Numerical Methods, dramatically. ... Applied numerical methods using MATLAB,
W. Y. Yang and etc. ... Applied Numerical Analysis, Gerald and Wheatley.
Applied Numerical Methods Lecturer: E d Fatemizadeh Emad F i d h
1 E. Fatemizadeh
Alternative Names: z z z
Numerical Computation Numerical Analysis y Numerical Methods
2 E. Fatemizadeh
Course Definition: z z
Solve Mathematical Problem with Arithmetic Operations. Efficient Digital Computers increase role of Numerical Methods, dramatically.
3 E. Fatemizadeh
Why Numerical Computation (1 (1) z
Problems with non-analytical solution, for example: – Integral:
z
1
I =∫ e 0
−t 2
dt
Problems with non-closed form, for example: – Differential Equation: y ′′ (t ) + sin (t ) ( y ′ (t ) ) + t 2 y = e −t 2
2
4 – Polynomial roots: x + x + 1 = 0
4 E. Fatemizadeh
Why Numerical Computation (2 (2) z
Large Scale Problems: – Large Systems on Equations (Even with analytical Solution), for example: • Algebraic Systems: AX = B , A1000×1000
z
Problems with non non-exact exact solution: – Algebraic Systems: AX = B , A 900×1000 , X 1000×1 , B 900×1
z
Hardware Implementation!
5 E. Fatemizadeh
Why Numerical Computation (3 (3) z
Understand the Basic Theory Underlying the methods in Available Package. – MATLAB – MATHEMATICA
6 E. Fatemizadeh
Course Syllabus (1 (1 ) z
Errors and Numbers Representation – Fixed Point – Floating Point
z z
z
Roots of Nonlinear Equations x 7 + sin ( x ) − Ln ( x ) = 0 Interpolation ⎡{x 1 , x 2 ," , x n } ⇒ f (x ) = ? ⎢ ⎢⎣{ y 1 , y 2 ," , y n } ⎛ ⎞ Numerical Differentiation f (θ ) = expp ⎜ sin ( cos θ ) ⎟ i θ)⎠ ⎝ cos ( sin 7 E. Fatemizadeh
Course Syllabus (2 (2 ) π
z
Numerical Integration (1D/2D)
∫
1 + a 2 cos 2 θ dθ
0
z
Numerical Solution of Ordinary Differential Equations Equations.
x′′ ( t ) + x 2 ( t ) = sin ( t ) z
M ti Matrices Manipulation: M i l ti – – – –
z
Linear Systems Solution Determinants Inversion Eigenvalues and Eigenvectors
MontCarlo Methods 8 E. Fatemizadeh
References: z z z z z z
Applied numerical methods using MATLAB, W. Y. Yang and etc. Numerical Mathematics and Computing, W. Cheney & D. Kincaid Computational Mathematics, B.P. Demidovich and I.A. Moran. Applied Numerical Analysis, Gerald and Wheatley. Numerical Methods Using MATLAB, J.H. Mathews and K.D. Fink Applied Numerical Methods for Engineers Using Matlab and C, Schilling and Harris z Numerical Methods With MATLAB: Implementation Application, G. Recktenwald
9 E. Fatemizadeh
Course Homepages: http://sina.sharif.edu/~ http://sina.sharif.edu/ ~fatemizadeh/ fatemizadeh/C Course ourses s/ANA ANA//ANA ANA.html .html
10 E. Fatemizadeh
Evaluation z z z z
Middle Exam: 40 40% % (8 (8 of 20 20)) 30% (6 of 20) Final Exam: 40 40% % (8 (8 of 20 20)) 65% (13 of 20) Homework (Paper+Code): 20 20% % (4 (4 of 20 20)) 5% (1 of 20) Homework Submission rules: – An email to
[email protected] iau course@gmail com with this typically subject:
ANA0n:studentnumber z
Where n is Homework number number.
11 E. Fatemizadeh
