- Nonlinear Analysis 52 (2003) 11291152 www.elsevier.com/locate/na
- Regularity Theory for Weak Solutions Recall that we have defined the weak solution u for the Poisson equation
- The Single Conservation Law: Existence and Uniqueness In this lecture we will prove the existence and uniqueness of entropy solutions to the single conservation
- MATHMATHMATHMATH 334:334:334:334: IntroductionIntroductionIntroductionIntroduction totototo DifferentialDifferentialDifferentialDifferential EquationsEquationsEquationsEquations FallFallFallFall 2010201020102010
- The Riemann Problem The Riemann problem for (scalar or system of) conservation laws is the following
- Prerequisites: Integration & "d" Most of the following problems should be easy for anyone aiming at a decent grade
- Last Update: April 4, 2011 Math 201 ES1 Winter 2010
- Solving First Order ODEs Table of contents
- Wave Equations Explicit Formulas In this lecture we derive the representation formulas for the wave equation in the whole space
- Midterm Review II: Linear 2nd Order PDEs We consider a general linear 2nd order PDE
- Asymptotic Behavior and Energy Methods In this lecture we first apply the maximum principles to study the asymptotic ( t ) behavior of the
- The Laplace/Poisson Equations: Explicit Formulas In this lecture we study the properties of the Laplace equation
- Discontinuous Solutions of Conservation Laws In this lecture we study 1 D conservation laws
- Week 01 : Introduction 1. What are partial differential equations.
- Last Update: November 5, 2010 The Method of Laplace Transform
- Weeks 09 1 0: Sturm-Liouville Theory and Special Functions We recall the basic steps of the method of separation of variables.
- Schauder Theory Intuitively, the solution u to the Poisson equation
- Advances in Mathematics 135, 76 144 (1998) Partial Differential Equations in the 20th Century*
- MATHMATHMATHMATH 527:527:527:527: IntermediateIntermediateIntermediateIntermediate PartialPartialPartialPartial DifferentialDifferentialDifferentialDifferential EquationsEquationsEquationsEquations FallFallFallFall 2010201020102010
- Heat Equation Maximum principles In this lecture we will discuss the maximum principles and uniqueness of solution for the heat equations.
- System of First Order Linear Equations Table of contents
- Uniqueness and Asymptotics In this lecture we prove the uniqueness for the wave equations. We also prove some asymptotic decay
- Probabilistic Interpretation of the Heat Equation In this lecture we give a probabilistic interpretation of the heat equation.
- SlAM REVIEW Vol. 27, No. 1, March 1985
- Theory of Linear Elliptic PDE We will sketch, in this section, the theory of general linear elliptic PDEs
- The Perron Method In this lecture we show that one can show existence of solutions using maximum principle alone.
- Semigroup Method In this lecture we establish properties of the heat equation through the abstract theory of semigroups. Let
- Harmonic Functions Since the Poisson equation
- Integral Transformation Methods 1. Fourier transforms.
- Prerequisites: Differentiation and Symbols Most of the following problems should be easy for anyone aiming at a decent grade
- This article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and
- Heat Equation Explicit Formulas We now turn to the heat equation
- Week 03: Classification of Second-Order Linear Equations In last week's lectures we have illustrated how to obtain the general solutions of first order PDEs using
- Introduction Table of contents
- Viscosity Solutions In this lecture we take a glimpse of the viscosity solution theory for linear and nonlinear PDEs. From our
- m > 19701023 Y r t l 2 l l $
- MATHMATHMATHMATH 201201201201 EV1:EV1:EV1:EV1: DifferentialDifferentialDifferentialDifferential EquationsEquationsEquationsEquations WinterWinterWinterWinter 2011201120112011
- Introductory Differential Equations: What's Different and How To Do Well
- Prerequisites: Complex Numbers & Algebraic Equations Most of the following problems should be easy for anyone aiming at a decent grade
- Solving Second Order Linear ODEs Table of contents
- Review Sol. of 2nd Exam Multiple Choice Problems.
- Math 527 Fall 2009 Lecture 15 (Oct. 28, 2009) Asymptotics
- Sep. 3, 2008 Introduction
- Sep. 8, 2008 The Cauchy-Kowalevski Theorem
- Sep. 1 0, 2008 Distributions
- The Dirichlet' s Principle In this lecture we discuss an alternative formulation of the Dirichlet problem for the Laplace equation
- The Single Conservation Law: Asymptotics In this lecture we study the behavior of entropy solutions at t . Intuitively, the total variation of the
- Midterm Review III: Cauchy Problems and Wave Equations In this last review lecture we will first clarify some steps in solving Cauchy problems for 1 st order quasi-
- Midterm Review I: Method of Characteristics Recall that we try to find general solutions of the following quasi-linear first order PDE
- Week 02: Method of Characteristics From now on we will study one by one classical techniques of obtaining solution formulas for PDEs. The
- Week 04 -05: Wave Equations In this chapter, we will consider the (1 D) wave equation
- Weeks 07 08: Separation of Variables In the past few weeks we have explored the possibility of solving first and second order PDEs by trans-
- Green' s Function In most of our lectures we only deal with initial and boundary value problems of homogeneous equation.
- Solving First Order ODEs Table of contents
- Solving Second Order Linear ODEs Table of contents
- Series Solutions of Differential Equations Table of contents
- Prerequisites: Manipulating Infinite Sums Most of the following problems should be easy for anyone aiming at a decent grade
- Lecture 05 Integrating Factors Sep. 16, 2011
- Lecture 26 Step Functions Last time we mentioned the necessity of considering functions with jumps, such as
- Lecture 06 Integrating Factors (Cont.) Sep. 19, 2011
- Lecture 27 Solving DEs involving Jumps One can use "unit step function"
- Lecture 30 System of Ordinary Differential Equations Mathematical Modeling.
- Lecture 03 Exact Equations Sep. 12, 2011
- Lecture 24 Solve Differential Equations (Cont.) Solving differential equations using Laplace Transform.
- Lecture 22 Laplace Transform One word about checking regular singular points.
- Lecture 16 Power Series Method Taylor Expansion.
- Lecture 32 Vectors, Matrices, Determinants, Eigenvalues/Eigenvec-tors (Cont.)
- Lecture 21 Power Series Method at Singular Points Frobenius The usual power series method, that is setting y = n=0
- Lecture 23 Using Laplace Transform to Solve Differential Equations Laplace transform and Its properties.
- Lecture 14 Higher Order Linear Equations (Cont.) Review: Solving constant-coefficient, homogeneous, linear equations.
- Lecture 11 Undetermined Coefficients (cont.) Sep. 30, 2011
- Lecture 31 Vectors, Matrices, Determinants, Eigenvalues/Eigenvec- General first order system
- Lecture 28 Impulse Functions Impulse functions.
- Lecture 07 Existence and Uniqueness Sep. 21, 2011
- Refreshments will be served in CAB 649 at 2:30 p.m. PIMS / AMI Seminar
- Math 334 Fall 2011 Review Nov. 30, 2011
- Lecture 29 Convolution Solution procedure of Laplace transform method
- MATHMATHMATHMATH 334:334:334:334: IntroductionIntroductionIntroductionIntroduction totototo DifferentialDifferentialDifferentialDifferential EquationsEquationsEquationsEquations FallFallFallFall 2011201120112011
- Lecture 02 Introduction (cont.), The Simplest DE Sep. 9, 2011
- Lecture 18 Power Series Method The Problem.
- Lecture 04 Simplest Non-Exact Equations Sep. 14, 2011
- Lecture 10 Undetermined Coefficients Sep. 26, 2011
- Lecture 12 Variation of Parameters Variation of parameters.
- Lecture 13 Higher Order Linear Equations dtn-1 + + Pn(t) y = G(t). (1)
- Lecture 15 Undetermined Coefficients Review: Computing (a + b i)1/n
- Lecture 09 2nd Order, Linear, Homogeneous, Constant Coefficient Sep. 23, 2011
- Lecture 20 Power Series Method (Cont.) Power series method for solving
- Lecture 01 Introduction Sep. 7, 2011
- Lecture 34 Solving First Order Homogeneous Constant Coefficient System (Cont.)
- Lecture 33 Solving First Order Homogeneous Constant Coefficient Need to solve
- Lecture 35 Matrix Exponentials What really happens when we have n linearly independent eigenvectors.
- Lecture 25 Review for Midterm 2 Main Topics. (Easy Hard)
- Lecture 17 Power Series Method: Introduction (Cont.) Radius of convergence.
- Lecture 08 2nd Order Equations Sep. 23, 2011
- Lecture 19 Power Series Method (Cont.) An Example.
- Math 201 Prerequisites for Week 3 (4.3 4.5) 1. Solving Cubic and Higher Order Algebraic Equations
- Q&A 03: General 2nd Order Equation Jan. 30 Feb. 03, 2012
- Math 201 Prerequisites for Week 2 (2.6, 4.2, 4.3) 1. Complex Numbers
- Collection of Common Mistakes 05: Laplace Transforms Feb. 11, 2012
- Math 201 Lecture 05 Bernoulli and Linear Coefficients Jan. 18, 2012
- Math 201 Lecture 07: Higher Order Equations Jan. 23, 2012
- Math 201 Lecture 13: Laplace Transform Feb. 6, 2012
- Math 201 Lecture 03: Exact Equations Jan. 13, 2012
- Math 201 Lecture 23: Power Series Method for Equations with Poly-nomial Coefficients
- Math 201 Prerequisites for Week 8 (8.2 8.4) 1. Taylor Expansion
- Math 201 Lecture 21: Review of Chapter 2 Mar. 2, 2012
- Math 201 Lecture 06 Second Order Equations Jan. 20, 2012
- Math 201 Lecture 24: Power Series Method: Analytic Coefficients Mar. 09, 2012
- Math 201 Lecture 15: Solving More Complicated Equations Feb. 10, 2012
- Collection of Common Mistakes 03: Constant Coefficients, Undeter-mined Coefficients
- Math 201 Lecture 02: Linear Equations Jan. 11, 2012
- Collection of Common Mistakes 01 Jan. 13, 2012
- Math 201 Lecture 12: Cauchy-Euler Equations Feb. 3, 2012
- Math 201 Lecture 22: Introduction to Power Series Method Mar. 5, 2012
- Math 201 Lecture 17: Discontinuous and Periodic Functions Feb. 15, 2012
- Math 201 Lecture 01: Separable Equations Jan. 09, 2012
- Jan. 1620 , 2012 1. Q. When solving
- Math 201 Lecture 10: Variation of Parameters Jan. 30, 2012
- Math 201 Lecture 16 Solving Equations using Laplace Transform Feb. 13, 2012
- Math 201 Lecture 18: Convolution Feb. 17, 2012
- Math 201 Lecture 20: Review of Chapter 4 and 8.5 Feb. 29, 2012
- Math 201 Prerequisites for Week 1 (2.1 -2.4) 1. Integration
- Math 201 Lecture 04: Homogeneous and = G(a x + b y)
- Math 201 Lecture 19: Impulse Functions Feb. 27, 2012
- Math 201 Prerequisites for Week 5 (7.2 7.4) 1. Improper Integrals
- Collection of Common Mistakes 04: Variation of Parameters, Cauchy-Feb. 03, 2012
- Math 201 Lecture 09: Undetermined Coefficient Cont. Jan. 27, 2012
- Math 201 Lecture 11: General 2nd Order Linear Equations Feb. 1, 2012
- Collection of Common Mistakes 02 Jan. 20, 2012
- Math 201 Lecture 08 Undetermined Coefficients Jan. 25, 2012
- Math 201 Lecture 14: Using Laplace Transform to Solve Equations Feb. 8, 2012
- MATHMATHMATHMATH 201201201201 EV1:EV1:EV1:EV1: DifferentialDifferentialDifferentialDifferential EquationsEquationsEquationsEquations WinterWinterWinterWinter 2012201220122012
