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)
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