MATH
21 B
Mathematics Math21b Spring 2015
Linear Algebra and Differential Equations
Syllabus
Course Head: Oliver Knill
Office: SciCtr 432




Math21b: Linear Algebra and Differential Equations This course is an introduction to linear algebra, including linear transformations, determinants, eigenvectors, eigenvalues, inner products and linear spaces. As for applications, the course introduces discrete dynamical systems, differential equations, Fourier series as well as some partial differential equations. Other highlights are applications in statistics like Markov chains or data fitting with arbitrary functions.
Instructors:
  • Oliver Knill
Course assistants: Head CA:
Lecture times:
  • Mo-We-Fr 9-10
  • Mo-We-Fr 10-11
  • Mo-We-Fr 11-12
  • Mo-We-Fr 12-1
  • Tue-Th 10-11:30
  • Tue-Th 11:30-1
MQC: This spring the MQC for Math 21b is in room 309. For details, see the MQC page.
Website: http://www.courses.fas.harvard.edu/~math21b bookmark this!
https://canvas.harvard.edu/courses/1803 canvas
http://isites.harvard.edu/icb/icb.do?keyword=k109254 Isites
Text: We use Otto Bretscher, Linear Algebra with Applications. The fourth or 5th edition both should work as we post HW independent of editions.
About this course:
  • teaches methods to solve systems of linear equations Ax = b,
  • allows you to analyze and solve systems of linear differential equations,
  • you learn to solve discrete linear dynamical systems like discrete Markov processes.
  • you will master the technique of least square fit with arbitrary function sets and know why it works,
  • you will learn the basics of Fourier series and how to use it to solve linear partial differential equations,
  • prepares you for the further study in other scientific fields like for example quantum mechanics or combinatorics or statistics
  • it improves thinking skills, problem solving skills, algorithmic and the ability to use more abstract tools.
Homework: HW will be assigned in each class and is due the next class. TTh sections submit two homework on Tuesday's except for the first week.
Exams: We have two midterm exams and one final exam. We plan to have the following midterm exam dates:
1. Midterm: 7-8:30pmHall B 2. Midterm: 7-8:30pmHall B
Grades:
                                          Grade1  Grade2 
 First hourly                              20     20   
 Second hourly                             20     20
 Homework                                  20     20
 Lab                                        5
 Final exam                                35     40      
 -------------------------------------------------------------
 Total                                    100    100
 
 
Calendar: (Registrar)
 --------------------------------------------------------
 So Mo Tu We Th Fr Sa week  Events
 --------------------------------------------------------
 25 26 27 28 29 30 31       Jan 26: 8:30AM SC B, 29/30 start
  1  2  3  4  5  6  7    1
  8  9 10 11 12 13 14    2
 15 16 17 18 19 20 21    3  Feb 16 Presidents day
 22 23 24 25 26 27 28    4
  1  2  3  4  5  6  7    5  First midterm March 3
  8  9 10 11 12 13 14    6
 15 16 17 18 19 20 21       Spring break Mar 14-22
 22 23 24 25 26 27 28    7
 29 30 31  1  2  3  4    8  
  5  6  7  8  9 10 11    9  Second midterm April 7
 12 13 14 15 16 17 18   10
 19 20 21 22 23 24 25   11
 26 27 28 29 30  1  2   12  April 29 last day of classes
  3  4  5  6  7  8  9       Until May 6: reading period
 10 11 12 13 14 15 16       May 7-16 exam period
 ---------------------------------------------------------
 
Day to day syllabus: (updated on February 8 as Feb 9 is a snow day)
    Lecture Date   Book Topic
 
 Week 0: Systems of linear equations
 
    Lect 1  F  1.1   introduction to linear systems  
 
 Week 1: Systems of linear equations
 
    Lect 2  M  1.2   matrices and Gauss-Jordan elimination
    Lect 3  W  1.3   on solutions of linear systems
    Lect 4  F  2.1   linear transformations and inverses
 
 Week 2: Matrix Algebra
 
    Lect    M  Snow day   (classes cancelled)
    Lect 5  w  2.2   linear transformations in geometry 
    Lect 6  F  2.3/4 matrix product and inverse
 
 Week 3: Basis, dimension
 
    Lect    M  Presidents day   (no classes) 
    Lect  7 W  3.1   image and kernel
    Lect  8 F  3.2   basis and linear independence
 
 Week 4: Coordinates, Projections
 
    Lect  9 M  3.3   dimension   
    Lect 10 W  3.4   coordinates   
    Lect 11 F  5.1   orthonormal bases and orthogonal projections
 
 Week 5: Orthogonality
 
    Lect 12 M        review for the first midterm        
    Lect 13 W  5.2   Gram-Schmidt and QR factorization 
    Lect 14 F  5.3   orthogonal transformations
 
 Week 6: Datafitting and Determinants
 
    Lect 15 M  5.4   least squares and data fitting
    Lect 16 W  6.1   determinants 1
    Lect 17 F  6.2/3 determinants 2
 
 Spring Break 
 
 Week 7: Eigenvalues Eigenvectors
 
    Lect 18    7.1-2 eigenvalues and eigenvectors
    Lect 19    7.3   eigenspaces
    Lect 20    7.4   diagonalization
 
 Week 8: Complex eigenvalues and Stability 
 
    Lect 21    7.5  complex eigenvalues
    Lect 22    7.6  stability          
    Lect 23    8.1  symmetric matrices
 
 Week 9: Differential equations
 
    Lect 24         review for second midterm
    Lect 25    9.1  differential equations I
    Lect 26    9.2  differential equations II
 
 Week 10: Function spaces and nonlinear systems
 
    Lect 27    9.4  nonlinear systems
    Lect 28    4.2  linear trafos on function spaces
    Lect 29    9.3  inhomogeneous differential equations
 
 Week 11:  Fourier series
 
    Lect 30   HH    Fourier series I
    Lect 31   HH    Fourier series II Parseval
    Lect 32   HH    PDE I
 
 Week 12: Partial differential equations 
 
    Lect 33   HH    PDE II
    Lect 34   HH    Overview                              
 
 
 
Please send questions and comments to knill@math.harvard.edu
Math21b Harvard College/GSAS: 1771, Exam group 3| Oliver Knill | Spring 2015 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas], [ISites]. Bookmark http://sites.fas.harvard.edu/~math21b/| Twitter