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