RRE001. Wolfram alpha: Differential Equations.
Available at: https://www.wolframalpha.com/examples/mathematics/differentialequations/
This is an online integrator of differential equations
RRE003. History of Differential Equations.
Available at: https://en.wikipedia.org/wiki/Differential_equation
This is a good source of information about Differential Equations and the authors involved in the development of the theory.
LRB001. "Differential Equations. Theory, Technique and Practice", Simmons, G.F., and Krantz, S.G. . McGrawHill Companies, Inc. 2007.
LRB002. "Elementary Applied Partial Differential Equations", Haberman, R. 3rd. ed. PrenticeHall. 1998.
LRB003. "Differential Equations with Applications and Historical Notes", Simmons, G.F. 3rd. ed. CRC Press Textbooks Mathematics, 2017.
LRB004. "A First Course in Differential Equations with Modelling Applications", Zill, D. 9th ed. Brooks Cole 2000.
LRB005. "Elementary Differential Equations with Boundary Value Problems", Edwards, C.H. and Penney, D.E., Pearson Education, 2014.
Chapter 1  FIRST ORDER DIFFERENTIAL EQUATIONS
Elena Romera ColmenarejoProfesora Titular de Universidad 
]]>
Units  Suggested Learning Time  Basic Learning Materials and Readings  Complementary Study Materials and Readings  Assesment Activities and Practical Assignments  Solutions of problems  Evaluation 
Chapter 1 FIRST ORDER DIFFERENTIAL EQUATIONS 
20 hours 
LNF001. ( PDF ) Capítulo 2 de LOB001. 
LRB001 Chapter 1 sections 1.1 to 1.9 
EPF001 Problems chapter 1( PDF ) 
EPF001b Problems solutions ( PDF ) 

Chapter 2 LINEAR EQUATIONS OF HIGHER ORDER 
15 hours  LNF002. ( PDF ) 
LRB001 Chapter 2 sections 2.1 to 2.5 
EPF002 Problems chapter 2( PDF ) 
EPF002b Problems solutions ( PDF ) 

Chapter 3 LAPLACE TRANSFORM 
10 hours 
LNF003. ( PDF ) 
LRB001 Chapter 7 sections 7.1 to 7.,5 
EPF003 Problems chapter 3 ( PDF ) 
EPF003b Problems solutions ( PDF ) 

Chapter 4 METHOD OF SEPARATION OF VARIABLES 
20 hours 
LNF004. ( PDF ) 
LRB001 Chapter 6 sections 6.1 to 6.4 LRB001 Chapter 5 sections 5.1 to 5.5 LRB002 Chapter 1 sections 1.1 to 1.4 LRB002 Chapter 2 sections 2.1 to 2.4 LRB002 Chapter 3 sections 3.1 to 3.5 LRB002 Chapter 4 section 4.4

EPF004 Problems chapter 4 ( PDF ) 
EPF004b Problems solutions ( PDF ) 

Chapter 5 STURMLIOUVILLE PROBLEMS 
15 hours 
LNF005. ( PDF ) 
LRB002 Chapter 5 sections 5.1 to 5.6 LRB002 Chapter 7 section 7.7 
EPF005 Problems chapter 5 ( PDF ) 
EPF005b Problems solutions ( PDF ) 

Chapter 6 FOURIER TRANSFORM 
10 hours 
LNF006. ( PDF ) 
LRB002 Chapter 10 sections 10.3 to 10.4 
EPF006 Problems chapter 6 ( PDF ) 
EPF006b Problems solutions ( PDF ) 

Final Evaluation 
ELENA ROMERA COLMENAREJO
Departamento de Matemáticas
Universidad Carlos III de Madrid
Area:
Mathematics
Degree:
Degree in Biomedical Engineering
December 2018
Theorethical and Lab hours: 56
Total hours:90
It is necessary a basis on Differential and Integral Calculus of One and Several variables and also Linear Algebra.
The first part of the course is dedicated to Ordinary Differential Equations. It is divided into three chapters:
1. First Order Diffferential Equations, with the introduction to differential equations and the resolution with different methods and applications.
2.Linear Equations of HIgher Order, with the general study and the resolution of linear equations with constant and also some nonconstant coefficients.
3. Laplace Transform, a useful tool to solve differential equations and systems of differential equations and also integral equations.
The second part is dedicated to Partial Differential Equations and also has three chapters:
4. Method of Separation of Variables, with the application to the solution of initial and boundary value problems in partial differential equations. It also includes Fourier series.
5. SturmLiouville Problems. This chapter extends the previous method to the case of more general eigenvalue problems and studies generalized Fourier series.
6. Fourier Transform. It is a very useful method to solve differential equations on nonbounded domains.
Modelization of physical problems and in other scientific areas in terms of differential equations. Resolution of a very wide variety of differential equations and its applications. Application of the Laplace transform to solve equations and linear systems. Study of the most important models of the Mathematical Physics: the Laplace equation, the heat equation and the wave equation. Use of techniques of separation of variables and of Fourier transform.
The course includes the Lecture Notes for each chapter, with many examples. Also there is a collection of problems for each chapter and the detailed resolution of the problems for each one of the chapters.
There are different kinds of evaluation activities: Selfevaluations to prepare the exams, partial exams and final exams, together with the solutions, so that it is possible to evaluate the results. Some exams from previous years are included.