User:EGM6341.S11.team5.cavalcanti/Mtg1

NM1 Mtg 1: Wed, 5 Jan 11 [[media: Nm1.s11.mtg1.djvu | Page 1-1]]

Engineering Analysis (Computation of stress, displacemnet, velocity fields)

Analysis:

Math Analysis (Theorem, proofs)

Hamming 1962 (Bell labs): goal of computation is insight (e.g., engineering analysis for optimal design, understand response...)

3 important classes of numerical methods of 20th century:

EGM 6241 includes topics related to FDM (int. ODEs) and spectral math. (Clenshaw Curtis quad, FFT), also FEM (for time-dep pbs, solving ODEs)
 * Finite diff. math (FDM), 1950s
 * Finite elements math (FEM): 1960s
 * Spectral math: 1970s

Numerical intengration (Atkinson, p249)

$$f\mathrm{\colon }\left\lbrack a,b\right\rbrack \rightarrow \mathbb{R}$$ [[media: Nm1.s11.mtg1.djvu | Page 1-2]] $$ f:= x \rightarrow f(x)$$ where x is the domain and f(x) is the range. $$\color{blue}\in $$ = belongs to, is an element of

$$\color{blue}{\left\lbrack a,b\right\rbrack} $$ = interval, closed (i.e., a, b, $$\color{blue}{\in \left\lbrack a,b\right\rbrack} $$)

]a, b[ = open interval (i.e., $$\color{blue}{a,b\notin \left(a,b\right)}$$)

$$\mathbb{R}$$ = set of real numbers $$\left\lbrack a,b\right\rbrack \subset \mathbb{R}$$

Note: At beginning of lecture, course organization: Wiki, syllabus, important docs to read, important videos to watch