MATH 53 -- Ordinary Differential Equations and Linear Algebra

Course syllabus

Course text

The text for the course will be Brannan and Boyce, Differential Equations: An Introduction to Modern Methods and Applications. Please note that I have placed three copies on reserve, in the Math / CS library, on the fourth floor of Bldg. 380. You can check a copy out for up to one day at a time. I also played Boyce & Diprima's book on reserve, which is a standard introductary text on differential equations. It is also available for one day checkout.

Lectures

June 23: Direction fields (Section 1.1)
June 24: Solving (some) differential equations (Section 1.2)
June 25: Numerical approximation, Euler method (Section 1.3)
June 26: First order differential equations (Section 2.1)
June 29: Separable equations (Section 2.2)
June 30: Modeling with first order equations (Section 2.3)
July 1: Linear versus non-linear equations (Section 2.4)
July 2: Autonomous equations and population dynamics (Section 2.5)
July 6: Exact equations (Section 2.6)
July 7: Linear algebra review (Section 3.1)
July 8: Systems of differential equations (Section 3.2)
July 9: Homogeneous linear systems with constant coefficeints (Section 3.3)
July 10: Complex eigenvalues (Section 3.4)
July 11: Repeated eigenvalues (Section 3.5)
July 13: Introduction to nonlinear systems (Section 3.6)
July 14: Introduction to second-order equations (Section 4.1)
July 15: More on second-order equations (Section 4.2)
July 16: Linear homogeneous equations with constant coefficients (Section 4.3)
July 17: Review for midterm
July 20: Midterm
July 21: Reduction of order (Section 4.3)
July 22: Review of complex variables, complex roots (Section 4.4)
July 23: Definition of Laplace transform (Section 5.1)
July 24: Laplace transform of a derivative (Section 5.2)
July 27: Inverse Laplace transforms (Section 5.3)
July 28: Solving differential equations with Laplace transforms (Section 5.4)
July 29: Heaviside functions and discontinuous functions (Section 5.5)
July 30: Laplace transforms of discontinuous and periodic functions (Section 5.5)
July 31: Differential equations with discontinuous or periodic forcing functions (Section 5.6)
August 3: Impulses: the Dirac delta function (Section 5.7)
August 4: Introduction to systems of first order equations (Section 6.1 and 6.2)
August 5: Linearity and linear independence of solutions to homogeneous systems (Section 6.2)
August 6: Review of diagonalizable versus defective matrices, homogeneous systems with constant coefficients (Section 6.3)
August 7: Complex eigenvalues (Section 6.4)

Office hours

My office hours (in 382-X) will be Monday, Tuesday, Thursday, 3:05-4:05. Our course assistant, Kaveh Fouladgar, will hold office hours (in 380-H) on Thursday and Friday, 9-10:30.

Exams

The midterm will be held in class, 2:15-3:05, on Monday, July 20. This exam will be based on the lectures and the homework, and will cover everything we talk about through Section 3.6. The final will be held on Saturday, August 15, 12:15-3:15.

Homework

Some online direction field plotters can be found here, and here.

Homework 1: due Friday 6/26 by 5pm
Section 1.1: # 1, 5, 7, 9, 11, 13, 21*
Section 1.2: # 1, 3*, 5, 6, 16, 21
Section 1.3: # 1(a)(b)*, 5, 6, 7, 8

Homework 2: due Monday 7/6 by 5pm
Section 2.1: # 1, 2, 3, 15*, 16
Section 2.2: # 3, 4, 13, 19*, 21, 24
Section 2.3: # 1, 2*, 9, 13
Section 2.4: # 1, 2, 3, 4, 22

Homework 3: due Friday 7/10 by 5pm
Section 2.5: # 1, 2, 3, 7, 20*
Section 2.6: # 1, 2, 3, 4, 15
Section 3.1: # 13, 14, 15, 33, 34*
Section 3.2: # 9, 10, 15, 16, 19*

Homework 4: due Friday 7/17 by 5pm
Section 3.3: # 1, 2, 6, 17(a)(b), 20(a)(b)*
Section 3.4: # 2, 3, 5, 13*
Section 3.5: # 1, 4, 6, 7, 14*
Section 3.6: # 1, 2, 7, 8, 16, 19

Homework 5: due Friday 7/24 by 5pm
Section 4.1: # 1, 2, 3, 4, 5
Section 4.2: # 10, 11, 12, 16, 17*
Section 4.3: # 1(a), 2(a), 9(a), 37, 42*, 45
Section 4.4: # 11(a), 12(a), 21, 22*, 34

Homework 6: Due Friday 7/31 by 5pm
Section 5.1: # 14, 15, 16*, 17, 31, 32
Section 5.2: # 1, 2, 3, 4, 12, 13, 23
Section 5.3: # 1, 2, 3, 4, 9, 20*
Section 5.4: # 1, 2, 5, 10*, 13

Homework 7: Due Friday, 8/7 by 5pm
Section 5.5: # 1, 2, 7, 9, 15, 16
Section 5.6: # 1, 3, 7, 11, 19*
Section 5.7: # 1, 2, 3, 12, 15(a)(c)*
Section 5.8: # 4, 5, 8, 9, 11*

Homework 8: Due Saturday, 8/15 by 3:15pm
Section 6.3: # 1, 2, 3, 5, 9, 10 (no plotting necessary on 9, 10)
Section 6.4: # 1, 2, 3, 5, 7
Section 6.5: # 1, 3, 4, 5, 6, 15, 17