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Books
Fundamentals of Differential Equations and
Boundary Value Problems (4th edition)
By: Nagle/Saff/Snider
Elementary Differential Equations
By: Rainville/Bedient
Syllabus
Functions of one and two variables. Basic concept of ordinary and partial derivatives
Chapter1: Introduction to Differential Equations
Background
Exercises page 5
1,2,3,4,5,6,7,8,9,10,11,12
Solutions and Initial Value Problems
Exercises page 14
1,2,4,6,8,9,10,11,12,13,14,15,16,17,19,22,23,24,25,27,28,29b
Chapter2: First Order Differential Equations
Separable Equations
Exercises page 46
1,2,3,4,5,6,11,12,13,15,16,17,18,21,24,26
Integrating Factors by Inspection
Exercises 1
Exercises page 66
30
Exact Equations
Exercises page 65
10,11,13,15,16,18,22,24,25,26,27,28
Special Integrating Factors
Exercises page 71
9,10,11,12,13,14,16
Linear Equations in one variable
Exercises page 54
1,4,5,8,9,11,14,16,17,18,20,21,22,28,29
Exercises page 65
(1,3,5,6,8) "solve"
Exercises page71, 72
(1,2,4,5) "solve" +18
Substitutions and Transformations
Homogeneous Equations
Exercises page 79
9,10,11,12,13,14,15,16
Equations of the Form dy/dx = G(ax + by)
Exercises page 79
17,18,19,41,42
Bernoulli Equations
Exercises page 79
21,22,23,24,25,26,27,28
Equations with Linear Coefficients
Exercises page 78
29,30,31,32,44+1,2,3,4,5,6,7 (solve)
Riccati Equation
Exercises page 80
46
Chapter4 & Chapter6: Linear Differential Equations
Basic Theory of Linear Differential Equations
Exercises page 168
27 28,29 , 39
Exercises page 324
15,16,17,18
Homogeneous Linear Equations
Differential Operators
Exercise 2
Homogeneous Linear Equations
Auxiliary Equations with distinct real and repeated roots
Exercises page 167
1,2,3,4,10,11,18,19,20,26 ,41,42,43,44,47,48
Auxiliary Equations with Complex Roots
Exercises page 177
1,2,5,7,13,15,21,25 , 29, 37
Exercises page 331
2,14,15,19,20,21
Cauchy-Euler Equation
Exercises page 179
39,40,41,42,43,44
Exercises page 231
27,28
Exercises page 345
10
Undetermined Coefficients and the annihilator
Exercises page 337
1,3,4,11,12,13,14,15,16,17,18,19,20
Exercises page 344
7
Method of Undetermined Coefficients
Exercises page 186
1,2,3,4,5,10,11,12,16,17,18,35
The Superposition Principle
Exercises page 192
1,10,12,13,29,31
Variation of Parameters
Exercises page 197
1,2,3,6,8,9,11,15,17,20
Chapter7: Laplace Transforms
Definition of the Laplace Transform
Exercises page 359
3,4,6,8,9,12,15,16,18,19,20,21,22,26
Properties of the Laplace Transform
Exercises page 365
8,9,10,11,12,14,15,16,17,20,22,24,25
Inverse Laplace Transform
Exercises page 374
5,7,9,10,11,15,21,23,25,27,29,31,33 , 36
Solving Initial Value Problems
Exercises page 383
3,5,7,9,11,13,18
Exercises page 418
3,5,11,16,19,21
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