Course - Advanced Mathematics

From the most basic knowledge of functions and limits, we go step by step into the field of differential science, including the concepts of derivatives and differentiation, algorithm rules, and applications of derivatives.

set and operation

set

10:31
operation of set

26:10
Interval and neighborhood

12:54

Mapping and Function

mapping

19:50
the concept of functions

23:53
Characteristics of functions

15:44
elementary function

13:13
Applications in machine learning

16:24
Examples in class

18:51

sequence limit

Sequence and sequence limits

19:34
Properties of convergent sequence

25:42
Practice in class

15:16

function limit

Function limit concept

25:37
Function limit examples and one-sided limits

21:41
Properties of function limits

23:01
chapter summarizes

21:43
Practice in class

28:50

Infinitesimal and infinite

infinitesimal

19:56
Infinity

20:27
chapter summarizes

18:52
Practice in class

13:10

limit operation

limit algorithm

17:11
Limit algorithm (example)

17:43
limit existence criterion

16:29
Comparison of infinitesimal

19:55
chapter summarizes

22:55
Practice in class

22:41

Continuity and discontinuity points of functions

continuity of a function

29:20
discontinuity of the first kind of function

17:51
discontinuity of the second kind of function

18:36
chapter summarizes

21:53
Examples in class

24:17

Derivative and differential

The concept of derivative

24:14
The concept of derivative (derivative of power function-one-sided derivative-tangent and normal equations)

25:32
Derivability and continuity of functions

26:46
derivative summary

27:17
Derivative rule of function

15:56
Derivative rule of compound functions

27:50
Formula for deriving constants and basic elementary functions

25:59
higher order derivatives

29:31
Algorithm for higher-order derivatives

18:11
derivative of implicit function

28:37
Derivation of power exponential functions

25:54
Function determined by parametric equations

22:15
differential of a function

20:51
differential algorithm

10:35

Differential median value theorem and application of derivatives

Differential Mean Value Theorem-Rolle Theorem

13:47
Differential Mean Value Theorem--Lagrange Mean Value Theorem

25:36
Differential Mean Value Theorem--Cauchy Mean Value Theorem

28:00
Lopida's rule type 00 indeterminate

16:25
L'Bedard's Rule-Other Undefinite Formulas

22:48
Taylor's formula-Taylor's median value theorem

11:22
Taylor's formula--McLaughin's formula

16:49
Monotonicity of a function

13:47
concave-convex nature of a curve

28:18
The concept of extreme value of a function

14:33
Method for finding extreme value of function

11:35
Maximum value of the function minimum value

17:56
Description of function graphs

26:49

course introduces