Lecture #
 Part
 Topic Description Page # in textbook
1 Introduction

Motivating examples. Definition and classification. Solutions.

 P. 2-5
2 Initial value problems. Existence and uniqueness for 1st-order IVP.

P. 13-15

2 First-Order Differential Equations Separable DEs. P. 50-52
3 Exact DEs. P. 67-70
4 Integrating factor and exact DEs. P. 71-72
5 First-order linear DEs. P. 59-63
6

Solving first-order DEs by special substitutions:
Homogeneous DEs. Bernoulli's equation. y'=F(Ax+By+C).

P. 75-77
7 Linear models by 1st-order DEs:
Growth/Decay. Cooling/heating. Mixture problem. 		P. 92-96
8 Nonlinear models by 1st-order DEs:
Logistic (population growth) model. Chemical reaction.		 P. 103-108
9 Second-Order Linear DEs IVP. Existence & uniqueness. Linear dependence/independence. P. 127-135
10

Structure of solutions:
Superposition principle. Wronskian and linear independence of solutions. Formulation of general solutions.
11
12 Reduction of order. P. 139-141
13 Homogeneous DEs with constant coefficients:
Characteristic equations. Fundamental set. General solutions.		 P. 143-144
14 Method of undetermined coefficients. P. 150-156
15
16 Method of variation of parameters. P. 168-170
17 Midterm review.  
18  
19 (In-class) Midterm test.  
20 Cauchy-Euler equations.

P. 173-177
21 Higher-order equations. Nonlinear 2nd-order equations. P. 145-146, 184-185
22 Vibrations in mechanical systems. P. 195-205
23 Series Solutions of Linear DEs Existence of power series solutions. P. 241-246
24 Series solutions and singular points. P. 250-251
25 Method of Frobenius. P. 251-254
26 Method of Frobenius II. P. 255-256
27 The Laplace Transform Definition of Laplace transform. P. 278-280
28 Existence of Laplace transform. P. 281-282
29 Inverse transform. Translation theorems. P. 284-286, 293-299
30 Transforms of derivatives. IVPs. P. 287-290
31 Derivatives of transforms. P. 305-306
32 Convolution theorem. P. 306-309
33 Unit impulse functions. P. 315-317
34 Summary and more examples.  
35 Applications to LRC series circuits. P. 309-312