Mathematics for E&BE
(University of Groningen)
Summary 2022-2023
Stuvia: marcellaschrijver
2. Algebra................................................................................................................................................ 2
3. Solving Equations ............................................................................................................................... 2
4. Functions of One Variable .................................................................................................................. 2
5. Properties of Functions ...................................................................................................................... 5
6. Differentiation .................................................................................................................................... 5
7. Derivatives in Use ............................................................................................................................... 6
8. Single-Variable Optimization ............................................................................................................. 6
11. Functions of Many Variables ........................................................................................................... 8
, 2. Algebra
Absolute values
|𝑥 − 2| = {𝑥 − 2 if 𝑥 ≥ 2
2 − 𝑥 if 𝑥 < 2
|3𝑥 − 2| ≤ 5 ⟺ −5 ≤ 3𝑥 − 2 ≤ 5
3. Solving Equations
Quadratic formula
−𝑏±√𝑏2 −4𝑎𝑐
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 ⟺ 𝑥 = 2𝑎
Quadratic factorization
𝑥1 and 𝑥2 are solutions of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 ⟹ 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 𝑎(𝑥 − 𝑥1 )(𝑥 − 𝑥2 )
4. Functions of One Variable
The coordinate system
Some important graphs
(University of Groningen)
Summary 2022-2023
Stuvia: marcellaschrijver
2. Algebra................................................................................................................................................ 2
3. Solving Equations ............................................................................................................................... 2
4. Functions of One Variable .................................................................................................................. 2
5. Properties of Functions ...................................................................................................................... 5
6. Differentiation .................................................................................................................................... 5
7. Derivatives in Use ............................................................................................................................... 6
8. Single-Variable Optimization ............................................................................................................. 6
11. Functions of Many Variables ........................................................................................................... 8
, 2. Algebra
Absolute values
|𝑥 − 2| = {𝑥 − 2 if 𝑥 ≥ 2
2 − 𝑥 if 𝑥 < 2
|3𝑥 − 2| ≤ 5 ⟺ −5 ≤ 3𝑥 − 2 ≤ 5
3. Solving Equations
Quadratic formula
−𝑏±√𝑏2 −4𝑎𝑐
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 ⟺ 𝑥 = 2𝑎
Quadratic factorization
𝑥1 and 𝑥2 are solutions of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 ⟹ 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 𝑎(𝑥 − 𝑥1 )(𝑥 − 𝑥2 )
4. Functions of One Variable
The coordinate system
Some important graphs
