Week 1

1.2 Direction Fields

1.3 Separable ODEs

1.4 Exact ODEs

Week 9

6.1 Laplace Transform. Inverse Transform.Linearity.

6.2 Transroms of Derivatives and Integrals.

6.3 Unit Step Function.

Week 2

1.6 Orthogonal Trajectories

1.7 Existence and Uniqueness Theorems

Week 10

6.4 Short Impulses. Dirac's Delta Function. Partial Fractions

6.5 Convolution. Integral Equations

6.6 Differentiation and Intefration of Transforms

Week 3

2.1 Homogeneous Linear ODEs of Second Order

2.2 Homogeneous Linear ODEs with Constant Coefficients

Week 11

6.7 Systems of ODEs

6.8 Laplace Transform: General Formulas

6.9 Table of Laplace Transforms

Week 4

2.3 Differential Operators

2.4 Modeling: Free Oscillations

2.5 Euler-Cauchy Equations

Week 12

9.1 Vectors in 2-Space and 3-Space

9.2 Inner Product

9.3 Vector Product

9.4 Vector and Scalar Functions and Fields

Week 5

2.6 Existence and Uniqueness of Solutions

2.7 Nonhomogeneous ODEs

2.8 Modeling: Forced Oscillations

Week 13

9.5 Curves. Arc Length. Curvature. Torsion

9.7 Gradient of a Scalar Field

9.8 Divergence of a Vector Field

9.9 Curl of a Vector Field

Week 6

2.9 Modeling: Electric Circuits

2.10 Solution by Variation of Parameters

Week 14

10.1 Line Integrals

10.2 Path Independence of Line Integrals

10.4 Green's Theorem in the Plane

10.5 Surfaces for Surface Intefrals

Week 7

3.1 Homogeneous Linear ODEs

3.2 Homogeneous Linear ODEs with Constant Coefficients

3.3 Nonhomogeneous Linear ODEs

Week 15

10.6 Surface Integrals

10.7 Triple Integrals . Divergence Theorem of Gauss

10.8 Further Alpplications of the Divergence Theorem

10.9 Stokes's Theorem

Week 8

Week 16

  + Final Exam