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Cours : Fonctions usuelles

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<span style="font-size: large;">A près un rappel concernant les fonctions le ca logarithmes, exponentielles et circulaires, près un rappel concernant les fonctions le ca loga- ta logue des fonctions usuelles s’enrichit ici de plusieurs spécimens dont les étudiants disposent déjà sur leur calculatrice : quelles sont ces mystérieuses touches : sin−1, cosh, tanh−1 ? Ces fonctions seront uti lisées couramment en analyse, notamment dans les calculs de primitives.</span></div>
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<li style="text-align: left;"><span style="font-size: large;">Réviser les fonctions déjà connues : exponentielles, logarithmes, puissances, fonctions circulaires.</span></li>
<li style="text-align: left;"><span style="font-size: large;"> Découvrir de nouvelles fonctions : fonctions hyperboliques et hyperboliques réciproques, fonctions circulaires réciproques.</span></li>
<li style="text-align: left;"><span style="font-size: large;">Préparer le cours d’analyse en disposant de nombreux exemples.</span></li>
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<span style="color: #cc0000; font-weight: normal;"><i>Télécharger les  Cours </i></span><span style="font-weight: normal; text-align: right;"><span style="color: #cc0000;"><i> Fonctions usuelles</i></span></span></h2>
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Cours : Fonctions usuelles

A près un rappel concernant les fonctions le ca logarithmes, exponentielles et circulaires, près un rappel concernant les...

lundi 1 août 2016

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samedi 30 juillet 2016

COURS : Lois de Newton et Forces

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<li><span style="font-family: inherit; font-size: large;"> Principe d’inertie (1re loi de Newton)</span></li>
<li><span style="font-family: inherit; font-size: large;"> Principe fondamental (2e loi de Newton)</span></li>
<li><span style="font-family: inherit; font-size: large;"> Actions réciproques (3e loi de Newton)</span></li>
<li><span style="font-family: inherit; font-size: large;"> Les forces</span></li>
<li><span style="font-family: inherit; font-size: large;"> Conclusion</span></li>
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<span style="font-family: inherit; font-size: large;">➤ Savoir faire le bilan des forces appliquées sur un système préalablement </span><span style="font-family: inherit; font-size: large;">déﬁni.</span></div>
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<span style="font-family: inherit; font-size: large;">➤ Connaître la méthode de résolution d’un problème de dynamique.</span></div>
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COURS : Lois de Newton et Forces

Principe d’inertie (1re loi de Newton) Principe fondamental (2e loi de Newton) Actions réciproques (3e loi de Newton)...

Cours : Équations différentielles linéaires PCSI-PTSI-SMPC

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<div class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; margin-top: 0cm; text-indent: 37pt;">
<i><span style="font-family: inherit; font-size: large;"><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2Exact"><span lang="FR">e tres nombreuses
applications des mathema</span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2Exact" style="text-indent: 37pt;"><span lang="FR">tiques conduisent h la
recherche dunefonction assujettie h une certaine relation avec ses derivees
successives. C’est ce qu ’on appelle une equation dif- ferentielle. L ’immense
progres scientifique des </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERSIZE11Exact" style="text-indent: 37pt;"><span lang="FR">XYlf </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2Exact" style="text-indent: 37pt;"><span lang="FR">et </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERSIZE11Exact" style="text-indent: 37pt;"><span lang="FR">XVIlf </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2Exact" style="text-indent: 37pt;"><span lang="FR">siecles, en particulier
en astronomie, repose sur la capacite de prevoir le comportement fu- tur dun
systeme grace h la resolution d’equations differentielles. De tres nombreux
noms de mathema- ticiens sont attaches h la theorie des equations differentielles
: Euler, d’Alembert, Lagrange, Riccati, Clairaut, Bernoulli, Legendre,
Cauchy... Malheu- reusement, il n existe pas de methode systematique pour
resoudre exactement toutes les equations differentielles. Nous devrons nous
contenter d’etudier quelques types tres simples, comme les equations lineaires.
Par ailleurs il existe une branche des ma- thematiques en plein essor, l’analyse
numerique, qui developpe, h l usage des physiciens et des ingenieurs, des algorithmes
tresperformants de resolution approchee d’equations differentielles.</span></span></span></i></div>
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<span style="font-size: large;"><span style="line-height: 16px;"><i>•    Etudier les equations differen- tielles lineaires du premier ordre.</i></span></span><br />
<span style="font-size: large;"><span style="line-height: 16px;"><i>•    Donner un exemple de resolution approchee : la methode d’Euler.</i></span></span><br />
<span style="font-size: large;"><span style="line-height: 16px;"><i><span style="font-family: inherit;"><span style="font-family: inherit; font-size: medium;"><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT5Exact"><span lang="FR"></span></span></span><span style="font-family: inherit; font-size: medium;"><span lang="FR"></span></span></span>
</i></span></span>
<span style="font-size: large;"><span style="line-height: 16px;"><i>•    Etudier les equations differen- tielles lineaires du second ordre a coefficients constants et a second membre du type polynome- exponentiel.</i></span></span><br />
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Cours : Équations différentielles linéaires PCSI-PTSI-SMPC

e tres nombreuses applications des mathema tiques conduisent h la recherche dunefonction assujettie h une certaine rel...

Cinématique

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<span style="font-size: large;"><i>La cinématique est la branche de la mécanique consacrée à l'étude purement descriptive du mouvement.</i></span></div>
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<span style="font-size: large;"><i>Les notions d'espace, de temps et de mouvement sont universelles, mais leur description précise et quantitative n 'est pas immédiate ; pour aboutir à la forme actuelle de la cin ématique, il a fallu se poser et résoudre un certain nombre de problèmes, tant conceptuels que techniques.</i></span></div>
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<span style="font-size: large;"><i>Comm en t repérer précisémen t un évén emen t dans l'espace et dans le temps ?</i></span></div>
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<span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><i><span style="text-indent: -13.3333px;"><span style="color: #dc8e22;">•  </span></span><span style="line-height: 11pt; text-align: left; text-indent: 29pt;">Comment mesurer une
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<i><span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><span style="color: #dc8e22;">•  </span></span><span style="font-size: large; line-height: 11pt; text-indent: 29pt;">Qu'est ce que le
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<span style="text-indent: 29pt;"><span style="font-size: large;"><i>Cette compréhension de plus en plus fine des phénomènes physiques est allée de pair avec la mise au point de méthodes mathématiques adaptées.</i></span></span></div>
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<i><span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><span style="color: #dc8e22;">•<span style="font-stretch: normal; line-height: normal;">  </span></span></span><span style="font-size: large;">Dérivée d'une grandeur vectorielle.</span></i></div>
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<i><span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><span style="color: #dc8e22;">•</span></span><span style="font-size: large;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Notion de référentiel.</span></i></div>
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<i><span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><span style="color: #dc8e22;">•</span></span><span style="font-size: large;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Expression des vecteurs vitesse et accélération d'un mobile ponctuel.</span></i></div>
<i><span style="font-size: large; line-height: 16px; text-align: justify; text-indent: -13.3333px;"><span style="color: #dc8e22;">•</span></span><span style="font-size: large;"><span class="Apple-tab-span" style="white-space: pre;"> </span>Représentations du mouvement.</span></i><br />
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Cinématique

La cinématique est la branche de la mécanique consacrée à l'étude purement descriptive du mouvement. Le...

cours :Dynamique du point matériel

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La théorie de la dynamique classique (ou newtonienne) s'est peu à peu construite aux XVIIe, XVIIIe et XIXe siècles. La réfutation des conceptions qui faisaient jusque-là autorité s'est accompagnée de l'émergence d'idées nouvelles et particulièrement fécondes.</div>
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Ainsi, le principe d'inertie contredit l'ancienne théorie qui associait mouvement efforce motrice.</div>
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La notion d'interaction, décrite par des lois quantitatives, est une idée essentielle de la mécanique moderne. Une pomme ne tombe pas parce que, étant pesante, sa tendance naturelle est d'aller vers le bas, mais en raison de l'attraction réciproque qui existe entre elle et la Terre.</div>
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<i><span style="font-family: inherit; font-size: large;">•	Connaître les notions d'inertie, de référentiel galiléen et de force.</span></i></div>
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<i><span style="font-family: inherit;">•	Relier le mouvement d'un mobile ponctuel aux actions</span></i></div>
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cours :Dynamique du point matériel

La théorie de la dynamique classique (ou newtonienne) s'est peu à peu construite aux XVIIe, XVIIIe et XIXe siècles. La ré...

lundi 25 juillet 2016

Exercices :Fonctions usuelles PCSI-PTSI-SMPC

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<span style="font-family: inherit; font-size: medium;"><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20"><span lang="FR"><span style="font-size: x-large;">N</span><span style="font-size: large;">es de la resolution generale de l’equation du troisieme degre par Bombelli</span></span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERNOTITALIC" style="font-size: large;"><span lang="FR"> (1572) — </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20" style="font-size: large;"><span lang="FR">voir </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERNOTITALIC" style="font-size: large;"><span lang="FR">Exercice resolu — </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20" style="font-size: large;"><span lang="FR">les nombres complexes sont long- temps consideres comme de commodes intermediates de calcul n ’ayant pas d’existence propre. C’est Hamilton en</span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERNOTITALIC" style="font-size: large;"><span lang="FR"> 1837 </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20" style="font-size: large;"><span lang="FR">qui donnepour la premiere fois une construction satisfaisante des nombres complexes h partir des couples de nombres reels.</span></span><span lang="FR" style="font-size: large;"><o:p></o:p></span></span></div>
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<span style="font-family: inherit; font-size: large;"><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20"><span lang="FR">L ’interet majeur du corps des complexes reside dans le theoreme de d’Alembert que nous evoquerons dans le chapitre</span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT2MSGENFONTSTYLEMODIFERNOTITALIC"><span lang="FR"> Polynomes </span></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT20"><span lang="FR">(chapitre 12) : tout polynome non constant h coefficients complexes possede des racines !Par ailleurs, les nombres complexes constituent un outil commode en geometrieplane et en trigono- metrie</span></span></span></div>
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<span style="font-family: inherit; font-size: large;"><span style="color: #dc8e22;">•<span style="font-stretch: normal;">    </span></span><span dir="LTR"></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT5Exact"><span lang="FR">Reviser et enrichir les notions vues en Terminate.</span></span><span lang="FR"><o:p></o:p></span></span></div>
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<span style="font-family: inherit; font-size: large;"><span style="color: #dc8e22;">•<span style="font-stretch: normal;">    </span></span><span dir="LTR"></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT5Exact"><span lang="FR">Preparer le cours d’algebre en donnant des premiers exemples de structures.</span></span><span lang="FR"><o:p></o:p></span></span></div>
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<span style="font-family: inherit; font-size: large;"><span style="color: #dc8e22;">•<span style="font-stretch: normal;">    </span></span><span dir="LTR"></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT5Exact"><span lang="FR">Preparer le cours d’analyse, ou les fonctions pourront etre aussi bien a valeurs complexes que reelles.</span></span><span lang="FR"><o:p></o:p></span></span></div>
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<span style="font-family: inherit; font-size: large;"><span style="color: #dc8e22;">•<span style="font-stretch: normal; line-height: normal;">    </span></span><span dir="LTR"></span><span class="MSGENFONTSTYLENAMETEMPLATEROLENUMBERMSGENFONTSTYLENAMEBYROLETEXT5Exact"><span lang="FR">Utiliser les nombres complexes pour la trigonometrie.</span></span></span><span lang="FR"><o:p></o:p></span><br />
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Exercices :Fonctions usuelles PCSI-PTSI-SMPC

N es de la resolution generale de l’equation du troisieme degre par Bombelli (1572) — voir Exercice resolu — les...

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Well, the way they make shows is, they make one show. That show's called a pilot. Then they show that show to the people who make shows, and on the strength of that one show they decide if they're going to make more shows.

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Like you, I used to think the world was this great place where everybody lived by the same standards I did, then some kid with a nail showed me I was living in his world, a world where chaos rules not order, a world where righteousness is not rewarded. That's Cesar's world, and if you're not willing to play by his rules, then you're gonna have to pay the price.

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You think water moves fast? You should see ice. It moves like it has a mind. Like it knows it killed the world once and got a taste for murder. After the avalanche, it took us a week to climb out. Now, I don't know exactly when we turned on each other, but I know that seven of us survived the slide... and only five made it out. Now we took an oath, that I'm breaking now. We said we'd say it was the snow that killed the other two, but it wasn't. Nature is lethal but it doesn't hold a candle to man.

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You see? It's curious. Ted did figure it out - time travel. And when we get back, we gonna tell everyone. How it's possible, how it's done, what the dangers are. But then why fifty years in the future when the spacecraft encounters a black hole does the computer call it an 'unknown entry event'? Why don't they know? If they don't know, that means we never told anyone. And if we never told anyone it means we never made it back. Hence we die down here. Just as a matter of deductive logic.

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