MATH
21 B
Mathematics Math21b Spring 2018
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.
Course head:
  • 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 takes place in room 309. For details, see the MQC page.
Website: http://www.courses.fas.harvard.edu/~math21b bookmark this!
canvas
Text: We recommend Otto Bretscher, Linear Algebra with Applications but it is not required. Any edition work as we post homework 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:TBA 7-8:30pmHall 2. Midterm:TBA 7-8:30pmHall Final exam:May, 2018 TBA Hall
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
 --------------------------------------------------------
 21 22 23 24 25 26 27    0  Jan 22: 8:30AM SC B, Jan 25/26 lectures start
 28 29 30 31  1  2  3    1  
  4  5  6  7  8  9 10    2
 11 12 13 14 15 16 17    3  
 18 19 20 21 22 23 24    4  Mon Feb 19 Presidents day   
 25 26 27 28  1  2  3    5  First midterm:   Feb 27
  4  5  6  7  8  9 10    6
 11 12 13 14 15 16 17       Spring recess Mar 10-18
 18 19 20 21 22 23 24    7
 25 26 27 28 29 30 31    8  
  1  2  3  4  5  6  7    9  Second midterm: April 3
  8  9 10 11 12 13 14   10
 15 16 17 18 19 20 21   11
 22 23 24 25 26 27 28   12  April 25 Wed, last class day
 29 30  1  2  3  4  5       Apr 26 May 2: reading period
  6  7  8  9 10 11 12       May 3-12 exam period
 ---------------------------------------------------------
 
Day to day syllabus:
   Lecture Date   Book Topic
 
 Week 0: Systems of linear equations   Jan 25/26 
     
    Lect 1  F  1.1   introduction to linear systems  
 
 Week 1: Systems of linear equations   Jan 29-Feb 2
 
    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 5 -  9
 
    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 12 - 16
 
    Lect    M  Presidents day   (no classes) 
    Lect  7 W  3.2   basis           
    Lect  8 F  3.3   dimension
 
 Week 4: Coordinates, Projections      Feb 19 - 23
 
    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 26-Feb 30 
 
    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 5- Mar  9
 
    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 12- Mar 16 
 
 Week 7: Eigenvalues Eigenvectors      Mar 19- Mar 23
 
    Lect 18    7.1-2 eigenvalues and eigenvectors
    Lect 19    7.3   eigenspaces
    Lect 20    7.4   diagonalization
 
 Week 8: Complex eigenvalues, Stability  Mar 26- Mar 30 
 
    Lect 21    7.5  complex eigenvalues
    Lect 22    7.6  stability          
    Lect 23    8.1  symmetric matrices
 
 Week 9: Differential equations         Mar  2 - Apr 6
 
    Lect 24         review for second midterm
    Lect 25    9.1  differential equations I
    Lect 26    9.2  differential equations II
 
 Week 10: Function spaces, nonlinear systems  Apr 9 - Apr 13 
 
    Lect 27    9.4  nonlinear systems
    Lect 28    4.2  operator method 
    Lect 29    9.3  cookbook for Differential equations
 
 Week 11:  Fourier series                  Apr 16 - Apr 20
 
    Lect 30   HH    Fourier series I
    Lect 31   HH    Fourier series II Parseval
    Lect 32   HH    PDE I
 
 Week 12: Partial differential equations   Apr 23 - Apr 25
 
    Lect 33   HH    PDE II
    Lect 34   HH    Overview                              
 
 
 
Please send questions and comments to knill@math.harvard.edu
Math21b Harvard College Course ID:110989| Oliver Knill | Spring 2018 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas, for admin], Twitter