2014-2015-2 Course Information

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2014-2015-2 Mathematical analysis to improve

Lesson Notes

[Number of points to improve]2014-2015-2 7th teaching Week 1th Lecture lecture 4.1 points and limit 2015-04-14

[Number of points to improve]2014-2015-2 6th teaching Week 2nd Lecture Lecture 3.4 The comprehensive application of derivative 2015-04-09

[Number of points to improve]2014-2015-2 6th teaching Week 1th lecture 3.3 Taylor formula 2015-04-07

[Number of points to improve]2014-2015-2 5th teaching Week 2nd Lecture Lecture 3.2 Differential mean value theorem 2015-04-02

[Number of points raised]2014-2015-2 5th teaching Week 1th Lecture lecture 3.1 derivative 2015-03-31

Job Reference solutions [topics on this page, reference solutions at links]

[Number of points to improve]2014-2015-2 10th teaching Week 2nd Class (2015-05-07)

[Number of points to improve]2014-2015-2 10th teaching Week 1th Class (2015-05-04)

[Number of points to improve]2014-2015-2 9th teaching Week 2nd Class (2015-04-30)

[Number of points to improve]2014-2015-2 9th teaching Week 1th Class (2015-04-28)

[Number of points to improve]2014-2015-2 8th teaching Week 2nd Class (2015-04-23)

[Number of points to improve]2014-2015-2 8th teaching Week 1th Class (2015-04-21)

[Number of points to improve]2014-2015-2 7th teaching Week 2nd Class (2015-04-16)

[Number of points to improve]2014-2015-2 7th teaching Week 1th Class (2015-04-14)

[Number of points to improve]2014-2015-2 6th teaching Week 2nd Class (2015-04-09)

[Number of points to improve]2014-2015-2 6th teaching Week 1th class 2015-04-07

1. If $f (x) $ is available, and $f ' (X_0) >0$, is there a certain point $x _0$ a neighborhood that causes a monotonically increasing in that neighborhood?

2. Set $f \in c^2[a,b]$ for $f (a) =f (b) =0$. Trial: $$\bex \forall\ x\in [a,b],\ \exists\ \xi\in (A, B), \st f (x) =\frac{1}{2} (x-a) (x-b) F ' (\XI). \eex$$

[Number of points to improve]2014-2015-2 5th teaching Week 2nd Class 2015-04-02

Set $f $ at the $x =a$, the $|f|$ in the $x =a$ Place can guide. Trial: $f $ at $x =a$.

[Number of points to improve]2014-2015-2 5th teaching Week 1th class 2015-03-31

Set $f \in c^1 (\BBR) $, then $$\bex f\mbox{is}k\mbox{sub-homogeneous function}\lra XF ' (x) =KF (x). \eex$$

[Number of points to improve]2014-2015-2 4th teaching Week 2nd Class 2015-03-26

Set $|f|$ on $\bbr$ consistent continuous, $f $ continuous. Trial Certificate: $f $ consistent continuous.

[Number of points to improve]2014-2015-2 4th teaching Week 1th class 2015-03-24

Set $f \in c[0,1]$, $f (0) =f (1) $. Trial: $$\bex \forall\ 2\leq n\in\bbn,\ \exists\ \xi_n\in [0,1],\st f\sex{\xi_n+\frac{1}{n}}=f (\xi_n). \eex$$

[Number of points to improve]2014-2015-2 3rd teaching Week 2nd Class 2015-03-19

Limit $$\bex \vlm{n}\frac{1^k+2^k+\cdots+n^k}{n^{k+1}},\quad \vlm{n}\sex{\frac{1^k+2^k+\cdots+n^k}{n^{k}}-\frac{n}{ K+1}}. \eex$$

[Number of points to improve]2014-2015-2 3rd teaching Week 1th class 2015-03-17

$$\bex \lim_{x\to +\infty} \sex{\sqrt[6]{x^6+x^5}-\sqrt[6]{x^6-x^5}}. \eex$$

[Number of points to improve]2014-2015-2 2nd teaching Week 2nd Class 2015-03-12

Known $$\bex x_n=\sum_{i=1}^n \frac{1}{i (i+1) (i+2) (i+3)}. \eex$$ test: $\sed{x_n}$ Convergence, and seek its limit.

[Number of points to improve]2014-2015-2 2nd teaching Week 1th class 2015-03-10

Set $a _n\to a$, trial certificate: $$\bex \vlm{n}\frac{a_1+2a_2+\cdots+na_n}{1+2+\cdots+n}=a. \eex$$

[Number of points to improve]2014-2015-2 1th teaching Week 2nd Class 2015-03-05

Set $$\bex x_n=\sum_{k=2}^n \frac{\cos k}{k (k-1)}, \eex$$ to determine whether the $\sed{x_n}$ convergence?

[Number of points to improve]2014-2015-2 1th teaching Week 1th class 2015-03-03

1. Limit $$\bex \vlm{n}\dfrac{(n^2+1) (n^2+2) \cdots (N^2+n)} {(n^2-1) (n^2-2) \cdots (N^2-n)}. \eex$$

2. Trial Certificate: $$\bex 0<e-\sex{1+\frac{1}{n}}^n<\frac{e}{n}. \eex$$

2014-2015-2 Partial differential equations

2014-2015-2 Ordinary differential equation

MIT's ordinary differential equation video tutorial

[Ordinary differential equations] Lecture 8: First order constant coefficient linear equation (cont.)

[Ordinary differential equations] Lecture 7: First order constant coefficient linear equation

[Ordinary differential equations] Lecture 6: Complex and complex indices

[Ordinary differential equations] Lecture 5: First-order autonomous differential equations

[Ordinary differential equations] Lecture 4: First Order equation substitution method

[Ordinary differential equations] Lecture 3: Solution of First order linear ordinary differential equation

[Ordinary differential equations] Lecture 2: Euler numerical method and its generalization

[Ordinary differential equations] Geometric solution of Lecture 1:ode: Direction field, Integral curve

Some lectures in class

[Ordinary differential equation]2014-2015-2 7th teaching Week 1th Lecture lecture 3.2 Continuation of the solution 2015-04-13

[Ordinary differential equation]2014-2015-2 5th Teaching Week 2nd Lecture Lecture 3.1 Existence and uniqueness theorem of solution and stepwise approximation method 2015-04-02

Exercise 2.5 question 1th (32) $$\bex \frac{\rd y}{\rd x}+\frac{1+xy^3}{1+x^3y}=0. The solution of \eex$$ 2015-03-30

The method of integrating factor in grouping 2015-03-23

2014-2015-2 Course Information