Line Integrals on a 2D plane

週次	課程內容	課程影音	課程下載
第一週	Cartesian Plane、Vector in The Cartesian Plane、Vector Addition	線上觀看	MP4下載
	Vector Addition、Vector in R^3 and R^n、Algebraic Properties of Vector in R^n and Proof	線上觀看	MP4下載
	Using Algebraic Properties for computation、Independent Vector Spanning R^2 Space、Linear Combination、Binary Vector	線上觀看	MP4下載
	Dot Product、Definition and Example、Algebraic Properties of Dot Product	線上觀看	MP4下載
	Length、Unit Vector、The Cauchy-Schwartz and Triangle Inequality、Distance between Two Vector	線上觀看	MP4下載
	Angle between Two Vectors、Angle and Orthogonal Property、Dot Operation and Orthogonality of Function、Pythagoras’ Theorem and Projection	線上觀看	MP4下載
	Lines in R^2 and R^3	線上觀看	MP4下載
	Lines in R^2 and R^3、Planes in R^3	線上觀看	MP4下載
	Distance from a Point to a Line/Plane、Applications	線上觀看	MP4下載
第二週	Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices	線上觀看	MP4下載
	Row Echelon Form、Elementary Row Operation and Row Equivalent、Gaussian Elimination	線上觀看	MP4下載
	Rank and Gaussian-Jordan Elimination、Gaussian-Jordan Elimination、Homogeneous Systems、Linear Systems over Z_p	線上觀看	MP4下載
	Vector Concepts for Linear Combinations、Spanning Set for Space R^n	線上觀看	MP4下載
	Spanning Set for Space R^n、Linear independence	線上觀看	MP4下載
	Linear independence	線上觀看	MP4下載
	Application(Chemical、Network Analysis)	線上觀看	MP4下載
	Application(Circuit、Economic Models)	線上觀看	MP4下載
	Application(Finite Linear Games)、Numerical Solutions-Iterative Methods	線上觀看	MP4下載
第三週	Introduction to Matrix Operations、Matrix Operations、Matrix’s Equality	線上觀看	MP4下載
	Matrix Addition and Scalar Multiplication、Matrix Multiplication、Partitioned Matrices	線上觀看	MP4下載
	Partitioned Matrices、Matrix Power、The Transpose of a Matrix	線上觀看	MP4下載
	Properties of Addition and Scalar Multiplication、Properties of Matrix Multiplication	線上觀看	MP4下載
	Properties of The Transpose、The inverse of a Matrix	線上觀看	MP4下載
	Properties of Invertible Matrices、Elementary Matrices	線上觀看	MP4下載
	The Fundamental Theorem of Invertible Matrices、The Gaussian-Jordan Method for Computing The Inverse	線上觀看	MP4下載
	The Gaussian-Jordan Method for Computing The Inverse、The LU Factorization	線上觀看	MP4下載
	An Easy Way to Find LU Factorizations、The P^TLU Factorization、Computational Consideration	線上觀看	MP4下載
第四週	Subspace、Row and Column Space of Matrice(Introduction)	線上觀看	MP4下載
	Row and Column Space of Matrice、Basis and Effective Procedures to Find Basis	線上觀看	MP4下載
	Dimension、Rank、The Fundamental Theorem of Invertible Matrices	線上觀看	MP4下載
	Introduction to Linear Transformations、Linear Transformations	線上觀看	MP4下載
	Linear Transformations、Rotation About The Origin、Composition of Two Transformations	線上觀看	MP4下載
	Composition of Two Transformations、Inverse of Linear Transformations、Associativity	線上觀看	MP4下載
	Introduction to Markov Chain、Markov Chain-State Vector、Transition Matrix and Steady State Vector	線上觀看	MP4下載
	Application Example of Markov Chain、Linear Economic Model-Leontief Model、Productive、Population Growth-Leslie Model	線上觀看	MP4下載
	Population Growth-Leslie Model、Graph、Digraph	線上觀看	MP4下載
	Digraph、Error-Correction Codes	線上觀看	MP4下載
第五週	Introduction to Eigenvalues and Eigenvectors、Eigenspace	線上觀看	MP4下載
	Eigenspace、Eigenpicture	線上觀看	MP4下載
	Eigenpicture-Zero Determinant、Calculate Eigenvalues	線上觀看	MP4下載
	Concept of Determinant and How to calculate、Determinant of n×n matrices、The Laplace Expansion	線上觀看	MP4下載
	The Examples of Laplace Expansion、Properties of Determinants	線上觀看	MP4下載
	Determinants of Elementary Matrices、Determinants and Matrix Operations、Cramer’s Rule and The Adjoint	線上觀看	MP4下載
	Eigenvalues of a Square Matrix	線上觀看	MP4下載
	Eigenvalues of a Square Matrix、The Fundamental Theorem of Invertible Matrices	線上觀看	MP4下載
	Polynomial of a matrix A and Its corresponding eigenvalues	線上觀看	MP4下載
第七週	Similar Matrices	線上觀看	MP4下載
	Diagonalization	線上觀看	MP4下載
	Diagonalization、The Diagonalization Theorem	線上觀看	MP4下載
	The Power Method	線上觀看	MP4下載
	The Power Method、The Shifted Power Method、The Inverse Power Method	線上觀看	MP4下載
	The Shifted Inverse Power Method、Gerschgorin’s Theorem	線上觀看	MP4下載
	Markov Chains	線上觀看	MP4下載
	Population Growth、Leslie matrix、Perron-Frobenius Theorem	線上觀看	MP4下載
	Linear Recurrence Relation	線上觀看	MP4下載
	System of Linear Differential Equations	線上觀看	MP4下載
	Exponential of A - e^A、Discrete Linear Dynamical Systems	線上觀看	MP4下載
	Discrete Linear Dynamical Systems	線上觀看	MP4下載
第八週	Orthogonal Sets of Vectors、Coordinate	線上觀看	MP4下載
	Orthogonal Matrices、Orthogonal Complements	線上觀看	MP4下載
	Orthogonal Projections、Orthogonal Decompositions	線上觀看	MP4下載
	The Gram-Schmidt Process、QR Factorization	線上觀看	MP4下載
	Orthogonal Diagonalizable	線上觀看	MP4下載
	Spectral Theorem	線上觀看	MP4下載
	Dual Codes-The generated Code Space C、Dual Codes-The Same or Equivalent Code	線上觀看	MP4下載
	Quadratic Forms、Quadratic Forms-diagonalization and Principle Axes Theorem	線上觀看	MP4下載
	Quadratic Forms、Definition and Example、Diagonalization and Principal Axes Theorem	線上觀看	MP4下載
	The Fundamental Theorem of Quadratic Forms	線上觀看	MP4下載
	Graphing Quadratic Equations、Identify and graph the conic	線上觀看	MP4下載
	Graphing Quadratic Equations、Identify the quadric surface of the equation	線上觀看	MP4下載
第九週	Vector Space、Examples of Kinds of Vector Space	線上觀看	MP4下載
	Examples of Vector or Non-Vector Space、Zero and Negative vector、Subspace	線上觀看	MP4下載
	Spanning Set	線上觀看	MP4下載
	Linear Independence、 Bases	線上觀看	MP4下載
	Coordinate	線上觀看	MP4下載
	Dimension	線上觀看	MP4下載
	Change-of-Basis Matrices	線上觀看	MP4下載
	The Gauss-Jordan Method for Computing a change-of-Basis Matrix	線上觀看	MP4下載
第十週	Linear Transformations、Definition and Example	線上觀看	MP4下載
	Properties of Linear Transformations,、Composition of Linear Transformations, Inverse of Linear Transformation	線上觀看	MP4下載
	The Kernel and Range of a Linear Transformations、Definition and Example	線上觀看	MP4下載
	The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations	線上觀看	MP4下載
	The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations	線上觀看	MP4下載
	Linear Transformations Represented by a Matrix	線上觀看	MP4下載
	Matrices of Composite and Inverse Linear Transformations	線上觀看	MP4下載
	Change of Basis and Similarity	線上觀看	MP4下載
	The Fundamental Theorem of Invertible Matrices	線上觀看	MP4下載
	1st Order Homogeneous,Linear,Differential,Equations、2nd Order Homogeneous,Linear,Differential,Equations	線上觀看	MP4下載
第十一週	Extends from 1D to 3D Vector Space、Scalar Functions , Functions of Scalar of Functions of Vector、Vector Functions of Vector	線上觀看	MP4下載
	Vector-Function Curve,3D to 1D Vsinf Parameter 、Find the Intersection Curve 、Limits of a Vector Functions 、Continuity and Derivative of Vector Function	線上觀看	MP4下載
	Calculate the tangent line of a curve、Differentiation and Integration of the Curve、 The length of a Curve、The Arc length Parameter	線上觀看	MP4下載
	Trajectory of a particle	線上觀看	MP4下載
	Calculation of Curvature	線上觀看	MP4下載
	Normal and Binormal Vectors、Tangent, Normal and Binormal Vectors、Another Method for the Calculation of Curvature、Curvature of Twisted Cubic	線上觀看	MP4下載
	Level Curves for Functions of two variables、Functions of three variables F(x,y,z)、 Partial Derivatives of Functions	線上觀看	MP4下載
	Scalar Functions to Vector Functions、Gradient Calculation	線上觀看	MP4下載
	Concept of Gradient Calculation、Gradient Calculation	線上觀看	MP4下載
第十三週	Level Curves and Gradient	線上觀看	MP4下載
	Vector fields,The del operator	線上觀看	MP4下載
	Concept of Divergence Calculation、Curl less or Divergent less Potential、Scalar or Vector Potential	線上觀看	MP4下載
	Line Integrals on a 2D plane	線上觀看	MP4下載
	Line Integrals on a 2D plane	線上觀看	MP4下載
	Line Integrals on a 2D plane-Plane Work done by force	線上觀看	MP4下載
	Path Independence Integration Result、Conservative Vector Fields	線上觀看	MP4下載
	Conservative Vector Fields	線上觀看	MP4下載
	Test for a Conservative Vector field	線上觀看	MP4下載
第十四週	Introduction to Double Integrals、Applications of Double Integrals	線上觀看	MP4下載
	Calculation of Double Integrals、Change of Variables、Double Integrals in Poar coordinates	線上觀看	MP4下載
	Change of variables	線上觀看	MP4下載
	Proof of Green’s Theorem	線上觀看	MP4下載
	Green’s Theorem and Calculation 、Stoke’s Theorem、Application of Green’s Theorem	線上觀看	MP4下載
	Application of Green’s Theorem、Apply Green’s Theorem in the region with holes	線上觀看	MP4下載