MATH
21 B
Mathematics Math21b Spring 2016
Linear Algebra and Differential Equations
Syllabus
Course Head: Oliver Knill
Office: SciCtr 432


Syllabus Broshure [PDF] ,


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:
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 309a (subject to change). For details, see the MQC page.
Website: http://www.courses.fas.harvard.edu/~math21b bookmark this!
https://canvas.harvard.edu/courses/1803 canvas
Text: We recommend 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.
  • 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 quantum mechanics, 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. Homework is online and no book is required. TTh sections submit two homework sets 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: (they need still be confirmed)
1. Midterm:Tuesday,March 1 7-8:30pmHall B 2. Midterm:Tuesday,April 5 7-8:30pmHall B Final exam:May, 2016 TBA Hall 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
 --------------------------------------------------------
 24 25 26 27 28 29 30    0  Jan 25: 8:30AM SC B, 28/29 Lecture
 31  1  2  3  4  5  6    1  
  7  8  9 10 11 12 13    2
 14 15 16 17 18 19 20    3  Mon Feb 15 Presidents day
 21 22 23 24 25 26 27    4                              
 28 29  1  2  3  4  5    5  First midterm March 1 (planned)
  6  7  8  9 10 11 12    6
 13 14 15 16 17 18 19       Spring break Mar 13-20
 20 21 22 23 24 25 26    7
 27 28 29 30 31  1  2    8  
  3  4  5  6  7  8  9    9  Second midterm April 5 (planned)
 10 11 12 13 14 15 16   10
 17 18 19 20 21 22 23   11
 24 25 26 27 28 29 30   12  April 27: last day of classes
  1  2  3  4  5  6  7       Until May 4: reading period
  8  9 10 11 12 13 14       May 5-14 exam period
 ---------------------------------------------------------
 
Day to day syllabus:
   Lecture Date   Book Topic
 
 Week 0: Systems of linear equations   Jan 28/29 
     
    Lect 1  F  1.1   introduction to linear systems  
 
 Week 1: Systems of linear equations   Feb 1-5
 
    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
 
 Week 2: Matrix Algebra                Feb 8-12
 
    Lect    M  2.2   linear transformations in geometry
    Lect 5  W  2.3   matrix product                     
    Lect 6  F  3.1   image and kernel
 
 Week 3: Basis, dimension              Feb 15-19
 
    Lect    M  Presidents day   (no classes) 
    Lect  7 W  3.2   basis           
    Lect  8 F  3.3   dimension
 
 Week 4: Coordinates, Projections      Feb 22-26
 
    Lect  9 M  3.4   coordinates   
    Lect 10 W  4.1   linear spaces 
    Lect 11 F  5.1   orthonormal basis and projection
 
 Week 5: Orthogonality                 Feb 29-Mar 4
 
    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  Mar 7- Mar 11
 
    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                          Mar 14- Mar 18 
 
 Week 7: Eigenvalues Eigenvectors      Mar 21- Mar 25
 
    Lect 18    7.1-2 eigenvalues and eigenvectors
    Lect 19    7.3   eigenspaces
    Lect 20    7.4   diagonalization
 
 Week 8: Complex eigenvalues and Stabilitya  Mar 28- Apr 1
 
    Lect 21    7.5  complex eigenvalues
    Lect 22    7.6  stability          
    Lect 23    8.1  symmetric matrices
 
 Week 9: Differential equations           Mar  4 - Apr 8
 
    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  Apr 11 - Apr 15 
 
    Lect 27    9.4  nonlinear systems
    Lect 28    4.2  differential operators
    Lect 29    9.3  inhomogeneous differential equations
 
 Week 11:  Fourier series                  Apr 18 - Apr 22
 
    Lect 30   HH    Fourier series I
    Lect 31   HH    Fourier series II Parseval
    Lect 32   HH    PDE I
 
 Week 12: Partial differential equations   Apr 25 - Apr 27
 
    Lect 33   HH    PDE II
    Lect 34   HH    Overview                              
 
 
 
Please send questions and comments to knill@math.harvard.edu
Math21b Harvard College Class Number:16325 Course ID:110989| Oliver Knill | Spring 2016 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas, for admin], Twitter