**Complex Numbers, Cartesian and Polar Representation**

Page 8 Number 1, 3-
**Complex Exponentials**

Represent a function of the form as the real part of a complex exponential . Interpretation of the absolute value and phase angle of the complex amplitude*A*as real amplitude and phase shift. -
**Powers and Roots of Complex Numbers**

Page 8 Number 5 -
**Solving Linear Systems by Row Reduction (Gaussian Elimination)**

Page 22 Number 6-13 -
**Matrix Algebra**

Page 30 Number 1, 4 -
**Matrix Inversion**

Page 40 Number 1-15 -
**Determinants by Row Reduction and Cofactor Expansion**

Page 45 Number 3-10; Page 47 Number 4 -
**Linear Independence, Bases, and Homogeneous Systems**

Page 53 Number 1

Problems on homogeous systems in the supplementary notes. -
**First Order Differential Equations by Euler's Method**

Page 398 Numbers 1-6 (We won't ask for computer code on the exam, but you should be able to come up with the recursion formula, and run through a couple of iterations with a calculator.) -
**Symbolic Solutions of First Order Linear and Separable Equations**

Page 75 Number 1, 2; Page 97 Number 1 -
**Modeling using Differential Equations: Mixture, Motion, Cooling, Circuits**

Page 79 Number 1; Page 81 Number 5; Page 85 Number 2; Page 89 Number 2