Schedule: MWF 9:55 – 10:45 AM. Van Vleck B 102
Syllabus: Can be found here
Textbook: Edwards and Penney, Differential Equations and Linear Algebra, third ed., Prentice Hall
Teaching assistants webpages for this course:
Sections 301, 302: Hesamaddin Dashti
Sections 303-306: Erkao Bao
Homework assignments:
Hw 1 Due Wednesday, February 1st. Solutions
Hw 2 Due Wednesday, February 8th. Solutions
Hw 3 Due Friday, February 17. Solutions
Hw4 Due Wednesday February 22. Solutions
Hw5 Due Friday March 2. Solutions
Hw6 Due Friday March 9. Solutions
Hw7 Due Friday March 16. Solutions
Hw8 Due Wednesday, March 21. Solutions
Hw9 Due Monday, March 26 Solutions
Hw10 Due Friday, April 13 Solutions
Hw11 Due Friday, April 20 Solutions
Hw12 Due Friday, April 27 Solutions
Hw13 Due Friday, May 4 Solutions
Hw 14 Optional
Practice Exam You can now find the solution HERE
Practice Exam 2 You can now find the solution HERE
Practice Exam 3 You can now find the solution HERE
Brief lecture outline:
Lecture 1: January 23
Section 1.1 Differential equations and mathematical models
Newton's law of cooling
Population growth
Lecture 2: January 25
Section 1.2: Integrals as general and particular solutions
Second order Equations
Velocity and acceleration
Lecture 3: January 27
Section 1.3 Slope fields and solution curves
Graphical method
Existence and uniqueness of solutions
Lecture 4: January 30
Section 1.4 Separable equations and applications
Implicit, general and singular solutions
Cooling and heating
Lecture 5: February 1
Section 1.5 Linear first order equations
Integrating factors
Mixture problems
Lecture 6: February 3
Section 1.6 Substitution methods and exact solutions
Homogeneous equations
Lecture 7: February 6
Bernoulli equations
Exact differential equations
Reducible second-order equations
Lecture 8: February 8
Chapter 2: Mathematical Models and Numerical Analysis
Section 2.1 Population models
Bounded populations and the logistic equation
Section 2.2 Equilibrium solutions and stability, autonomous equations
Lecture 9: February 10
Logistic population with harvesting
Bifurcation and dependance on parameters
Section 2.4 Numerical approximation: Euler's method
Lecture 10: February 13
Local and cumulative errors
Section 2.5: A closer look at Euler's method
Improved Euler's method
Lecture 11: February 15
Chapter 3: Linear systems and matrices
Section 3.1: Introduction to linear systems
Two equations in two unknowns
The method of elimination
Three equations in three unknowns
Lecture 12: February 17
Section 3.2: Matrices and Gaussian elimination
Elementary row operations. Row equivalent matrices
Gaussian elimination method
Lecture 13: February 20
Echelon matrices
Leading and free variables
Section 3.3: Reduced row-echelon matrices
Lecture 14: February 22
Gauss-Jordan elimination
Lecture 15: February 24: Exam 1
Lecture 16: February 27
Homogeneous linear systems
Section 3.4: Matrix operations
Multiplication of matrices
Lecture 17: February 29
Multiplication of matrices. Matrix algebra
Section 3.5: Inverse of matrices.
Lecture 18: March 2
Algorithm for finding A^{-1}
Section 3.6 Determinants
2x2 and nxn determinants
Lecture 19: March 5
Row and column properties for determinants
Cramer's rule for nxn systems
Lecture 20: March 7
Chapter 4: Vector spaces
Addition and multiplication by scalars
Collinear vectors. Linear dependance
Linear independence in R^3
Lecture 21: March 9
Basis vectors in R^3
Subspaces of R^3
Lecture 22: March 12
Section 4.2: The vector space R^n and subspaces
Addition and multiplication by scalars. Properties of vector spaces.
The vector space of real valued functions
Lecture 23: March 14
Subspaces
Section 4.3: Linear combinations and independence of vectors
Linear span
Linear independence.
Lecture 24: March 16
Section 4.4 Bases and dimension for vector spaces
Basis
Finite dimensional spaces
Lecture 25: March 19:
Bases for solution spaces
Algorithm for find a basis by elementary row operations
Lecture 26: March 21
Section 4.5: Row and column space
Row and column rank
Extracting or completing bases
Lecture 27: March 23
Chapter 5: Higher order linear differential equations
Section 5.1 Intro: 2nd order linear equations
Homogeneous equations
A typical application
Linear combinations: General solutions
Lecture 28: March 26
Wronskians and linear independence
Linear 2nd order equations with constant coefficients
Case: Distinct roots
Case: Repeated roots
Section 5.2: General solutions of linear equations
Lecture 29: March 28
Midterm 2
Lecture 30: March 30
Non-homogeneous equations
Particular and complementary solutions
Section 5.3: Homogeneous equations with constant coefficients
The characteristic equation
Lecture 31: April 09
1. Case: Distinct roots
2. Case: Repeated roots
Lecture 32: April 11
1. Case: Complex roots
2. Case: Repeated complex roots
Lecture 33: April 13
1. Section 5.4: Mechanical vibrations
2. Application: The simple pendulum
3. Free undamped motion
Lecture 34-36: April 16,18,20 (Covered by Uri Andrews) Sections 5.5, Section 5.6 (pages 353-357) and started 7.1
Lecture 37: April 23
Chapter 7: Linear systems of differential equations
Section 7.1: First order systems and applications
Simple two dimensional systems
Lecture 38: April 25
Section 7.2: Matrices and linear systems
Homogeneous equations
Lecture 39: April 27
Homogeneous equations
Wronskians and linear independence
General solutions
Non-homogeneous solutions and the superposition principle
Lecture 40: April 30
Section 7.3: The eigenvalue method for linear systems
Eigenvalues and eigenvectors
The characteristic polynomial
Lecture 41: May 2
Eigenvalues, eigenvectors and linearly independent solutions
The eigenvalue method
Distinct real eigenvalues
Complex eigenvalues (compartmental analysis has been excluded, as well as applications)
Lecture 42: May 4
Section 7.5 Multiple eigenvalue solutions (section 7.4 has been excluded)
Repeated eigenvalues, multiplicity
Complete eigenvalues (defective eigenvalues have been excluded)
Lecture 43: May 7
Chapter 8: Matrix exponential methods
Section 8.1: Matrix exponentials and linear systems
Fundamental matrices
Solving initial value problems with the fundamental matrix
Lecture 44: May 9
Matrix exponential solutions
Initial value problems and the exponential solution
How to compute the exponential of a matrix: for nilpotent matrices, using the fundamental matrix and by diagonalizing the matrix.
Lecture 45: May 11
Examples: Computation of exponential matrices
Review session
Discussion sessions:
Section |
Time |
Room Number |
Teaching Assistant |
|
301 |
T 8:50-9:40AM |
B119 Van Vleck Hall |
Hesamaddin Dashti |
dashti at math dot wisc dot edu |
302 |
R 8:50-9:40AM |
B119 Van Vleck Hall |
Hesamaddin Dashti |
dashti at math dot wisc dot edu |
303 |
T 11:00-11:50AM |
115 Ingraham Hall |
Erkao Bao |
bao at math dot wisc dot edu |
304 |
R 11:00-11:50AM |
115 Ingraham Hall |
Erkao Bao |
bao at math dot wisc dot edu |
305 |
T 9:55-10:45AM |
B329 Van Vleck Hall |
Erkao Bao |
bao at math dot wisc dot edu |
306 |
R 9:55-10:45AM |
B329 Van Vleck Hall |
Erkao Bao |
bao at math dot wisc dot edu |
Other important information:
Exam 1: February 24 Time: 9:55 - 10:45 AM. Room: Van Vleck B 102 20% of the Final Grade
Exam 2: March 28 Time: 9:55 - 10:45 AM. Room: Van Vleck B 102 25% of the Final Grade
Exam 3: May 13 Time: 7:45 – 9:45 AM. Room: Van Vleck B 102 30% of the Final Grade
*See the syllabus for more information on exam policies.
The TAs will grade a subset of the homework problems given out each week (with some points also given for completeness). The homework scores will count for 15% of the grade. The lowest homework score will be dropped.
There will be an estimate of 6 quizzes, to be scheduled during section meetings on dates to be determined by the TA. Quizzes will be graded and will count for 5% of the overall grade. The lowest quiz score will be dropped. There will be no make-up quizzes.
Class participation: 5 % of the final grade
Grading:
Exam 1: 20 %
Exam 2: 25 %
Exam 3: 30 %
Homework: 15%
Quizzes: 5%
Class participation: 5%
Note: Any student with a documented disability should contact me as soon as possible so that we can discuss arrangements to fit your needs.