Ordinary Differential Equations
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WIGDV07 
Vaknaam  Ordinary Differential Equations 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Ordinary Differential Equations  
Leerdoelen  1. The student is able to apply various techniques to solve ordinary differential equations, such as separation of variables, integrating factors, variation of parameters, series expansions, and substitutions. The student can calculate solutions for Bernoulli, Riccati, and exact equations. 2. The student can formulate conditions that guarantee existence and uniqueness of solutions and can check these conditions in concrete problems. The student can formulate Banach’s Fixed Point Theorem, can explain its role in existence and uniqueness proofs, and he/she can apply this theorem in concrete problems. 3. The student can state theorems on the dependence of solutions on initial conditions and parameters, and he/she can apply these theorems in concrete problems. 4. The student can explain the solution structure of linear differential equations. In particular, he/she can solve homogeneous systems of linear equations with constant coefficients for different algebraic and geometric multiplicities of the eigenvalues of the associated coefficient matrix. In addition, the student can compute particular solutions for inhomogeneous equations. 5. The student can solve SturmLiouville boundary/eigenvalue problems and compute their associated Green’s functions. 

Omschrijving  This is an introductory course to the theory of ordinary differential equations. Ordinary differential equations are equations involving one independent variable and derivatives with respect to this variable (as opposed to partial differential equations which involve more than one independent variables and derivatives with respect to these variables). Ordinary differential equations are omnipresent in mathematics and science (social and natural). This is because changes are described mathematically in terms of derivatives. Since various differentials, derivatives, and functions become inevitably related to each other via equations, a differential equation is the result, describing dynamical phenomena, evolution and variation. In this course various types of differential equations are studied. The types are distinguished by one another by the method of how to solve the differential equation (e.g. exact, homogeneous, linear or systems of linear differential equations) or the structure of the solution set (e.g. linear versus nonlinear differential equations). Besides techniques to solving different types of ordinary differential equations also the existence and uniqueness of solutions and the dependence of solutions on initial conditions and parameters are discussed. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The grade for this course is computed as max(WE, 0.7 WE + 0.3 HW) provided that WE=4.5 or higher otherwise the grade is WE, where WE is the mark for the written exam and HW is the mark for the average of the 3 homework assignments.) 

Vaksoort  bachelor  
Coördinator  dr. A.E. Sterk  
Docent(en)  dr. A.E. Sterk  
Verplichte literatuur 


Entreevoorwaarden  
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