課程大綱 OUTLINE Functions of Several Variables

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Presentation transcript:

課程大綱 OUTLINE Functions of Several Variables Limits and Continuity（極限與連續） Partial Derivatives（偏導數） Linear Approximations and chain Rule （線性估計與鏈鎖律) Directional Derivatives and The Gradient Vector（方向導數和梯度） Maximum and Minimum Values（極值）

Functions of Several Variables -R3

Functions of Several Variables -R3

Functions of Several Variables -Rn

Functions of Several Variables -Rn

Functions of Several Variables -Rn

Functions of Several Variables -Rn

Functions of Several Variables -Rn 長度及相關的等式

Functions of Several Variables

Functions of Several Variables - FUNCTIONS OF 2 VARIABLES

Functions of Several Variables - FUNCTIONS OF 2 VARIABLES

Functions of Several Variables - FUNCTIONS OF 2 VARIABLES

Functions of Several Variables - FUNCTIONS OF 2 VARIABLES

Functions of Several Variables - LEVEL CURVES 等值線

Functions of Several Variables - LEVEL CURVES 等值線

Functions of Several Variables - LEVEL CURVES 等值線

Functions of Several Variables - LEVEL CURVES 等值線

LIMITS AND CONTINUITY 極限與連續 - LIMIT

LIMITS AND CONTINUITY 極限與連續 - LIMIT

LIMITS AND CONTINUITY 極限與連續 - LIMIT

LIMITS AND CONTINUITY 極限與連續 - LIMIT

LIMITS AND CONTINUITY 極限與連續 - LIMIT

LIMITS AND CONTINUITY 極限與連續 - THEOREM

LIMITS AND CONTINUITY 極限與連續 - THEOREM

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

LIMITS AND CONTINUITY 極限與連續 - CONTINUITY連續

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - INTERPRETATIONS OF PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - INTERPRETATIONS OF PARTIAL DERIVATIVES

PARTIAL DERIVATIVES偏導數 - HIGHER DERIVATIVES高階偏導數

PARTIAL DERIVATIVES偏導數 - HIGHER DERIVATIVES高階偏導數

PARTIAL DERIVATIVES偏導數 - HIGHER DERIVATIVES高階偏導數

PARTIAL DERIVATIVES偏導數 - HIGHER DERIVATIVES高階偏導數

PARTIAL DERIVATIVES偏導數 - HIGHER DERIVATIVES高階偏導數

PARTIAL DERIVATIVES偏導數 - PARTIAL DIFFERENTIAL EQUATIONS

PARTIAL DERIVATIVES偏導數 - PARTIAL DIFFERENTIAL EQUATIONS

PARTIAL DERIVATIVES偏導數 - PARTIAL DIFFERENTIAL EQUATIONS

LINEAR APPROXIMATIONS AND CHAIN RULE - TANGENT PLANES 切平面

LINEAR APPROXIMATIONS AND CHAIN RULE - TANGENT PLANES 切平面

LINEAR APPROXIMATIONS AND CHAIN RULE - TANGENT PLANES 切平面

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - LINEAR APPROXIMATION 線性估計

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 1)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 1)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 1)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 1)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 2)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 2)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 2)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 2)

LINEAR APPROXIMATIONS AND CHAIN RULE - THE CHAIN RULE 鏈鎖律(CASE 2)

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

LINEAR APPROXIMATIONS AND CHAIN RULE - IMPLICIT DIFFERENTIATION 隱微分

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - DIRECTIONAL DERIVATIVES 方向導數

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - DIRECTIONAL DERIVATIVES 方向導數

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - DIRECTIONAL DERIVATIVES 方向導數

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - DIRECTIONAL DERIVATIVES 方向導數

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - THE GRADIENT VECTOR 二變數函數的梯度

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - FUNCTIONS OF THREE VARIABLES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - TANGENT PLANES TO LEVEL SURFACES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - TANGENT PLANES TO LEVEL SURFACES

DIRECTIONAL DERIVATIVES AND THE GRADIENT VECTOR - TANGENT PLANES TO LEVEL SURFACES

MAXIMUM AND MINIMUM VALUES - LOCAL MAXIMUM AND LOCAL MINIMUM VALUES

MAXIMUM AND MINIMUM VALUES - LOCAL MAXIMUM AND LOCAL MINIMUM VALUES

MAXIMUM AND MINIMUM VALUES - LOCAL MAXIMUM AND LOCAL MINIMUM VALUES

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - CRITICAL POINT AND SADDLE POINT

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS

MAXIMUM AND MINIMUM VALUES - LAGRANGE MULTIPLIERS