Solutions for Numerical Methods in Chemical Engineering Using Python® and Simulink®, 1st Edition Ghasem (All Chapters included)

Numerical Methods in Chemical
Engineering Using Python® and
Simulink®, 1st Edition by Nayef
Ghasem




Complete Chapter Solutions Manual
are included (Ch 1 to 9)




** Immediate Download
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** All Chapters included
** Program Files included

, Chapter 1

Introduction to Numerical Methods




Problems

1. Solve the following linear algebraic equation.

𝑥 + 7 = 12

Find the value of 𝑥



Solution

𝑥 = 12 − 7 = 5

2. Solve the following system of linear algebraic equations.

2𝑥 + 𝑦 = 6

𝑥+𝑦 =4

Find the value of 𝑥, 𝑦

Solution

2𝑥 + 𝑦 = 6 (1)

𝑥+𝑦 =4 (2)

(1) − (2): 𝑥 = 2

Substitute 𝑥 = 2 𝑖𝑛 (2) → 𝑦 = 2



3. A system of nonlinear equations consists of two or more equations with at least one

equation that is not linear

𝑥 2 + 𝑦 2 = 25

3𝑥 + 4𝑦 = 0




1

, Find the value of 𝑥, 𝑦

Solution

𝑥 2 + 𝑦 2 = 25 (1)

3𝑥 + 4𝑦 = 0 (2)
3
From (2) 4𝑦 = −3𝑥 ==> 𝑦 = − 4 𝑥

Substitute in (1)

2
3 2
𝑥 + (− 𝑥) = 25
4
9 2
𝑥2 + 𝑥 = 25
16
16 + 9 2
𝑥 = 25
16

25 2
𝑥 = 25
16
16
𝑥 2 = 25 ∗ = 16
25

𝑥 = ∓4



4. Solve the system of two nonlinear equations

𝑥 2 + 𝑦 2 = 45

𝑥 2 − 𝑦 2 = −27

Find the value of 𝑥, 𝑦

Solution

𝑥 2 + 𝑦 2 = 45 (1)

𝑥 2 − 𝑦 2 = −27 (2)

Add (1) and (2)

2𝑥 2 = 45 − 27 = 18

𝑥2 = 9

Hence




2