BSTE:HighPerformanceComputing - Revision history

I.konyukhov: /* Course Characteristics */

2021-10-18T07:15:54Z

Course Characteristics

← Older revision		Revision as of 07:15, 18 October 2021
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	* Differential Equations		* Differential Equations
	* Digital signal processing		* Digital signal processing
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	=== Resources and reference material ===		=== Resources and reference material ===
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	* Sanders, J., Kandrot, E. (2010) CUDA by example : an introduction to general-purpose GPU programming, Addison-Weslye		* Sanders, J., Kandrot, E. (2010) CUDA by example : an introduction to general-purpose GPU programming, Addison-Weslye
	* Scarpino, M. (2011) OpenCL in Action: How to Accelerate Graphics and Computations, Manning.		* Scarpino, M. (2011) OpenCL in Action: How to Accelerate Graphics and Computations, Manning.
−	* Banger, R., Bhattacharyya, K. (2013) OpenCL Programming by Example, Packt Publishing.	+	* Banger, R., Bhattacharyya, K. (2013) OpenCL Programming by Example, Packt Publishing.

	== Course Sections ==		== Course Sections ==

I.konyukhov: /* High Performance Computing */

2021-10-18T07:15:45Z

High Performance Computing

← Older revision		Revision as of 07:15, 18 October 2021
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	* Digital signal processing		* Digital signal processing

−	=== Course objectives based on Bloom’s taxonomy ===
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−	=== - What should a student remember at the end of the course? ===
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−	By the end of the course, the students should be able to:
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−	=== - What should a student be able to understand at the end of the course? ===
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−	By the end of the course, the students should be able to understand:
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−	=== - What should a student be able to apply at the end of the course? ===
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−	By the end of the course, the students should be able to:
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	=== Resources and reference material ===		=== Resources and reference material ===

I.konyukhov: /* Topics covered in this section: */

2021-10-18T07:15:06Z

Topics covered in this section:

← Older revision		Revision as of 07:15, 18 October 2021
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	* Matrix multiplication (demonstration of optimization based on different types of device's memory)		* Matrix multiplication (demonstration of optimization based on different types of device's memory)
−	* Direct methods of solving SLAE ~~(Gaussian elimination, Cholessky decomposition, sweep methods in parallel)~~	+	* Direct methods of solving SLAE
		+	- Gaussian elimination
		+	- Cholessky decomposition
		+	- Sweep methods
	* Iterative methods of solving SLAE		* Iterative methods of solving SLAE
−	- Solution of sparse SLAE by iterative methods in the problem of heat propagation in a plate	+	- Solution of sparse SLAE by iterative methods in the problem of heat propagation in a plate
−	- Solution of symmetric sparse SLAE by upper relaxation method with Chebyshev acceleration	+	- Solution of symmetric sparse SLAE by upper relaxation method with Chebyshev acceleration
−	- Solution of symmetric sparse SLAE by conjugate gradients with preconditioning	+	- Solution of symmetric sparse SLAE by conjugate gradients with preconditioning
−	- Solution of sparse SLAE by generalized minimal residuals with preconditioning	+	- Solution of sparse SLAE by generalized minimal residuals with preconditioning

	==== Section title: ====		==== Section title: ====

I.konyukhov: /* Topics covered in this section: */

2021-10-18T07:14:15Z

Topics covered in this section:

← Older revision		Revision as of 07:14, 18 October 2021
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	* Direct methods of solving SLAE (Gaussian elimination, Cholessky decomposition, sweep methods in parallel)		* Direct methods of solving SLAE (Gaussian elimination, Cholessky decomposition, sweep methods in parallel)
	* Iterative methods of solving SLAE		* Iterative methods of solving SLAE
−	- Solution of sparse SLAE by iterative methods in the problem of heat propagation in a plate	+	- Solution of sparse SLAE by iterative methods in the problem of heat propagation in a plate
−	- Solution of symmetric sparse SLAE by upper relaxation method with Chebyshev acceleration	+	- Solution of symmetric sparse SLAE by upper relaxation method with Chebyshev acceleration
−	- Solution of symmetric sparse SLAE by conjugate gradients with preconditioning	+	- Solution of symmetric sparse SLAE by conjugate gradients with preconditioning
−	- Solution of sparse SLAE by generalized minimal residuals with preconditioning	+	- Solution of sparse SLAE by generalized minimal residuals with preconditioning

	==== Section title: ====		==== Section title: ====

I.konyukhov: /* High Performance Computing */

2021-10-18T07:13:41Z

High Performance Computing

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I.konyukhov: Created page with "= High Performance Computing = == Course Characteristics == === Key concepts of the class === * Multivariate calculus: derivatives, differentials, maxima and minima * Multi..."

2021-10-15T08:28:54Z

Created page with "= High Performance Computing = == Course Characteristics == === Key concepts of the class === * Multivariate calculus: derivatives, differentials, maxima and minima * Multi..."

New page

= High Performance Computing =

== Course Characteristics ==

=== Key concepts of the class ===

* Multivariate calculus: derivatives, differentials, maxima and minima
* Multivariate integration
* Functional series. Fourier series
* Integrals with parameters

=== What is the purpose of this course? ===

The goal of the course is to study basic mathematical concepts that will be required in further studies. The course is based on Mathematical Analysis I, and the concepts studied there are widely used in this course. The course covers differentiation and integration of functions of several variables. Some more advanced concepts, as uniform convergence of series and integrals, are also considered, since they are important for understanding applicability of many theorems of mathematical analysis. In the end of the course some useful applications are covered, such as gamma-function, beta-function, and Fourier transform.

=== Course objectives based on Bloom’s taxonomy ===

=== - What should a student remember at the end of the course? ===

By the end of the course, the students should be able to:

* find partial and directional derivatives of functions of several variables;
* find maxima and minima for a function of several variables
* use Fubiniâ€™s theorem for calculating multiple integrals
* calculate line and path integrals
* distinguish between point wise and uniform convergence of series and improper integrals
* decompose a function into Fourier series
* calculate Fourier transform of a function

=== - What should a student be able to understand at the end of the course? ===

By the end of the course, the students should be able to understand:

* how to find minima and maxima of a function subject to a constraint
* how to represent double integrals as iterated integrals and vice versa
* what the length of a curve and the area of a surface is
* properties of uniformly convergent series and improper integrals
* beta-function, gamma-function and their properties
* how to find Fourier transform of a function

=== - What should a student be able to apply at the end of the course? ===

By the end of the course, the students should be able to ...

* find multiple, path, surface integrals
* find the range of a function in a given domain
* decompose a function into Fourier series

=== Resources and reference material ===

* Robert A. Adams, Christopher Essex (2017) Calculus. A Complete Course, Pearson
* Jerrold Marsden, Alan Weinstein (1985) Calculus (in three volumes; volumes 2 and 3), Springer

== Course Sections ==

The main sections of the course and approximate hour distribution between them is as follows:

{|
|+ Course Sections
!align="center"| '''Section'''
! '''Section Title'''
!align="center"| '''Teaching Hours'''
|-
|align="center"| 1
| Differential Analysis of Functions of Several Variables
|align="center"| 24
|-
|align="center"| 2
| Integration of Functions of Several Variables
|align="center"| 30
|-
|align="center"| 3
| Uniform Convergence of Functional Series. Fourier Series
|align="center"| 18
|-
|align="center"| 4
| Integrals with Parameter(s)
|align="center"| 18
|-
|align="center"| hline
|
|align="center"|
|}

=== Section 1 ===

==== Section title: ====

Differential Analysis of Functions of Several Variables

=== Topics covered in this section: ===

* Limits of functions of several variables
* Partial and directional derivatives of functions of several variables. Gradient
* Differentials of functions of several variables. Taylor formula
* Maxima and minima for functions of several variables
* Maxima and minima for functions of several variables subject to a constraint

=== Section 2 ===

==== Section title: ====

Differential Analysis of Functions of Several Variables

=== Topics covered in this section: ===

* Limits of functions of several variables
* Partial and directional derivatives of functions of several variables. Gradient
* Differentials of functions of several variables. Taylor formula
* Maxima and minima for functions of several variables
* Maxima and minima for functions of several variables subject to a constraint

=== Section 3 ===

==== Section title: ====

Differential Analysis of Functions of Several Variables

=== Topics covered in this section: ===

* Limits of functions of several variables
* Partial and directional derivatives of functions of several variables. Gradient
* Differentials of functions of several variables. Taylor formula
* Maxima and minima for functions of several variables
* Maxima and minima for functions of several variables subject to a constraint

=== Section 4 ===

==== Section title: ====

Differential Analysis of Functions of Several Variables

=== Topics covered in this section: ===

* Limits of functions of several variables
* Partial and directional derivatives of functions of several variables. Gradient
* Differentials of functions of several variables. Taylor formula
* Maxima and minima for functions of several variables
* Maxima and minima for functions of several variables subject to a constraint