國立陽明交通大學開放式課程(OpenCourseWare, OCW).

應用數學-線性代數 (Applied Maths-Linear Algebra, Vector Analysis) - Week 1 Cartesian Plane、Vector in The Cartesian Plane、Vector Addition

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周次	課程內容	課程影音
Week 1	Cartesian Plane、Vector in The Cartesian Plane、Vector Addition	線上觀看
	Vector Addition、Vector in R^3 and R^n、Algebraic Properties of Vector in R^n and Proof	線上觀看
	Using Algebraic Properties for computation、Independent Vector Spanning R^2 Space、Linear Combination、Binary Vevtor	線上觀看
	Dot Product、Definition and Example、Algebraic Properties of Dot Product	線上觀看
	Length、Unit Vector、The Cauchy-Schwartz and Triangle Inequality、Distance between Two Vector	線上觀看
	Angle between Two Vectors、Angle and Orthogonal Property、Dot Operation and Orthogonality of Function、Pythagoras’ Theorem and Projection	線上觀看
	Lines in R^2 and R^3	線上觀看
	Lines in R^2 and R^3、Planes in R^3	線上觀看
	Distance from a Point to a Line/Plane、Applications	線上觀看
Week 2	Linear or Nonlinear Equation、A system of Linear Equation in R^2 and R^3、Coefficient and Augmented Metrices	線上觀看
	Row Echelon Form、Elementary Row Operation and Row Equivalent、Gaussian Elimination	線上觀看
	Rank and Gaussian-Jordan Elimination、Gaussian-Jordan Elimination、Homogeneous Systems、Linear Systems over Z_p	線上觀看
	Vector Concepts for Linear Combinations、Spanning Set for Space R^n	線上觀看
	Spanning Set for Space R^n、Linear independence	線上觀看
	Linear independence	線上觀看
	Application(Chemical、Network Analysis)	線上觀看
	Application(Circuit、Economic Models)	線上觀看
	Application(Finite Linear Games)、Numerical Solutions-Iterative Methods	線上觀看
Week 3	Introduction to Matrix Operations、Matrix Operations、Matrix’s Equality	線上觀看
	Matrix Addition and Scalar Multiplication、Matrix Multiplication、Partitioned Matrices	線上觀看
	Partitioned Matrices、Matrix Power、The Transpose of a Matrix	線上觀看
	Properties of Addition and Scalar Multiplication、Properties of Matrix Multiplication	線上觀看
	Properties of The Transpose、The inverse of a Matrix	線上觀看
	Properties of Invertible Matrices、Elementary Matrices	線上觀看
	The Foundamental Theorem of Invertible Matrices、 The Gaussian-Jordan Method for Computing The Inverse	線上觀看
	The Gaussian-Jordan Method for Computing The Inverse、The LU Factorization	線上觀看
	An Easy Way to Find LU Factorizations、The P^TLU Factorization、Computational Consideration	線上觀看
Week 4	Subspace、Row and Column Space of Matrice(Introduction)	線上觀看
	Row and Column Space of Matrice、Basis and Effective Procedures to Find Basis	線上觀看
	Dimension、Rank、The Fundamental Theorem of Invertible Matrices	線上觀看
	Introduction to Linear Transformations、Linear Transformations	線上觀看
	Linear Transformations、Rotation About The Origin、Composition of Two Transformations	線上觀看
	Composition of Two Transformations、Inverse of Linear Transformations、Associativity	線上觀看
	Introduction to Markov Chain、Markov Chain-State Vector、Transition Matrix and Steady State Vector	線上觀看
	Application Example of Markov Chain、Linear Economic Model-Leontief Model、Productive、Population Growth-Leslie Model	線上觀看
	Population Growth-Leslie Model、Graph、Digraph	線上觀看
	Digraph、Error-Correction Codes	線上觀看
Week 5	Introduction to Eigenvalues and Eigenvectors、Eigenspace	線上觀看
	Eigenspace、Eigenpicture	線上觀看
	Eigenpicture-Zero Determinant、Calculate Eigenvalues	線上觀看
	Concept of Determinant and How to calculate、Determinant of n×n matrices、The Laplace Expansion	線上觀看
	The Examples of Laplace Expansion、Properties of Determinants	線上觀看
	Determinants of Elementary Matrices、Determinants and Matrix Operations、Cramer’s Rule and The Adjoint	線上觀看
	Eigenvalues of a Square Matrix	線上觀看
	Eigenvalues of a Square Matrix、The Fundamental Theorem of Invertible Matrices	線上觀看
	Polynomial of a matrix A and Its corresponding eigenvalues	線上觀看
Week 7	Similar Matrices	線上觀看
	Diagonalization	線上觀看
	Diagonalization、The Diagonalization Theroem	線上觀看
	The Power Method	線上觀看
	The Power Method、The Shifted Power Method、The Inverse Power Method	線上觀看
	The Shifted Inverse Power Method、Gerschgorin’s Theorem	線上觀看
	Markov Chains	線上觀看
	Population Growth、Leslie matrix、Perron-Frobenius Theorem	線上觀看
	Linear Recurrence Relation	線上觀看
	System of Linear Differential Equations	線上觀看
	Exponential of A - e^A、Discrete Linear Dynamical Systems	線上觀看
	Discrete Linear Dynamical Systems	線上觀看
Week 8	Orthogonal Sets of Vectors、Coordinate	線上觀看
	Orthogonal Matrices、Orthogonal Complements	線上觀看
	Orthogonal Projections、Orthogonal Decompositions	線上觀看
	The Gram-Schmidt Process、QR Factorization	線上觀看
	Orthogonal Diagonalizable	線上觀看
	Spectral Theorem	線上觀看
	Dual Codes-The generated Code Space C、Dual Codes-The Same or Equivalent Code	線上觀看
	Quadratic Forms、Quadratic Forms-diagonalization and Principle Axes Theorem	線上觀看
	Quadratic Forms、Definition and Example、Diagonalization and Principal Axes Theorem	線上觀看
	The Foundamental Theorem of Quadratic Forms	線上觀看
	Graphing Quadratic Equations、Identify and graph the conic	線上觀看
	Graphing Quadratic Equations、Identify the quadric surface of the equation	線上觀看
Week 9	Vector Space、Examples of Kinds of Vector Space	線上觀看
	Examples of Vector or Non-Vector Space、Zero and Negative vector、Subspace	線上觀看
	Spanning Set	線上觀看
	Linear Independence、 Bases	線上觀看
	Coordinate	線上觀看
	Dimesion	線上觀看
	Change-of-Basis Matrices	線上觀看
	The Gauss-Jordan Method for Computing a change-of-Basis Matrix	線上觀看
Week 10	Linear Transformations、Definition and Example	線上觀看
	Properties of Linear Transformations,、Composition of Linear Transformations, Inverse of Linear Transformation	線上觀看
	The Kernel and Range of a Linear Transformations、Definition and Example	線上觀看
	The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations	線上觀看
	The Kernel and Range of a Linear Transformations、The Rank Theorem、One-to-One and Onto Linear Transformations	線上觀看
	Linear Transformations Represented by a Matrix	線上觀看
	Matrices of Composite and Inverse Linear Transformations	線上觀看
	Change of Basis and Similarity	線上觀看
	The Fundemantal Theorem of Invertible Matrices	線上觀看
	1st Order Homogeneous,Linear,Differential,Eqations 、2nd Order Homogeneous,Linear,Differential,Eqations	線上觀看
Week 11	Extends from 1D to 3D Vector Space、Scalar Functions , Functions of Scalar of Functions of Vector、Vector Functions of Vector	線上觀看
	Vecor-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
	Calculate the tangent line of a curve、Differentiation and Integration of the Curve、 The length of a Curve、TheArc length Parameter	線上觀看
	Trajectory of a particle	線上觀看
	Calculation of Curvature	線上觀看
	Normal and Binormal Vectors、Tangent, Normal and Binormal Vectors、Another Method for the Calculation of Curvature、Curvature of Twisted Cubic	線上觀看
	Level Curves for Functions of two variables、Functions of three variables F(x,y,z)、 Partial Derivatives of Functions	線上觀看
	Scalar Functions to Vector Functions、Gradient Calculation	線上觀看
	Concept of Gradient Calculation、Gradient Calculation	線上觀看
Week 13	Level Curves and Gradient	線上觀看
	Vector fields,The del operator	線上觀看
	Concept of Divergence Calculation、Curl less or Divergent less Potential、 Scalar or Vector Potential	線上觀看
	Line Integrals on a 2D plane	線上觀看
	Line Integrals on a 2D plane	線上觀看
	Line Integrals on a 2D plane-Plane Work done by force	線上觀看
	Path Independence Integration Result、Conservative Vector Fields	線上觀看
	Conservative Vector Fields	線上觀看
	Test for a Conservative Vector field	線上觀看
Week 14	Introduction to Double Integrals、Applications of Double Integrals	線上觀看
	Calculation of Double Integrals、Change of Variables、Double Integrals in Poar coordinates	線上觀看
	Change of variables	線上觀看
	Proof of Green’s Theorem	線上觀看
	Green’s Theorem and Calculation 、Stoke’s Theorem、Application of Green’s Theorem	線上觀看
	Application of Green’s Theorem、Apply Green’s Theorem in the region with holes	線上觀看