MATH V2010: Linear Algebra

Fall, 1999
Tuesdays and Thursdays, 9:10am-10:25am, 312 Mathematics
Dave Bayer (x42643, 426 Mathematics)

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http://www.math.columbia.edu/~bayer/F99/linalg.html

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Grades: The following is an Acrobat PDF file (without names) giving the numerical grades (but not the final letter grades) for the course:

• Grades
  

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Prerequisites: Math V1106 Calculus 2S or Math V1201 Calculus 3A or the equivalent.

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Text: Linear Algebra with Applications Fifth Edition, by Steven J. Leon. Prentice Hall, 1998, ISBN 0-13-849308-1. University bookstore or Amazon.com. This semester we will cover chapters 1, 2, 3, 4, 5, 6.

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Exams: There will be two exams (30 points each) and a final (40 points).

• Exam 1, Thursday, October 7, in class.
  
• Exam 2, Thursday, November 11, in class.
  
• Final, Thursday, December 16, 9:00am-NOON. Master University Examination Schedule
  

These dates do not coincide with any religious holiday which causes suspension of New York City's alternate side parking regulations; see NYC Parking Calendar. Please discuss other conflicts with me well in advance of the exam in question.

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Office Hours: My office hours for the Fall '99 semester are

• Tuesday, 10:30am-11:30am
• Thursday, 2:00pm-3:00pm

and by appointment.

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Teaching Assistant: Chad Shampine is our T.A. His Help Room Schedule is Mondays and Wednesdays, 3-4pm, 406 Mathematics.

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Problem Sessions for Final:

• Chad Shampine, Tuesday, December 14, 1-3pm, 417 Math
  
• Dave Bayer, Wednesday, December 15, 7-9pm, 507 Math
  

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Course materials: Course materials are posted in Acrobat PDF format. Your browser can be trained to automatically open these files with Acrobat Reader, a free program which you can download from http://www.adobe.com/products/acrobat/readermain.html.

• linalg_F99.pdf (all course materials in a single file)
  
  
• Practice Exam 1
  
• Exam 1
  
• Practice Exam 2
  
• Exam 2
  
• Practice Problems for Final
  
  
• Final Exam
  
• Final Exam Solutions (748 Kb)
  

(TeX sources, for instructors wishing to borrow format: practice1.tex, graph.eps, midterm1.tex, graph2.eps, practice2.tex, midterm2.tex, practicefin.tex, final.tex, extrapage.tex.)

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Class Schedule and Homework Assignments:

• Tues, Sep 7:
  1.1 Systems of Linear Equations. Exercises 1-8.
  
  
• Thurs, Sep 9:
  1.2 Row Echelon Form. Exercises 1-3, 5, 6, 19.
  
  
• Tues, Sep 14:
  1.3 Matrix Algebra. Exercises 1-10, 12, 20, 30.
  
  
• Thurs, Sep 16:
  1.4 Elementary Matrices. Exercises 1-5, 7, 9, 15
  
  
• Tues, Sep 21:
  1.5 Partitioned Matrices. Exercises 4, 5, 7-10.
  
  
• Thurs, Sep 23:
  2.1 The Determinant of a Matrix. Exercises 1-4, 6, 10
  
  
• Tues, Sep 28:
  2.2 Properties of Determinants.
  
  
• Thurs, Sep 30:
  2.3 Cramer's Rule.
  
  
• Tues, Oct 5:
  exam review
  
  
• Thurs, Oct 7:
  EXAM 1 (chapters 1 and 2)
  
• Tues, Oct 12:
  3.1 Vector Spaces. Exercises 1-10.
  
  
• Thurs, Oct 14:
  3.2 Subspaces. Exercises 1-8.
  
  
• Tues, Oct 19:
  3.3 Linear Independence. Exercises 1-9.
  
  
• Thurs, Oct 21:
  3.4 Basis and Dimension. Exercises 1-8, 11
  3.5 Change of Basis. Exercises 1-5, 8-10
  
  
• Tues, Oct 26:
  3.6 Rowspace, column space. Exercises 1-7
  
  
• Thurs, Oct 28:
  4.1 Linear transformations, definitions and examples.
  4.2 Matrix representation of linear transformations.
  
  
• Tues, Nov 2:
  Election holiday; no class
  
  
• Thurs, Nov 4:
  4.3 Similarity.
  
  
• Tues, Nov 9:
  exam review.
  
  
• Thurs, Nov 11:
  EXAM 2 (chapters 3 and 4)
  
  
• Tues, Nov 16:
  5.1 The scalar product. Exercises 1-8
  5.2 Orthogonal subspaces. Exercises 1, 2
  
  
• Thurs, Nov 18:
  5.3 Inner product spaces. Exercises 1-4
  5.4 Least squares problems. Exercises 1-6
  
  
• Tues, Nov 23:
  5.5 Orthonormal sets. Exercises 1, 2, 4, 7, 8
  5.6 The Gram-Schmidt orthogonalization process. Exercises 1-4
  
  
• Thurs, Nov 25:
  Thanksgiving holiday; no class
  
  
• Tues, Nov 30:
  6.1 Eigenvalues and eigenvectors. Exercises 1-5
  6.2 Systems of linear differential equations. Exercise 1
  
  
• Thurs, Dec 2:
  6.3 Diagonalization. Exercises 1-4
  6.4 Hermitian matrices. Exercises 1, 4
  
  
• Tues, Dec 7:
  6.5 Quadratic forms. Exercises 1, 3
  6.6 Positive definite matrices. Exercises 1, 3, 4
  
  
• Thurs, Dec 9:
  exam review.
  
  
• Thurs, Dec 16: FINAL EXAM (chapters 5 and 6, some review questions)
  

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