CALCULUS PRESENTED BY GUO CHENG GUANG（06-02）

How to find the area of circle using integrations in calculs? The equation of the circle is x^2+y^2=R^2 and the circle is asymmetric with respect to the x-axis and y-axis, so first, we can solve the area of one quarter of circle and then multiple by 4 in order to get the total area of the circle.

In this video, we used three ways to integrate the area of the circle:

1. By circumference

2. By horizontal bar

3. By vertical bar

Calculus--Indefinite Integrals (06-02,S/N: 325) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGX...

We can use substition to the limit towards one point whenever the function is continuous at that point, that's one of the definition of continuity.If the function is not continuous at the point we can't get the limit by direct substitution.

Find limits of functions at specific points just easily by directly plugging the point into the function.

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGXI(1-02，S/N: 71) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（06-01）

Integral can be used to find displacement, areas, volumes, central points and other concepts that arise by combining infinitesimal date.

A definite integral is an integral with upper and lower limits, in other words it has start and end end values or there is an interval.

Calculus--Indefinite Integrals (06-01,S/N: 324) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-10)

Locus is if a point moves on a plane satisfying some given geometrical condition then the path trace out by the point in the plane.

The equation to the locus of the moving point is  the algebraic form of the given geometrical condition which is satisfy by the coordinate of all points on the locus.

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-10,S/N: 10) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGX...

Using direct substituion with limits: It's easily find limits of functions at points where the functions are continuous, simly plug in the value into the function.

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGXI(7-01，S/N: 70) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-09)

Five techniques to find area of a triangle:

1.shoelace formula

2.Heron's formula or Hero's formula

3.law of sines: a half of absinC

4.Cross Product

5.area of a triangle: a half of base times high【A=(1/2)bh】

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-09,S/N: 9) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

CALCULUS PRESENTED BY GUO CHENG GUANG（05-58）

Three methods to integrate ∫(sin(x))^2(cos(x))^4.

1.double/half angle formulae【sin(x))^2=(1-cos2x)/2,(cos(x))^2=(1+cos2x)/2)】

2.double/half angle formulae【sin2x=2sinxcosx,(cos(x))^2=(1+cos2x)/2)】

3.complex variable【z=cosθ+isinθ,z+1/z=2cosθ】

Calculus--Indefinite Integrals (05-58,S/N: 323) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-08)

Prove Heron's Formula or Hero's Formula A=sqrt(s(s-a)(s-b)(s-c)), where a,b and c are side lengths of triangle, s=(a+b+c)/2.

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-08,S/N: 8) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-57）

Using partial fraction and trigonometric substitution integrate ∫((1+x)/sqrt(1-4x^2))dx and ∫((2-x)/sqrt(2x-x^2))dx

Calculus--Indefinite Integrals (05-57,S/N: 322) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-53-56）--Four Methods to Integrate

Guess, how many formulae have been used for integral ∫(1/(sinx+cosx))dx? More than eighteen formulae.

A.Trigonometric identitis:

   a. Pythagorean trigonometric identity:

      1. (sinα)^2+(cosα)^2=1

   b. co-function identities:

      2. sinx=cos(π/2-x)

      3. cosx=sin(π/2-x)

   c. angle sum identity

      4. tan(α+β)=(tanα+tanβ)/(1-tanαtanβ)

   d. double-angle formulae

      5. cos2x=(cosx)^2-(sinx)^2=2(cosx)^2-1=1-2(sinx)^2

      6. sin2x=2sinxcosx

   e. sum-to-product identities

      7. sinα+sinβ= 2sin((α+β)/2)cos((α-β)/2)

      8. cosα-cosβ= 2cos((α+β)/2)cos((α-β)/2)

      9. sinα+sinβ= 2cos((α+β)/2)sin((α-β)/2)

      10. cosα-cosβ= -2sin((α+β)/2)sin((α-β)/2)

B. Algebra Formulas - Factoring formulas- Difference of squares:

      11. a^2-b^2=(a-b)(a+b)

C. Euler's formula

      12. e^(ix)=cosx+isinx

      13. sinx=(e^(ix)-e^(-ix))/2i

      14. cosx=(e^(ix)+e^(-ix))/2

 D. Logarithm rules

      15. ln(x/y)=lnx-lny

 E.The complex inverse trigonometric function

      16. arctanz=i/2(ln((1-iz)/(1+iz)))

 F. Basic Integration formulae:

      17. ∫(1/x)dx=lnx+c

      18. ∫(1/(x^2+y^2))dx=1/a(arctan(x/a))+c

Calculus--Indefinite Integrals (05-53-56,S/N: 321) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

PHYSICAL CHEMISTRY BY GUO CHENG GUANG (01-01)

In this video, we compared the three groups of concepts about macroscopic and microscopic quantities and units in physical chemistry or theoretical chemistry. First group: Physical and chemical, second group: state and procss, third group: matter, substance, body, object and material.

PHYSICAL CHEMISTRY BY GUO CHENG GUANG (aged 11) and GUO CHENGXI(aged 8) in Engling and Chinese (01-01,S/N: 4). Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-56）

Forth method of integration the ∫(1/(sinx+cosx))dx, using the integral by complex variable.

Calculus--Indefinite Integrals (05-56,S/N: 321) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01...

Heron's Formula (Hero's formula): Area of Triangle whose sides have lengths a, b and c is   = sqrt(s(s-a)(s-b)(s-c)), s is the semiperimeter of the triangle that is s=(a+b+c)/2.

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01-06,S/N: 6) Presented By Guo Cheng Guang (aged 11), LIM ZI JIE(aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

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CALCULUS PRESENTED BY GUO CHENG GUANG（05-55）

Third method of computing the ∫(1/(sinx+cosx))dx, using the integral by substitution.

Calculus--Indefinite Integrals (05-55,S/N: 320) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-54）

Second method of solving the ∫(1/(sinx+cosx))dx, using the integral by trigonometric identities.

Calculus--Indefinite Integrals (05-54,S/N: 319) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-53）

The following methods have been used to solve this example:

1.Denominate Rationalization

2. Factorization

3. Partial Fraction

4. Trigonometric Identities

5. Logarithmic Integral

Calculus--Indefinite Integrals (05-53,S/N: 318) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01...

area of polygen =1/2|x1  x2  x3 x4...xn x1|

                    |y1  y2  y3 y4...xn y1|

=1/2(x1*y2+x2*y3+x3*y4+...+xn*y1-x2*y1-x3*y2-x4*y3-...-xn*y4)

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01-05,S/N: 5) Presented By Guo Cheng Guang (aged 11), LIM ZI JIE(aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZIJIE,GUO CHENGXI(01-05)

1. Finding the points of intersection of perpendicular line. To find the slope of the slope of the perpendicular line, flip the fraction and change the sign. For any linear equation y=mx+b, the perpendiculars will all have a slope of (-1/m), the opposite reciprocal of the original slope.

2. Finding the angle between two line equations.Using α=arctan(m)[Here, α is the angle of inclination, m is the slope. ] and tan(α+β)= [tan(α)+tan(β)]/[1-tan(α)tan(β)]

3. Finding the area of quadrilateral.  Using shoelace formula, suppose the quadrilateral has vertices (x1,y1),(x2,y2),(x3,y3),(x4,y4), listed in clockwise order.

area of quadrilateral =1/2|x1  x2  x3 x4 x1|

                                              |y1  y2  y3 y4 y1|

 =1/2(x1*y2+x2*y3+x3*y4+x3*y1-x2*y1-x3*y2-x4*y3-x1*y4)

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01-05,S/N: 5) Presented By Guo Cheng Guang (aged 11), LIM ZI JIE(aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-51）-- Integration by substitution

The integral by substitution technique amounts to applying the Chain Rule in reverse: to compute ∫f(x)g'(x)dx, we let u=g(x), du=g'(x)dx. Then ∫f(x)g'(x)dx= ∫f(u)du=F(u)=F(g(x)) where F is an antidifferenciation of f.

Let's computer ∫(1/sqrt((4+x^2)^3)) dx and ∫(1/sqrt((3+x^2)^5)) dx by making the substitution.

Calculus--Indefinite Integrals (05-50,S/N: 313) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-50）-- integral by substitution

How does the substitution technique work? Let's solve the problems[1.∫sinxcosxdx; 2. ∫(x^5)(e^2x )dx] step-by-step to make sure our understand the process.

STEP 1: - Determine which expression to be substituted

STEP 2: - Substitute, rewrite the integral in simpler form and integrate

STEP 3: - Substitute back

Calculus--Indefinite Integrals (05-50,S/N: 313) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZIJIE,GUO CHENGXI(01-04)

We used the Gaussian elimnation method for solving a pair of simultaneous linear equations reduces one equation to one that has only a single variable.

shoelace theorem also known as shoelace algorithm or Gauss's area formula or the surveyor's formula, is an algorithm, a nifty formula for finding the area of a polygon given the coordinates of its vertices, is equal to the absolute value of :Suppose the triangle has vertices (x1,y1),(x2,y2),(x3,y3), listed in clockwise order.

area of triangle =1/2|x1  x2  x3 x1|

                                     |y1  y2  y3 y1|

                            =1/2(x1*y2+x2*y3+x3*y1-x2*y1-x3*y1-x1*y3)

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-49）

Integration by Substitution also called u-substition, is the most easily technique by means of a change of variable. We are able to rewrite the integral into a very siple integral that we can do.

The substitution rule in general: ∫f(x)g'(x)dx= ∫f(u)du, where u=g(x).

In this lesson, we will prove that d(arcsin(x))/dx = 1/sqrt(1-x^2) by definition of differentiation and show that ∫(1/sqrt(1-x^2))dx= arcsin(x)+c by substitution

Calculus--Indefinite Integrals (05-49,S/N: 312) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-48）-- integral by parts

We will use the integral by parts or partial integration ∫f(x)g'(x)dx=f(x)g(x)-∫g'(x)f(x) to evaluate ∫[x(tanx)^-1/sqrt((1+x^2)^5)]dx and  ∫[ln(x+sqrt(1+x^2))]^2dx.

Calculus--Indefinite Integrals (05-48,S/N: 311) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZI JIE,GUO CHENGXI(01...

Using the following methods to Exemplify the equation of a straight lines:

1.  Slop-intercept Form

2.  General Form

3. Two Point Form

4. Two-intercept Form

5. Cross product Form

include finding parallel and perpendicular lines.

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-47）-- Integral by parts

Using Integration by parts to solve  two indefinite integrals.

Calculus--Indefinite Integrals (05-47,S/N: 310) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZIJIE,GUO CHENGXI(01-02)

Five methods to find the equation of a straight line:

1.  Slop-intercept Form

2.  General Form

3. Two Point Form

4. Two-intercept Form

5. Cross product Form

LECTURER:

         GUO CHENG GUANG (11 years old, Primary 5 from YUMIN Primary School)

         LIM ZIJIE (11 years old, Primary 5 from YUMIN Primary School)

         GUO CHENGXI( 8 years old, Primary 2 from YUMIN Primary School)

Wechat: Go-Singapore

E-mail: forstudentsg@gmail.com

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

Calculus--Indefinite Integrals (05-46) -- integral by parts

Calculus--Indefinite Integrals (05-46,S/N: 309) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG (05-45)-- Integral by pars

To do these three indefinite integrals we all need to use integration by parts.

Calculus--Indefinite Integrals (05-45, S/N: 308) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-44,s/n:307）-- Trigonometric Int...

In these three indefinite integrals, we all need to use integral by parts. And we used the following methods to solve these integration:

1. Integral by parts

2. Factarization

3. Partial Fraction

4. Binomial Expansion

5. Trigonometric Identities

6. Integration of Trigonometric Integral

7. Logarithmic Integral

Calculus--Indefinite Integrals (05-44,S/N: 307) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-43）

CALCULUS PRESENTED BY GUO CHENG GUANG（05-43,S/N: 306）-- trigonometric integrations. Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG,LIM ZIJIE,GUO CHENGXI 01-01

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG(aged 11),LIM ZIJIE(aged 11),GUO CHENGXI(aged 8)(01-01)

Analytic Geometry: In classical mathematics, analytic geometry also called as coordinate geometry or Cartesian geometry, is the study of geometry using the rectangular coordinate system or the Cartesian coordinate system.In modern analytic geometry is included concept of real or complex algeraic variety, is essentially equivalent to real and comple algebraic geometry.

Cartesian corrdinate system: In the plane, two perpendicular lines are chosen and the coordintaes of a point that can be identifired with ordered pairs of real numbers are taken to be signed distances to the lines.

Application of Analytic geometry: Analytic geometry can be widely used in algebraic, differential, discrete, physics, engineering, electrostatic and electrictity theory, designing machine, aviation,space science, sapceflight, computer science and so on.

LECTURER:

GUO CHENG GUANG (11 years old)

LIM ZIJIE (11 years old)

GUO CHENGXI( 8 years old)

Contents： Basic concepts

Wechat: Go-Singapore

E-mail: forstudentsg@gmail.com