臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/1---------------00:00:00 OPENING ~ 單元名稱00:00:15 課程介紹00:14:59 Octave 程式介紹00:31:54 Vectors and Matrices00:50:22 Linear Combination of 3D Vectors00:56:04 Dot Product and Length01:03:25 Properties01:19:09 Matrix01:40:08 ENDING---------------

01. Prologue, Vectors and Matrices

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/2---------------00:00:00 OPENING ~ 單元名稱00:00:15 Solving Linear Equations00:00:43 Linear Equations00:23:29 Elimination00:50:12 Matrix Operations01:13:39 課程內容更正01:14:57 Block Matrix01:27:19 Invertible01:37:19 Gauss-Jordan Elimination01:50:59 Elimination via Matrices02:16:22 ENDING---------------

02. Solving Linear Equations

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/3---------------00:00:00 OPENING ~ 單元名稱00:00:15 Matrix Transpose00:12:03 Meaning of Transpose00:26:01 Hermitian Adjoint00:55:40 Vector Spaces and Subspaces00:57:07 Vector Space01:14:36 Subspace01:24:29 Independence, Basis, Dimension01:29:47 Test for Independence01:50:30 Identify the Space Spanned by the Vectors02:05:20 ENDING---------------

03. Transposes and Permutations, Vector Spaces and Subspaces, The Four Spaces

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/4---------------00:00:00 OPENING ~ 單元名稱00:00:15 Four Spaces00:07:57 Rank00:34:15 Dimensions and Basis of the Four Spaces01:11:08 課程內容提問回答01:14:57 Application 1: Reduce a m*n Matrix into the Sum of r Rank-1 Matrices01:23:26 Application 2: General Solution to Ax=b02:01:36 ENDING---------------

04. Dimensions and Basis of the Four Spaces, The Complete Solution to Ax=b

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/5---------------00:00:00 OPENING ~ 單元名稱00:00:15 前次課程內容複習00:01:23 Orthogonality00:41:33 Projections onto a Subspace01:18:04 Least Squares Approximations01:44:49 Orthonormal Basis & Gram-Schmidt01:51:01 Gram-Schmidt02:02:52 Properties of Q02:18:19 A=QR02:26:41 ENDING---------------

05. Orthogonality, Projections, Least-Square Approximations, Orthonormal Bases and Gram-Schmidt

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/6---------------00:00:00 OPENING ~ 單元名稱00:00:15 前次課程內容更正、補充00:06:58 Determinants00:09:37 Rules of det A00:48:01 Formula for det A01:24:01 Applications of Determinants01:43:29 Triangular Area Formula01:50:34 Cross Product02:02:49 ENDING---------------

06. Determinants

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/7---------------00:00:00 OPENING ~ 單元名稱00:00:15 前次課程內容複習00:02:59 Eigenvalue Problem00:17:51 Reflection Matrix00:27:16 Special Cases00:50:14 Matrix Diagonalization01:11:39 Symmetric Matrix01:39:00 Applications of Matrix Diagonalization02:26:17 ENDING---------------

07. Eigenvalues and Eigenvectors, Applications of Diagonalization

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/8---------------00:00:00 OPENING ~ 單元名稱00:00:15 Real versus Complex Spaces00:14:02 Complex Vectors & Matrices00:19:11 Hermitian Matrices00:21:07 Properties of S01:03:32 Finding a Good Basis01:13:57 Expectation Value01:18:04 Trace Invariant01:21:01 Linear Transformation & Matrix01:45:03 Matrix Representation of T02:10:26 Function Space02:22:58 課程內容更正02:24:02 ENDING---------------

08. Complex Vectors and Matrices, Hilbert Space, Linear Transformations

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/9---------------00:00:00 OPENING ~ 單元名稱00:00:15 前次課程內容複習00:04:44 Fourier Series and Transforms00:11:23 Even & Odd Functions00:16:58 Fourier Series00:47:40 Dirichlet Condition01:09:45 Parseval's Theorem01:18:03 Fourier Transform01:30:43 Properties of F.T.01:48:18 Dirac Delta Function02:20:13 ENDING---------------

09. Fourier Series and Transforms

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/10---------------00:00:00 OPENING ~ 單元名稱00:00:15 本次課程內容介紹00:03:20 Partial Differentials00:22:33 Useful Identities00:56:11 Application01:33:18 Inverse Transform01:34:50 Integration01:58:21 Boltzmann Distribution02:25:10 ENDING---------------

10. Partial Differentiation, Maximum and Minimum Problems

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/11---------------00:00:00 OPENING ~ 單元名稱00:00:15 Classifications of Differential Equations00:27:31 Partial Differential Equation00:49:08 Ordinary Differential Equation00:49:46 Separable Equation01:02:01 Linear First-order Equation01:25:19 Non-linear, First-order: Bernoulli Equation01:55:05 Second-order Linear Equation with Constant Coefficients02:24:37 ENDING---------------

11. Ordinary Differential Equations

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/12---------------00:00:00 OPENING ~ 單元名稱00:00:15 本次課程內容介紹00:00:59 前次課程內容複習00:02:26 Numerical Solutions of Differential Equations00:55:53 Group, Symmetry Groups01:51:13 Properties of a Point Group02:36:47 版權聲明 ~ ENDING---------------

12. Numerical ODE Solutions for Dummies, Group, Symmetry Groups

臺大開放式課程課程名稱：化學數學授課教師：化學系 鄭原忠單元連結：http://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/112S101/13---------------00:00:00 OPENING ~ 單元名稱00:00:15 前次課程內容複習00:01:41 本次課程內容介紹00:02:34 Matrix Representations of Symmetry Operators00:49:27 Orthogonality Relationship01:22:42 Applications of Point Groups01:57:09 ENDING---------------

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