Mathematics for
Material Scientists

course:

Mathematics for Materials Scientists

type:

lecture + exercises

lecturer:

Stolwijk 

semester:

WS

 

 

hours per week:

3

ECTS credits:

4

 

 

 

 

content:

(A)

+ Recapitulation of Basic Requirements

+ Notation, Textbooks, Formularies, Calculators + PC Programs

(B) ALGEBRA

+ Complex Numbers

+ Vectors + Matrices in N-Dimensions

+ Linear Systems of Equations

+ Eigenvalues and Eigenvectors

+ Scalar Product + Vector Product

(C) CALCULUS I: FUNCTIONS DEPENDING ON ONE VARIABLE

+ Recapitulation: Derivatives + Integrals

+ Sequences + Series

+ Taylor Series + Fourier Series

+ Important Non-Elementary Functions (Error Function etc.)

(D) CALCULUS II: N-DIMENSIONAL SPACE

+ Functions Depending on More Than One Variable

+ Partial Derivatives, Derivatives in Certain Directions

+ Total Derivatives

+ Minimization Problems in N-Dimensions

+ Simple N-Dimensional Integrals

(E) NUMERICAL METHODS

+ Searching for Zeros and Extreme Values of Functions

+ Newtons Algorithm

+ Gradient Methods for Minimization

+ Numerical Integration
 

literature:

All text book of advanced math are useable, but there is no real need of a book.
 

recommended:

Bachelor

examination:

Written

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