量子物理学的基础 Foundations of Quantum Physics PHYS104

0

这是一份liverpool利物浦大学PHYS1042的成功案例

量子物理学的基础 Foundations of Quantum Physics PHYS104

$$
\sum_{\lambda} F_{\lambda ‘ \lambda}^{j} C_{\lambda j}=\epsilon_{j} \sum_{\lambda} S_{\lambda^{\prime} \lambda} C_{\lambda j},
$$
where
$$
\begin{aligned}
F_{\lambda^{\prime} \lambda}^{j}=&\left\langle\chi_{\lambda^{\prime}}|h| \chi_{\lambda}\right\rangle+\sum_{\delta \kappa}\left[\gamma_{\delta_{k}}\left\langle\chi_{\lambda^{\prime}} \chi_{\delta}|g| \chi_{\lambda} \chi_{\chi^{\prime}}\right\rangle\right.\
&\left.-\gamma_{\delta \kappa}^{\text {exch }}\left\langle\chi_{\lambda^{\prime} \cdot} \chi_{\delta}|g| \chi_{\kappa} \chi_{\lambda}\right\rangle\right] .
\end{aligned}
$$
Here, $h$ is the one-electron part of the full Hamiltonian, $g$ is an electron-electron repulsion potential energy, and
$$
\begin{gathered}
\gamma_{\delta x}=\sum_{i}^{\prime} C_{\delta i} C_{\kappa i}, \
\gamma_{\delta \kappa}^{\text {exch }}=\sum_{i}^{n \prime} C_{\delta i} C_{\kappa i},
\end{gathered}
$$

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PHYS104 COURSE NOTES :

Show that
if $f(x)=x^{3}$, then $f^{\prime}(x)=3 x^{2}$.
Prove by induction that for each positive integer $n$, $f(x)=x^{n} \quad$ has derivative $\quad f^{\prime}(x)=n x^{n-1} .$
HINT:
$$
(x+h)^{k+1}-x^{k+1}=x(x+h)^{k}-x \cdot x^{k}+h(x+h)^{k} .
$$








微积分 Calculus MATH101/MATH102

0

这是一份liverpool利物浦大学MATH101/MATH102的成功案例

微积分 Calculus MATH101/MATH102

For $h \neq 0$ and $x+h$ in the domain of $f$,
$$
f(x+h)-f(x)=\frac{f(x+h)-f(x)}{h} \cdot h
$$
With $f$ differentiable at $x$,
$$
\lim {h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=f^{\prime}(x) $$ Since $\lim {h \rightarrow 0} h=0$, we have
$$
\lim {h \rightarrow 0}[f(x+h)-f(x)]=\left[\lim {h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\right] \cdot\left[\lim _{h \rightarrow 0} h\right]=f^{\prime}(x) \cdot 0=0 .
$$

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MATH101/MATH102 COURSE NOTES :

Show that
if $f(x)=x^{3}$, then $f^{\prime}(x)=3 x^{2}$.
Prove by induction that for each positive integer $n$, $f(x)=x^{n} \quad$ has derivative $\quad f^{\prime}(x)=n x^{n-1} .$
HINT:
$$
(x+h)^{k+1}-x^{k+1}=x(x+h)^{k}-x \cdot x^{k}+h(x+h)^{k} .
$$








微积分 Calculus MATH1006

0

这是一份nottingham诺丁汉大学MATH1006作业代写的成功案例

微积分 Calculus MATH1006
问题 1.

Given a series $\Sigma_{m=1}^{m} a_{n}=a_{1}+a_{2}+a_{s}+\cdots$, let $s_{a}$ denote its rth partial sum:
$$
s_{n}=\sum_{i=1}^{n} a_{i}=a_{1}+a_{2}+\cdots+a_{n}
$$


证明 .

If the sequence $\left{s_{\mathrm{n}}\right}$ is convergent and $\lim {\mathrm{a} \rightarrow \mathrm{m}} s{\mathrm{a}}=s$ exists as a real number, then the series $\Sigma a_{n}$ is called convergent and we write
$$
a_{1}+a_{2}+\cdots+a_{n}+\cdots=s \quad \text { or } \quad \sum_{n=1}^{\infty} a_{n}=s
$$
The number $s$ is called the sum of the series. Otherwise, the series is called divergent.

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MATH1006 COURSE NOTES :

If $r=1$, then $s_{n}=a+a+\cdots+a=n a \rightarrow \pm \infty$. Since $\lim {n \rightarrow-} s{n}$ doesn’t exist, the geometric series diverges in this case.
If $r \neq 1$, we have
$$
\begin{aligned}
&s_{\mathrm{a}}=a+a r+a r^{2}+\cdots+a r^{\mathrm{n}-1} \
&r s_{\mathrm{a}}=\quad a r+a r^{2}+\cdots+a r^{\mathrm{n}-1}+a r^{\mathrm{n}}
\end{aligned}
$$
Subtracting these equations, we get
$$
\begin{array}{r}
s_{\mathrm{a}}-r s_{\mathrm{a}}=a-a r^{n} \
s_{\mathrm{n}}=\frac{a\left(1-r^{\mathrm{n}}\right)}{1-r}
\end{array}
$$
If $-1<r<1$, we know from $(11.1 .9)$ that $r^{n} \rightarrow 0$ as $n \rightarrow \infty$, so
$$
\lim {n \rightarrow \infty} s{n}=\lim {n \rightarrow \infty} \frac{a\left(1-r^{n}\right)}{1-r}=\frac{a}{1-r}-\frac{a}{1-r} \lim {n \rightarrow \infty} r^{n}=\frac{a}{1-r}
$$








微积分 Calculus MAT00001C

0

这是一份YORK约克大学MAT00001C作业代写的成功案例

微积分 Calculus MAT00001C
问题 1.

This is
$$
\left[\left[\begin{array}{c}
R \circ g \
-Q \circ g \
P \circ g
\end{array}\right] \cdot\left[\left[\frac{\partial g}{\partial u}\right] \times\left[\frac{\partial g}{\partial v}\right]\right]\right] d u \wedge d v
$$
(The permutation of the $P, Q, R$ (and the minus sign) come from the way the $d x \wedge d y$ acts on a piece of surface normal to the $(d) z$ direction.)

证明 .

We can rewrite this as
$$
\left|\frac{\partial g}{\partial u} \times \frac{\partial g}{\partial v}\right|\left[\left[\begin{array}{c}
R \circ g \
-Q \circ g \
P \circ g
\end{array}\right] \cdot \hat{\boldsymbol{n}}[u, v]\right] \quad d u \wedge d v
$$
where $\hat{\boldsymbol{n}}[u, v]$ is the unit normal to the surface at $g\left[\begin{array}{l}u \ v\end{array}\right]$, and
$$
\left|\frac{\partial g}{\partial u} \times \frac{\partial g}{\partial v}\right|
$$
is the “area stretching factor”.
We have that
$$
\int_{g\left(I^{2}\right)} \omega
$$

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BMAT00001C COURSE NOTES :

is the limit of the sums of values of $\omega$ on small elements of the surface $g\left(I^{2}\right)$. Suppose $g$ takes a rectangle $\triangle u \times \triangle v$ in $I^{2}$ to a (small) piece of the surface. $\omega$ at $g\left[\begin{array}{l}u \ v\end{array}\right]$ is, say,
$$
P d x \wedge d y+Q d x \wedge d z+R d y \wedge d z
$$
and the unit normal to the surface is $\hat{\boldsymbol{n}}[u, v]$ (located at $\left.g\left[\begin{array}{l}u \ v\end{array}\right]\right)$.
Write $\hat{\boldsymbol{n}}[u, v]$ as
$$
\left[\begin{array}{l}
\hat{n} x \
\hat{n} y \
\hat{n} z
\end{array}\right]
$$








微积分I|Calculus I代写   4CCM111A

0

这是一份kcl伦敦大学学院 4CCM111A作业代写的成功案

微积分I|Calculus I代写   4CCM111A
问题 1.

so
$e^{y}-2 x-e^{-y}=0$
or, multiplying by $e^{y}$,
$$
e^{2 y}-2 x e^{y}-1=0
$$
This is really a quadratic equation in $e^{y}$ :
$$
\left(e^{y}\right)^{2}-2 x\left(e^{y}\right)-1=0
$$


证明 .

Solving by the quadratic formula, we get
$$
e^{y}=\frac{2 x \pm \sqrt{4 x^{2}+4}}{2}=x \pm \sqrt{x^{2}+1}
$$
Note that $e^{y}>0$, but $x-\sqrt{x^{2}+1}<0$ (because $x<\sqrt{x^{2}+1}$ ). Thus the minus sign is inadmissible and we have
$$
e^{y}=x+\sqrt{x^{2}+1}
$$
Therefore
$$
y=\ln \left(e^{y}\right)=\ln \left(x+\sqrt{x^{2}+1}\right)
$$

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4CCM111A COURSE NOTES :

Using Table 6 and the Chain Rule, we have
$$
\begin{aligned}
\frac{d}{d x}\left[\tanh ^{-1}(\sin x)\right] &=\frac{1}{1-(\sin x)^{2}} \frac{d}{d x}(\sin x) \
&=\frac{1}{1-\sin ^{2} x} \cos x=\frac{\cos x}{\cos ^{2} x}=\sec x
\end{aligned}
$$




微积分作业代写calculus代考

0

如果你也在 怎样代写微积分calculus这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。

微积分calculus,最初被称为无穷小微积分或 “无穷小的微积分”,是对连续变化的数学研究,就像几何学是对形状的研究,而代数是对算术运算的概括研究一样。

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代写微积分作业代写calculus

无限小数微积分是由艾萨克-牛顿和戈特弗里德-威廉-莱布尼茨在17世纪末独立开发的。后来的工作,包括对极限概念的编纂,使这些发展在概念上有了更坚实的基础。今天,微积分在科学、工程和经济领域有着广泛的应用。

微积分包含几个不同的主题,列举如下:

函数极限Limit of a function代写

在数学中,一个函数的极限是微积分和分析中关于该函数在特定输入附近的行为的一个基本概念。

无穷小量Infinitesimal代写

在数学中,一个无限小数或无限小数是一个比任何标准实数更接近于零的量,但它不是零。无限小数这个词来自于17世纪现代拉丁语中的一个词infinitesimus,它最初指的是一个序列中的 “无限大 “的项目。

微分学Differential calculus代写

在数学中,微积分是微积分的一个子领域,研究数量变化的速率。它是微积分的两个传统分支之一,另一个是积分微积分–研究曲线下的面积。

线性映射Linear map代写

在数学中,特别是在线性代数中,线性映射(也称为线性映射、线性变换、向量空间同构,或在某些情况下称为线性函数)是两个向量空间之间保留了向量加法和标量乘法操作的映射}Vto W。同样的名称和定义也用于环上模块的更一般的情况;见模块同态。

微分的记号Notation for differentiation代写

在微分学中,没有一个统一的微分符号。相反,不同的数学家提出了各种函数或变量的导数符号。

其他相关科目课程代写:

  • 莱布尼茨的记号Leibniz’s notation
  • 微积分基本定理Fundamental theorem
  • 策梅洛-弗兰克尔集合论Zermelo–Fraenkel set theory
  • 连续统的势 Cardinality of the continuum

微积分的历史

约翰内斯-开普勒的作品Stereometrica Doliorum构成了微积分的基础。开普勒开发了一种方法,通过将从椭圆的一个焦点引出的许多半径的长度相加来计算椭圆的面积。

微积分作业代写calculus代考

Johannes Kepler’s work Stereometrica Doliorum formed the basis of integral calculus.Kepler developed a method to calculate the area of an ellipse by adding up the lengths of many radii drawn from a focus of the ellipse.

 

微积分课后作业代写

The first equation yields $y=3 x^{2}$, substituting that into the second equation yields $x-6 x^{2}=0$, which has the solutions $x=0$ and $x=\frac{1}{6}$. So $x=0 \Rightarrow y=3(0)=0$ and $x=\frac{1}{6} \Rightarrow y=3\left(\frac{1}{6}\right)^{2}=\frac{1}{12}$.
So the critical points are $(x, y)=(0,0)$ and $(x, y)=\left(\frac{1}{6}, \frac{1}{12}\right)$.
To use Theorem 2.6, we need the second-order partial derivatives:
$$
\frac{\partial^{2} f}{\partial x^{2}}=-6 x, \quad \frac{\partial^{2} f}{\partial y^{2}}=-2, \quad \frac{\partial^{2} f}{\partial y \partial x}=1
$$
So
$$
D=\frac{\partial^{2} f}{\partial x^{2}}(0,0) \frac{\partial^{2} f}{\partial y^{2}}(0,0)-\left(\frac{\partial^{2} f}{\partial y \partial x}(0,0)\right)^{2}=(-6(0))(-2)-1^{2}=-1<0 $$ and thus $(0,0)$ is a saddle point. Also, $$ D=\frac{\partial^{2} f}{\partial x^{2}}\left(\frac{1}{6}, \frac{1}{12}\right) \frac{\partial^{2} f}{\partial y^{2}}\left(\frac{1}{6}, \frac{1}{12}\right)-\left(\frac{\partial^{2} f}{\partial y \partial x}\left(\frac{1}{6}, \frac{1}{12}\right)\right)^{2}=\left(-6\left(\frac{1}{6}\right)\right)(-2)-1^{2}=1>0
$$


微积分课后作业代写的应用代写

微积分应用于物理科学的每一个分支。 1 精算科学、计算机科学、统计学、工程、经济学、商业、医学、人口学,以及其他任何可以对问题进行数学建模并希望获得最佳解决方案的领域。它允许人们从(非恒定)变化率到总变化率,或反之亦然,在研究一个问题时,很多时候我们知道一个问题,并试图找到另一个问题。

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微积分calculus|MAT‑012 Assignment

0

这是一份ucdavis加利福尼亚大学戴维斯分校MAT‑012作业代写的成功案例

微积分calculus|MAT‑012 Assignment代写
问题 1.

Suppose $a_{n} \rightarrow a$ and $b_{n} \rightarrow$ b as $n \rightarrow \infty$. Then the following results hold.
(i) $a_{n}+b_{n} \rightarrow a+b$ as $n \rightarrow \infty$.
(ii) $c a_{n} \rightarrow c$ a as $n \rightarrow \infty$ for any real number $c$.
(iii) If $a_{n} \leq b_{n}$ for all $n \in \mathbb{N}$, then $a \leq b$.
(iv) (Sandwich theorem) If $a_{n} \leq c_{n} \leq b_{n}$ for all $n \in \mathbb{N}$, and if $a=b$, then $c_{n} \rightarrow a$ as $n \rightarrow \infty$.

证明 .

Proof Let $\varepsilon>0$ be given.
(i) Note that, for every $n \in \mathbb{N}$,
$$
\begin{aligned}
\left|\left(a_{n}+b_{n}\right)-(a+b)\right| &=\left|\left(a_{n}-a\right)+\left(b_{n}-b\right)\right| \
& \leq\left|a_{n}-a\right|+\left|b_{n}-b\right|
\end{aligned}
$$
Since $a_{n} \rightarrow a$ and $b_{n} \rightarrow b$, the above inequality suggests that we may take $\varepsilon_{1}=\varepsilon / 2$, and consider $N_{1}, N_{2} \in \mathbb{N}$ such that
$$
\left|a_{n}-a\right|<\varepsilon_{1} \quad \forall n \geq N_{1} \text { and }\left|b_{n}-b\right|<\varepsilon_{1} \quad \forall n \geq N_{2}
$$
so that
$$
\left|\left(a_{n}+b_{n}\right)-(a+b)\right| \leq\left|a_{n}-a\right|+\left|b_{n}-b\right|<2 \varepsilon_{1}=\varepsilon
$$
for all $n \geq N:=\max \left{N_{1}, N_{2}\right}$.
(ii) Note that
$$
\left|c a_{n}-c a\right|=|c|\left|a_{n}-a\right| \quad \forall n \in \mathbb{N} .
$$

问题 2.

(Ratio test) Suppose $a_{n}>0$ for all $n \in \mathbb{N}$ such that $\lim {n \rightarrow \infty} \frac{a{n+1}}{a_{n}}=\ell$ for some $\ell \geq 0$. Then the following hold.
(i) If $\ell<1$, then $a_{n} \rightarrow 0$. (ii) If $\ell>1$, then $a_{n} \rightarrow \infty$.

证明 .

Suppose $\ell<1$. Let $q$ be such that $\ell1$. Let $q$ be such that $1<q<\ell$. Then, taking for example the open interval $I$ containing $\ell$ as $I=(q, \ell+1)$, there exists $N \in \mathbb{N}$


英国论文代写Viking Essay为您提供实分析作业代写Real anlysis代考服务

MAT 012: Precalculus


Instructor: Emily Meyer
Contact: Time & Place:
[email protected] MWF 8:00-9:40 am, Chemistry 166
Office: MSB 3127 Office hours MWR 3:00-5:00 pm
Course Website
Homework, worksheets, updates and supplementary material will be online at
http://math.ucdavis.edu/~emeyer/math12/~index.html, as well as on Canvas:
http://canvas.ucdavis.edu/courses/282963.
Textbook
• Precalculus (Seventh Edition, 2012) by Cohen, Lee, and Sklar.
Prerequisites/Placement Exam
• It is expected that you have taken two years of high school algebra, plane geometry, and
plane trigonometry.
• You must have received a qualifying score (25 or more) on the UC Davis Math Placement
Exam to take this course. If you have not yet taken the exam, you can take it during the
testing session from 1pm July 30 to 1pm August 7, 2018. See department website for
further details.
NOTE: after completing this course, you are also required to take the Math Placement Exam
again before you may enroll in calculus. There are two testing windows for fall quarter:
1pm September 5 to 1pm September 11, and 1pm September 26 to 1pm October 2.
Course Information
Grading Scheme
• 40% final exam
• 20% midterm exam
1
MAT 012 SSII18
• 20% quizzes
• 20% homework and worksheets
Class Expectations
Class time will be interactive. I will not take attendance, but you are expected to be in class.
Being present and engaged is crucial to your academic success.
Homework and Quizzes
• Homework will be in the form of worksheets given in class that you will have time to start
in class and will be due at the beginning of the following class. These will be graded out
of 2 points, and you can redo each one once for a regrade as long as your first version is
complete and your redo is turned in within one week of the original due date.
• Additional homework problems will be provided but will not be graded. It is not expected
that you do all of the additional problems, but that you work through enough problems
from each section to develop and solidify the skills and knowledge you have learned. This
is the best way to study for exams! You are welcome to ask about these problems in office
hours, or to ask for general qualitative feedback from the instructor on your work.
• Quizzes will be given every Friday on which there is no exam (see Exams below). These
are intended not to be especially difficult but to give you practice thinking about math in a
similar environment to an exam.
Exams
There will be two exams:
• Midterm on Friday, August 24
• Final on Friday, September 14 (last day of class)
Each will be 100 minutes.
Other
• Make-ups and Absences: Make-up exams and quizzes will be given only in the case of
documented emergencies. Your lowest quiz grade (out of four) will be dropped, so if you
need to miss a quiz for a non-emergency reason, plan on using that as your dropped quiz.
• Office hours: I will hold office hours (tentatively) 3-5pm Monday, Wednesday and Thursday. You are highly encouraged to attend! This is your opportunity to ask me to repeat
or rephrase anything that did not make sense in class, to get individualized help on your
homework, or to ask any lingering questions you might have.
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MAT 012 SSII18
Academic Policies
Academic Integrity and Honesty
You are expected to comply with the UC Davis Code of Academic Conduct, which can be found at http://sja.ucdavis.edu/cac.html.
Any evidence of misconduct will be reported to SJA and dealt with according to their policy. (Note that this does not
include working with your classmates in class and/or on homework, which is fine – and recommended!)
Accommodations for Disabilities
If you need any accommodations, you are required to register with the Student Disability Center (http://sdc.ucdavis.edu).
Once you have done this, the SDC will contact the instructor and/or the math department, and we will respond accordingly to meet your needs.