# 基礎数学Ⅰ

### 科目基礎情報

学校 開講年度 佐世保工業高等専門学校 令和02年度 (2020年度) 基礎数学Ⅰ 0028 一般 / 必修 講義 履修単位: 4 電子制御工学科 1 通年 4 Kiso Sugaku (Morikita Publishing Co., Ltd.)/Kiso Sugaku Mondaishu (Morikita Publishing Co., Ltd.) 三ッ廣 孝

### 目的・到達目標

1. Calculate basic mathematical and integral expressions.

### ルーブリック

Ideal Level Standard Level Unacceptable Level Perform complex calculations involving the following: real and complex numbers; addition, subtraction, multiplication, and division of integral expressions; and fractional expressions. Perform basic calculations involving the following: real and complex numbers; addition, subtraction, multiplication, and division of integral expressions; and fractional expressions. Unable to perform basic calculations involving the following: real and complex numbers; addition, subtraction, multiplication, and division of integral expressions; or fractional expressions. Solve a wide variety of equations and inequalities as well as simultaneous equations and inequalities. Solve basic equations and inequalities, simultaneous equations and inequalities. Unable to solve basic equations and inequalities, simultaneous equations or inequalities. Understand what sets and propositions are and be able to solve advanced problems. Understand what sets and propositions are and be able to solve basic problems. Unable to solve basic problems based on an understanding of what a set is and what a proposition is. Understand the basic methods for proving equalities and inequalities and be able to apply them to solve slightly advanced proof problems. Understand the basic methods for proving equalities and inequalities and be able to apply them to solve proof problems. Unable to solve proof problems based on an understanding of the basic methods for proving equalities and inequalities. Draw different types of graphs for various functions and be able to solve slightly advanced maximum value, equality, and inequality problems by using graphs. Draw basic graphs for various functions and be able to solve slightly advanced maximum value, equality, and inequality problems by using graphs. Unable to draw basic graphs for functions.

### 教育方法等

Understand and master the basics of mathematical expression processing and mathematical thinking in relation to engineering by learning about basic functions, equations, and inequalities.

Background knowledge: Mathematical knowledge that you learned in middle school and earlier.

Lecture room: HR classroom

### 授業計画

1stQ
1週 Equalities and inequalities Understand the properties of equalities and inequalities and be able to solve linear equations and inequalities.
2週 Real numbers and complex numbers Understand the properties of real and complex numbers and be able to add and subtract them.
3週 Addition and subtraction of integral expressions Add and subtract integral expressions.
4週 Multiplication of equalities Multiple equalities.
5週 Factorization Resolve expressions into factors.
6週 Division of equalities Multiple equalities.
7週 Remainder theorem and factor theorem Understand the remainder theorem and the factor theorem and resolve high-order expressions into factors.
8週 Fractional expressions Calculate fractional expressions.
2ndQ
9週 First semester midterm exam
11週 Solutions for cubic and quartic equations Solve high-order equations by using the factor theorem.
12週 Different types of equations Solve simultaneous, fractional, irrational, and other types of equations.
13週 Sets and propositions Deal with sets and propositions.
14週 Identities Understand what identities are and be able to apply this understanding in relation to the process of decomposition into partial fractions.
15週 Proof of equalities Prove equalities.
16週 First semester routine exam

3rdQ
1週 Properties and graphs for quadratic functions Understand the properties of quadratic functions and be able to graph them.
2週 Maximum and minimum values for quadratic functions Obtain the maximum and minimum values for quadratic functions.
5週 Functions and translations of function graphs Understand and be able to graph parallel and symmetric translations of functions graphs.
6週 Fractional functions/irrational functions Understand the properties of fractional functions and irrational functions and be able to graph them.
7週 Composite functions/inverse functions and graphs Be able to obtain and graph the composite and inverse functions of basic functions.
8週 Second semester midterm exam
4thQ
9週 Roots and exponential dilation Understand what roots are and extend the law of exponents for calculations.
10週 Exponential functions and graphs Understand the properties of exponential functions and be able to graph them.
11週 Equations and inequalities containing exponential functions Solve basic equations and inequalities containing exponential functions.
12週 Logarithms and their basic properties Understand what logarithms are and use them to perform calculations.
13週 Logarithmic functions and graphs Understand the properties of logarithmic functions and be able to graph them.
14週 Equations and inequalities containing logarithmic functions Solve basic equations and inequalities containing logarithmic functions.
15週 Common logarithms Understand what common logarithms are and be able to apply this understanding to calculations.
16週 Second semester routine exam

### 評価割合

Examination Assignments Total 合計 90 10 100 200 90 10 100 200