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• Bernoulli's principle dictates that for an inviscid flow, fluid speed increases in tandem with a decrease in pressure or potential energy.

Wing Lift Generation

• Airplane wings are designed so air flows faster over the top surface compared to the bottom.
• Faster airflow results in lower pressure, while slower airflow leads to higher pressure.
• This pressure difference generates lift, propelling the wing and airplane upward.

Bernoulli’s Equation

• The incompressible flow equation is $v^2/2 + gz + p/ρ = constant$.
• $v$ is fluid flow speed
• $g$ is gravitational acceleration
• $z$ is elevation
• $p$ is pressure
• $ρ$ is fluid density.

Venturi Effect

• The Venturi effect describes the reduction in fluid pressure when a fluid passes through a constricted section of a pipe.
• Fluid speed increases at the constriction to maintain mass flow rate.
• Pressure decreases at the constriction to conserve energy.

Exercice 1

• $f$ is an endomorphism of $\mathbb{R}^3$.
• The matrix in the canonical basis is $A = \begin{pmatrix} 1 & 1 & -1 \ 1 & 1 & 1 \ 1 & 1 & 1 \end{pmatrix}$
• $Ker(f) = Vect \left{ \begin{pmatrix} -1 \ 1 \ 0 \end{pmatrix}\right}$
• $Im(f) = Vect \left{ \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}, \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix} \right} = Vect \left{ \begin{pmatrix} 1 \ 1 \ 1 \end{pmatrix}, \begin{pmatrix} -1 \ 1 \ 0 \end{pmatrix} \right}$
• $Ker(f) \cap Im(f) = {0}$, $dim(Ker(f)) + dim(Im(f)) = 1 + 2 = 3 = dim(\mathbb{R}^3)$.
• $Ker(f)$ and $Im(f)$ are supplementary.
• $B = (u_1, u_2, u_3)$ is a basis of $\mathbb{R}^3$ such that $u_1 \in Ker(f)$ and $u_2, u_3 \in Im(f)$.
• The matrix of $f$ in the base $B$ is of the form: $A' = \begin{pmatrix} 0 & * & * \ 0 & * & * \ 0 & * & * \end{pmatrix}$

Exercice 2

• $f$ is an endomorphism of $\mathbb{R}^3$.
• The matrix in the canonical basis is $A = \begin{pmatrix} 5 & -4 & 4 \ 1 & 0 & 2 \ -2 & 2 & -1 \end{pmatrix}$
• The eigenvalues of $f$ are $\lambda_1 = 1$ and $\lambda_2 = 2$.
• $f$ is diagonalizable because the sum of the dimensions of the eigenspaces is equal to the dimension of the vector space.
• A basis of eigenvectors is given by: $B = \left{ \begin{pmatrix} 2 \ 1 \ 0 \end{pmatrix}, \begin{pmatrix} -2 \ 0 \ 1 \end{pmatrix}, \begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix} \right}$
• $P = \begin{pmatrix} 2 & -2 & 1 \ 1 & 0 & 1 \ 0 & 1 & 0 \end{pmatrix}$ and $D = \begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 2 \end{pmatrix}$ such that $A = PDP^{-1}$.

Introduction to C++

• C++ is a potent and versatile programming language widely used across industries.
• C++ enables writing high-performance code.
• It supports various programming styles, including procedural, object-oriented, and generic.
• C++ offers precise control over hardware resources.
• It it used in developing operating systems, game engines, browsers, and high-performance applications.

What You Will Learn

• Setting up a C++ development environment
• Basic programming concepts: variables, data types, and control structures
• Writing programs for user interaction
• Using functions and classes for code organization
• Working with pointers and dynamic memory
• Using the C++ Standard Template Library (STL)

Setting up the environment

• The development environment needs to be set up, including installing a compiler and a text editor.

Installing a Compiler

• A compiler translates C++ code into machine code.
• Compilers include GCC, Clang, and Microsoft Visual C++.
• GCC (GNU Compiler Collection) is a free, open-source compiler available on multiple platforms.
• Clang, based on LLVM, is known for fast compile times and informative error reporting.
• Microsoft Visual C++ comes with Visual Studio IDE for Windows.
• GCC is used in this book.

Installing GCC on Windows

• Download MinGW (Minimalist GNU for Windows).
• Select gcc, g++, and make packages during installation.
• Add the MinGW bin directory to the PATH environment variable.

Installing GCC on macOS

• Install Xcode from the App Store.
• Download Command Line Tools from Xcode Preferences > Downloads.
• Verify GCC installation by running gcc --version in the Terminal.

Installing GCC on Linux

• Open a terminal window.
• Install GCC using:

sudo apt update
sudo apt install gcc g++

Installing a Text Editor

• A text editor is used for writing and editing code.
• Options include Visual Studio Code, Sublime Text, and Atom.
• Visual Studio Code is a free, open-source editor with extensive language support and extensions.
• Sublime Text is a sophisticated text editor known for speed and flexibility.
• Atom is a customizable, open-source editor with a strong community.
• Visual Studio Code is used in this book

Installing Visual Studio Code

• Download Visual Studio Code
• Run the installer and follow the instructions.

First C++ Program

• Create a new file named hello.cpp.
• Write the following code in the file:

#include 

int main() {
  std::cout

Cardiovascular System

Blood Vessels

Arteries

• Carry blood away from the heart.
• Possess thick walls, elastic fibers, and smooth muscle.

Capillaries

• Facilitate exchange between blood and tissues due to thin, porous walls.

Veins

• Carry blood back to the heart.
• Have thin walls and valves.

Blood Pressure

Systolic Pressure

• The pressure exerted when the heart contracts.

Diastolic Pressure

• The pressure exerted when the heart relaxes.

Factors Affecting Blood Pressure

• Blood volume
• Heart rate
• Blood viscosity
• Arteriole diameter

Disorders

Hypertension

• High blood pressure, a risk factor for heart disease, stroke, and kidney disease.

Atherosclerosis

• Plaque buildup in arteries that can lead to heart attack and stroke.

Stroke

• Interruption of blood supply to the brain, potentially causing permanent brain damage.

Heart Attack

• Interruption of blood supply to the heart, potentially causing permanent heart damage.

Diagram of the Heart

• The right atrium receives deoxygenated blood from the body via the superior and inferior vena cava.
• Deoxygenated blood flows from the right atrium through the tricuspid valve into the right ventricle.
• The right ventricle pumps deoxygenated blood through the pulmonary valve into the pulmonary artery.
• The pulmonary artery carries deoxygenated blood to the lungs.
• The lungs are where blood becomes oxygenated.
• The pulmonary veins carry oxygenated blood from the lungs to the left atrium.
• The left atrium receives oxygenated blood from the pulmonary veins.
• Oxygenated blood flows from the left atrium through the mitral valve to the left ventricle.
• The left ventricle then pumps oxygenated blood through the aortic valve into the aorta.
• The aorta distributes oxygenated blood to the body.
• The inferior vena cava returns deoxygenated blood from the lower body to the right atrium.
• The superior vena cava returns deoxygenated blood from the upper body to the right atrium.
• The left ventricle wall is thicker than the right ventricle wall, reflecting the greater force needed to pump blood throughout the body..