : Fundamental mathematics (1st year), Fundamental mathematics practice (1)
Related subjects : Mathematics, physics, and other subjects after the 3rd year
Attendance advice : It is important to understand the content of the lecture and solve the problem yourself. I want you to value finding a solution on your own. If there are many late arrivals (those who came 10 minutes after the start of class), they may be treated as absent after giving a warning.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Guidance, functions and their properties, limits of functions |
The limits of various functions can be found.
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| 2nd |
Derivative coefficient, derivative |
Understand and obtain the meaning of differential coefficients. Understand the definition of derivatives.
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| 3rd |
Derivative properties |
Understand the nature of derivatives.
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| 4th |
Derivatives of trigonometric functions, derivatives of exponential functions |
The derivatives of trigonometric functions and exponential functions can be obtained.
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| 5th |
Derivatives of composite functions, derivatives of logarithmic functions |
Derivatives of composite functions and logarithmic functions can be obtained.
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| 6th |
Inverse trigonometric function and its derivative |
Understand inverse trigonometric functions. The derivative of the inverse trigonometric function can be obtained.
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| 7th |
Exercises |
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| 8th |
1st semester mid-term exam |
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| 2nd Quarter |
| 9th |
Return and commentary of exam answers, continuity of functions |
Understand the continuity of functions.
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| 10th |
tangents and normals, and Increase / decrease of functions |
You can find tangent and normal equations for basic functions. You can find the increase or decrease of the function.
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| 11th |
Maximum and minimum, and maximum and minimum of function |
You can write an increase / decrease table of a function, find an extremum, and draw an outline of a graph. The maximum and minimum values of the function can be calculated.
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| 12th |
Indeterminate limit, higher order derivative |
The limit of indeterminate form can be found. It is possible to obtain a derivative of degree 2 or higher.
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| 13th |
Curve unevenness, parameter representation and differential calculus |
The unevenness of the curve can be obtained. Understand the parameter representation of a function and be able to calculate its derivative.
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| 14th |
(Do not do velocity and acceleration), mean value theorem, exercises |
Understand the mean value theorem.
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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 |
Indefinite integral |
Understand the definition of indefinite integral and be able to perform basic calculations.
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| 2nd |
Definition of definite integral, basic theorem of differential integral method |
Understand the definition of definite integral and the basic theorem of the differential integral method, and be able to obtain the value of definite integral.
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| 3rd |
Definite integral calculation |
The definite integral can be calculated using the basic theorem of the differential integration method.
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| 4th |
Various indefinite integral formulas |
Various indefinite integral formulas can be used.
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| 5th |
Integration by substitution |
The integration by substitution method can be used to find the indefinite and definite integrals of basic functions.
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| 6th |
Integration by parts |
The integration by parts method can be used to find the indefinite and definite integrals of basic functions.
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| 7th |
Application of integration by substitution and integration by parts |
The integration by substitution method and integration by parts method can be applied.
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| 8th |
2nd semester mid-term exam |
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| 4th Quarter |
| 9th |
Integral of various functions |
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| 10th |
Area of figure |
The area of the figure surrounded by the basic curve can be obtained.
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| 11th |
Curve length, solid volume |
The lengths of various curves can be obtained. The volume of a basic solid can be obtained.
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| 12th |
Graphic by parametric display |
The area, length, volume, etc. of the figure can be obtained by displaying the parameters.
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| 13th |
Polar coordinates |
Understand polar coordinates, draw graphs of polar equations, and find relevant areas.
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| 14th |
Improper integral |
The improper integral can be calculated.
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| 15th |
2nd semester final exam |
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| 16th |
Return and commentary of exam answers |
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