What's New on this Course ?
This course helps students to master the material of a undergraduate-level linear algebra and vector calculus. The lecture will coverer Gaussian reduction, vector spaces, linear maps, determinants, eigenvalues and eigenvectors, and vector calculus. The audience must have a background of at least one semester of Calculus.
Course History:
(1) January 20, 2007-June 20, 2007
(2) January 20, 2008-June 20, 2008
Lecture notes have been posted whenever possible.
Grading：4 homeworks (60%) and final examination (40%). Students must fluently grasp the use of any of the following mathematical packages: Mathematica, or Maple, or Matlab.
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Chapter One: Linear Systems ( Lecture Note:  - 599 kB)
I Solving Linear Systems : 1. Gauss’ Method
2. Describing the Solution Set
3. General = Particular + Homogeneous
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II Linear Geometry of n-Space: 1. Vectors in Space; 2. Length and Angle Measures
III Reduced Echelon Form: 1. Gauss-Jordan Reduction; 2. Row Equivalence
( Homework Set 1---27 kB, Due: March 21, 2008)
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Chapter Two: Matrices and Determinants (Lecture Note: ppt - 1277 kB)
I. Definition, and Operations of Matrices
1. Sums and Scalar Products; 2. Matrix Multiplication; 3. Mechanics of Matrix Multiplication; 4. Inverses
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II Definition of a Determinant: 1. Exploration; 2. Properties of Determinants;
III Geometry of Determinants: Determinants as Size Functions
(Lecture Note: ppt - 1136 kB)
( Homework Set 2 --- 34kB, Due: May 9, 2008 )
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Chapter Three: Vector Spaces (Lecture Note: PPT - 1277kB)
I Vector Spaces and Subspaces
II Spanning Sets and Linear Independence
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III Basis and Dimension
IV Rank of a Matrix
V Change of Basis: Changing Representations of Vectors
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VI Inner Product Space: Inner Product, Length, Distance and Angles (Lecture Note: PPT - 1657 kB)
VII Orthonormal Basis: Gram-Schmidt Process
VIII Mathematical Models and Least Squares Analysis
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Chapter Four: Linear Transformations (Lecture Note: PPT - 3752 kB)
I Introduction to Linear Transformation
II The Kernel and Range of a Linear Transformation
III Matrices of Linear Transformations
IV. Transition Matrices and Similarity
( Homework Set 3 --- 36 kB, Due: May 28, 2008)
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Chapter Five: Eigenvalues and Eigenvectors (Lecture Note: PPT - 679 kB)
I Eigenvalues and Eigenvectors
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II Diagonolization
III Symmetric Matrices and Orthogonal Diagonalization
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Chapter Six: Singular Value Decomposition (SVD) (Lecture Note: doc - 4806 kB)
I Usage of SVD;
II Basic Idea of SVD;
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III An Example of SVD
IV Some Applications of SVD
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Chapter Seven: Vector Calculus (Lecture Note: PPT - 972 kB)
I Fluid Flow: 1.Geneal FLow and Curved Surfaces
II Vector Derivatives: Div, Curl, and Strain
III Computing the Divergence and the Curl of a Vector Field (Mathematica Notebook: vf_div_curl.nb - 607 kB)
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IV Gradient
V Integrals: Line Integral and Surface Integral (Line Integral: nb - 647 kB) (Surface Integral : nb - 976 kB)
VI Gauss's Theorem and Stokes' Theorem (Divergence Thm: nb - 398 kB) (Stokes Thm : nb - 90 kB)
VII Application Examples of Vector Calculus
( Homework Set 4 ---Due: June 20, 2008)
( Final Examination --- 2007)
( Final Examination --- June 20, 2008)
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