Week 1

Introduction. Integration. Existence and uniqueness. Sections: 1.1 - 1.3

Homework

1.1: 7, 12, 15, 22, 30, 39
1.2: 4, 6, 9, 10, 16, 25
1.3: 12, 15, 16, 25, 30, 31

Separable and linear equations. Applications. Sections: 1.4 - 1.5, 1.7

Homework

1.4: 4, 14, 17, 18, 22, 58
1.5: 17, 22, 25, 32, 37, 39
1.7: 2, 3, 9, 10, 14, 25

Numerical methods. Sections: 6.1 - 6.3

Homework

6.1: 5, 6, 11, 12
6.2: 5, 6, 11, 12
6.3: 5, 6, 11, 12 + computational project

Linear equations. Homogeneous constant coefficient equations. Sections: 2.1 - 2.3

Homework

2.1: 10, 11, 23, 25, 36, 41
2.2: 10, 13, 21, 24
2.3: 6, 9, 11, 21, 24, 28, 39, 40

Undetermined coefficients and variation of parameters. Forced oscillations, resonance, and circuits. Sections: 2.5-2.6/2.7, 2.8

Homework

2.5: 4, 6, 29, 49, 53, 56
2.6: 5, 6, 15
2.7: 1, 2, 3

Laplace transform methods. Sections: 4.1 - 4.2

Homework

4.1: 2, 9, 20, 23, 28, 29, 33, 36
4.2: 4, 8, 10, 14, 16, 22

Laplace transform methods. Sections: 4.3 - 4.4

Homework

4.3: 3, 10, 18, 19, 30, 31, 40
4.4: 6, 7, 8, 12, 18, 23, 33

Series solutions. Sections: 3.1 - 3.2

Homework

3.1: 5, 9, 14, 20, 22
3.2: 5, 9, 14, 23, 24, 27

Introduction to linear systems. Sections: 5.1, 5.2

Homework

5.1: 2, 6, 13, 22, 26, 27
5.2: 7, 8, 19, 31, 33

Matrices and linear systems. The Eigenvalue Method for Homogeneous Systems. Sections: 5.3-5.4

Homework

5.3: 17, 25, 29, 37
5.4: 4, 6, 12, 17, 23

Matrix Exponentials. Numerical methods for systems Sections: 5.7, 6.4

Homework

5.7: 3, 6, 9
6.4: 4, 5

Nonhomogeneous linear systems. Fourier series. Sections: 5.8, 8.1

Homework

5.8: 3, 5, 17, 19
8.1: 9, 11, 14, 16, 17 + computational project

Fourier series. Sections: 8.2, 8.3

Homework

8.2: 1, 9, 15, 16, 17
8.3: 2, 11, 14

Week 14

Separation of variables for PDEs. Review. Sections: 8.5

Homework

8.5: 3, 11, 20