Can calculate partial derivatives, multiple integrals, and first-order differential equations.
概要:
Learns more advanced contents and applications of calculus (partial differentiation and multiple integration).
授業の進め方・方法:
This class gives lectures explaining study contents according to the designated textbook. The students' self study is assumed to be necessary, and the class intends to allow them to consolidate their study contents through exercises. In the first semester, the students will study the continuation of "Mathematics II A" learned in the second year. In the second semester, partial differentiation and double integration will be covered. The class emphasizes the students' ability to perform various calculations based on an understanding of basic concepts.
注意点:
Office hours: Tuesday
|
|
週 |
授業内容 |
週ごとの到達目標 |
| 前期 |
| 1stQ |
| 1週 |
Guidance, Maclaurin expansion, Taylor expansion |
Can calculate the Maclaurin and Taylor expansions of basic functions. D1:3
|
| 2週 |
Euler's formula, Approximation by polynomials |
Can convert complex numbers between orthogonal and polar forms using Euler's formula. Understands the basic properties of approximate expressions and calculate approximate expressions of simple functions. D1:3
|
| 3週 |
First-order separable differential equations |
Can solve first-order separable differential equations. D1:3
|
| 4週 |
First-order homogeneous differential equations |
Can solve first-order homogeneous differential equations. D1:3
|
| 5週 |
First-order linear differential equations |
Can solve first-order linear differential equations. D1:3
|
| 6週 |
Second-order linear differential equations with constant coefficients (homogeneous) |
Can solve second-order homogeneous linear differential equations with constant coefficients. D1:3
|
| 7週 |
Second-order linear differential equations with constant coefficients (inhomogeneous) |
Can solve second-order inhomogeneous linear differential equations with constant coefficients. D1:3
|
| 8週 |
First semester midterm exam |
|
| 2ndQ |
| 9週 |
Exam solutions, Functions of 2 variables |
Understands the definition of functions of 2 variables. D1:3
|
| 10週 |
Functions of 2 variables and their limits |
Can calculate the limits of functions of 2 variables. D1:3
|
| 11週 |
Continuity, Partial derivatives |
Can determine the continuity of two-variable functions.
Can calculate partial derivatives. D1:3
|
| 12週 |
Tangent planes and Total differentiation |
Can calculate tangent planes of curved surfaces.
Can calculate the total derivatives of functions. D1:3
|
| 13週 |
Partial differentiation of composite functions (1) |
Can calculate the partial derivatives of composite functions of two-variable functions. D1:3
|
| 14週 |
Partial differentiation of composite functions (1) |
Can calculate the partial derivatives of composite functions of two-variable functions. D1:3
|
| 15週 |
Exercises |
Can combinedly use the contents learned up to this point. D1:3
|
| 16週 |
First semester final exam |
|
| 後期 |
| 3rdQ |
| 1週 |
Exam solutions, Higher-order partial derivatives |
Can calculate higher order partial derivatives of two-variable functions.
D1:3
|
| 2週 |
Higher-order partial derivatives |
Can calculate higher order partial derivatives of two-variable functions.
D1:3
|
| 3週 |
Higher-order partial derivatives |
Can calculate higher order partial derivatives of two-variable functions.
D1:3
|
| 4週 |
Tayler's theorem |
Understands Taylor's theorem for two-variable functions. D1:3
|
| 5週 |
Tayler's theorem |
Understands Taylor's theorem for two-variable functions. D1:3
|
| 6週 |
Extrema |
Can calculate the extrema of two-variable functions. D1:3
|
| 7週 |
Extrema |
Can calculate the extrema of two-variable functions. D1:3
|
| 8週 |
Second semester midterm exam |
Can combinedly use the contents learned up to this point. D1:3
|
| 4thQ |
| 9週 |
Exam solutions, Definition of multiple integration |
Understands the definition of multiple integration over rectangular regions and general regions. D1:3
|
| 10週 |
Definition of multiple integration |
Understands the definition of multiple integration over rectangular regions and general regions. D1:3
|
| 11週 |
Calculation of multiple integrals |
Can calculate multiple integrals in general regions. D1:3
|
| 12週 |
Calculation of multiple integrals |
Can calculate multiple integrals in general regions. D1:3
|
| 13週 |
Change of variables in multiple integrals |
Can calculate multiple integrals by using the change of variables. D1:3
|
| 14週 |
Improper integrals |
Can calculate improper multiple integrals. D1:3
|
| 15週 |
Second semester final exam |
Can combinedly use the contents learned up to this point. D1:3
|
| 16週 |
Exam solutions |
|
| 分類 | 分野 | 学習内容 | 学習内容の到達目標 | 到達レベル | 授業週 |
| 基礎的能力 | 数学 | 数学 | 数学 | 簡単な1変数関数の局所的な1次近似式を求めることができる。 | 3 | |
| 1変数関数のテイラー展開を理解し、基本的な関数のマクローリン展開を求めることができる。 | 3 | |
| オイラーの公式を用いて、複素数変数の指数関数の簡単な計算ができる。 | 3 | |
| 2変数関数の定義域を理解し、不等式やグラフで表すことができる。 | 3 | |
| 合成関数の偏微分法を利用して、偏導関数を求めることができる。 | 3 | |
| 簡単な関数について、2次までの偏導関数を求めることができる。 | 3 | |
| 偏導関数を用いて、基本的な2変数関数の極値を求めることができる。 | 3 | |
| 2重積分の定義を理解し、簡単な2重積分を累次積分に直して求めることができる。 | 3 | |
| 極座標に変換することによって2重積分を求めることができる。 | 3 | |
| 2重積分を用いて、簡単な立体の体積を求めることができる。 | 3 | |
| 微分方程式の意味を理解し、簡単な変数分離形の微分方程式を解くことができる。 | 3 | |
| 簡単な1階線形微分方程式を解くことができる。 | 3 | |
| 定数係数2階斉次線形微分方程式を解くことができる。 | 3 | |