MATH 451 Home Page

• Wednesday, 12
  Section 3.1 - Variational Problems
  Arc length (curve of shortest length)
  
• Friday, 14
  Section 3.1 - Variational Problems
  Section 3.2 - Necessary Conditions for Extrema
  Brachistochrone (curve of shortest time) Problem
  
  

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• Monday, 17
  Martin Luther King Day Holiday - No class
• Wednesday, 19
  Section 3.2 - Necessary Conditions for Extrema
  Homework #1 Due
  
• Friday, 21
  Section 3.2 - Necessary Conditions for Extrema - Gateaux Variation
  Section 3.3 - The Simplest Problem
  
  
  

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• Monday, 24
  Section 3.3 - The Simplest Problem
  Arc length (curve of shortest length)
  
• Wednesday, 26
  Section 3.3 - The Simplest Problem
  Brachistochrone (curve of shortest time) Problem
  Homework #2 Due
  
• Friday, 28
  Sufficient conditions for extrema - Second variation
  
  
  

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• Monday, 31
  Section 3.4 - Generalizations - Higher derivatives, many functions
  

• Wednesday, 2
  Section 3.4 - Generalizations - Higher dimensions, natural boundary conditions
  Minimal transit time across a flowing river
  Homework #3 Due
  
• Friday, 4
  Section 3.4 - Generalizations - Natural boundary conditions
  Section 3.5 - Hamiltonian Theory
  Minimal transit time across a flowing river
  
  
  

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• Monday, 7
  Section 3.5 - Hamiltonian Theory - Lagrangian
  Harmonic oscillator
  Simple pendulum
  
• Wednesday, 9
  Section 3.5 - Hamiltonian Theory - Hamilton's equations and the inverse problem
  Damped harmonic oscillator
  Surface area (surface of smallest area)
  Homework #4 Due
  
• Friday, 11
  Section 3.6 - Isoperimetric Problems - Lagrange multipliers
  Homework #5 Due
  
  
  

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• Monday, 14
  Section 3.6 - Isoperimetric Problems
  Shape of a hanging rope (catenary)
  
• Wednesday, 16
  The Finite Element Method
  Simple gravitational motion
  Simple gravitational motion with a resistive force
  Homework #6 Due
  
• Friday, 18
  The Finite Element Method
  Shortest arc enclosing a fixed area
  Homework #7 Due
  
  
  

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• Monday, 21
  President's Day Holiday - No class
• Wednesday, 23
  The Finite Element Method
  
• Friday, 25
  The Finite Element Method
  Homework #8 Due
  
  
  

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• Monday, 28
  Section 4.1 - Partial Differential Equations
  

• Wednesday, 1
  Section 4.2 - Diffusion Equations - First principles
  
• Friday, 3
  Section 4.2 - Diffusion Equations - Constitutive relations
  One-dimensional heat equation
  Reaction-diffusion equation
  Logistic population growth - Fisher's equation
  
  
  

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• Monday, 6
  Section 4.2 - Diffusion Equations - Existence, uniqueness, continuous dependence, maximum principle
  Homework #9 Due
  
• Wednesday, 8
  Midterm Exam
  
• Friday, 10
  Section 4.2 - Wave Equations - Existence, uniqueness, continuous dependence
  
  
  

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• Monday, 13
  Spring Break - No class
• Wednesday, 15
  Spring Break - No class
• Friday, 17
  Spring Break - No class
  
  

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• Monday, 20
  Section 4.3 - Equilibrium Equations - Existence, uniqueness
  
• Wednesday, 22
  Section 5.1 - Integral Equations
• Friday, 24
  Section 5.1 - Integral Equations - Volterra equations
  
  

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• Monday, 27
  Section 5.1 - Integral Equations - Volterra equations and the Neumann Series
• Wednesday, 29
  Section 5.1 - Integral Equations - Fredholm equations with separable kernels
  Homework #10 Due
  
• Friday, 31
  Section 5.1 - Integral Equations - Fredholm equations with symmetric kernels
  
  
  

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• Monday, 3
  Section 5.2 - Green's Functions
  
• Wednesday, 5
  Section 5.2 - Green's Functions - Sturm-Liouville problems
  Homework #11 Due
  
• Friday, 7
  Section 5.2 - Green's Functions - Sturm-Liouville problems
  
  
  

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• Monday, 10
  Section 5.2 - Green's Functions - Sturm-Liouville problems
  
• Wednesday, 12
  Section 5.2 - Green's Functions - Eigenfunctions
  Homework #12 Due
  
• Friday, 14
  Section 6.1 - Wave Phenomena in Continuous Systems - Linear waves, shocks, and rarefactions
  
  
  

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• Monday, 17
  Section 6.1 - Wave Phenomena in Continuous Systems - Characteristics
  
• Wednesday, 19
  Section 6.1 - Wave Phenomena in Continuous Systems - Nonlinear wave equation
  
• Friday, 21
  University Day - No class
  
  

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• Monday, 24
  Section 6.1 - Wave Phenomena in Continuous Systems - Conservation laws
  Homework #13 Due
  
• Wednesday, 26
  Section 6.1 - Wave Phenomena in Continuous Systems - Weak solutions, shocks
  
• Friday, 28
  Section 6.1 - Wave Phenomena in Continuous Systems - Jump (Rankine-Hugoniot) condition, entropy condition
  
  
  

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Homework, projects, and tests

• Read Sections 3.1-3.6
• Section 3.1, #1, 2
• Section 3.2, #3, 4, 5a,d,e, 8a,d,e, 10,11,14
• Section 3.3, #1a,c, 2a, 4, 7
• Section 3.4, #2, 7, 12a
• Section 3.5, #3, 7, 15
• Section 3.6, #1, 4

Homework #1, Section 3.1, #1, 2 Due Wednesday 1-19

Homework #2, Section 3.2, #3, 4, 5a,d,e, 8a,d,e, 10,11,14 Due Wednesday 1-26

Homework #3, Section 3.3, #1a,c, 2a, 4, 7 Due Wednesday 2-2

Homework #4, Section 3.4, #2, 7, 12a Due Wednesday 2-9

Homework #5 Due Friday 2-11

Homework #6, Section 3.5, #3, 7, 15 Due Wednesday 2-16

Homework #7, Section 3.6, #1,4 Due Friday 2-18

Homework #8 Due Friday 2-25

Chapter 4 Homework

• Read Sections 4.1-4.3
• Section 4.1, #3a,c, 5
• Section 4.2, #1, 3, 6
• Section 4.3, #2, 3, 4

Homework #9 Due Monday 3-6

Midterm Exam, Chapter 3 Wednesday 3-8

Homework #10 Due Wednesday 3-29

Chapter 5 Homework

• Read Sections 5.1-5.2
• Section 5.1, #2, 3, 7, 11
• Section 5.2, #2, 4, 5a, 7

Homework #11, Section 5.1, #2, 3, 7, 11, and Example 1.4 Due Wednesday 4-5

Homework #12, Section 5.2, #2, 4, 5a, 7 Due Wednesday 4-12

Chapter 6 Homework

• Read Section 6.1
• Section 6.1, #2a,b, 3, 4, 6, 9, 15

Homework #13, Section 6.1, #2a,b, 3, 4, 6, 9, 15 Due Monday 4-24

Project Due Thursday 5-4