A&S Ordinary Differential Equations
MA 321

Ma 321 Ordinary Differential Equations
3 semester hours

Solution of first and second order equations by formal methods, linear equations are studied in detail. Systems of linear equations, series of solutions, Laplace transforms, eigenvalues are covered as well as elementary PDE by separation of variables.
Prerequisite: MA 225 or equivalent.

Fr. MacDonnell B108 ex 7222
Text: A First Course in Differential Equations by Dennis Zill Ed. 6

Sylabus for MA 321

ch1,2 Elementary Methods LDE I

Existence and Uniqueness
Variables Separable
First-Order Linear D E
Exact Differential equations
Homogeneous Functions
ch4 LDE II



Linear Independence and Wronskians
The Characteristic Equation
Homogeneous D E w Const Coef
The general solution
Homogeneous D E w Variable Coef
Cauchy-Euler D E
Reduction of Order ( Abel's formula)
Nonhomogeneous D E
The Method of Undetermined Coef
Linear Systems
The Method of Elimination
The Matrix Method
ch5 Boundary Value Problems

Solution of Boundary Value Problems
Eigenvalues and Eigenfunctions
ch6 Series Solutions L D E II

Solutions of Linear Hom D E by Taylor
Ordinary Points and Singular Points
Power-Series Solutions about an Ord Pt
ch7 The Laplace Transform

Properties of Laplace Transform
The Laplace Transform Applied to D E
# Elemetary PDE

Boundary Value Problems

Suggested problems for homework

{using Zill}

Initial value 1.2 15/11-16
Seperating variables 2.1 35/1-34
Exact equations 2.2 42/1-30
Linear equations 2.3 51/1-30
Homogeneous functions 2.4 57/1-14
Wronskian 4.1 108/15-30
Abel 4.2 112/1-112
LDE w constant coef 4.3 119/1-28
Undetermined coef 4.4 130/1-32
Variation/parameters 4/6 146/1-24
Cauchy-Euler 4.7 153/1-22
Systems of lin equa 4.8 160/1-16
Systems of non-lin eq 4.9 166/1-8
Eigenvalues 5.2 198/9-14
Power series 6.1 222/15-24
PS about ordinary pts 6.2 229/1-14
Laplace transforms 7.1 266/19-38
Inverse transforms 7.2 272/1-22
Applications 7.5 301/1-13
Systems of DE 7.7 313/1-12
Partial diff eq # sheets

Some geometry, theorems and course syllabi

Geometry

Six types of Ruled Surfaces
Half Twist Ruled Surfaces
p/q Twist Ruled Surfaces
Saddle (hypar) Surfaces
Geometry of Bridge construction
The Seven Wonders of the Ancient World
The 13 Achimedian semiregular polyhedra

Theorems

The Mathematician's Quest for Superlatives . . .from geometrical and caculus considerations
The Mathematician's Quest for Superlatives . . .using caculus of variations
Certain Periodic Polar Curves
Monge's Twist-surface Theorems
Hyperpower Function _xx^{x . . .}
Theorems of Girolamo Sacceri, S.J. and his hyperbolic geometry
Saccheri's Solution to Euclid's BLEMISH

Course syllabi

Analysis III
Ordinary differential Equations

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