Computational Thinking for Modeling and Simulation

Brought by: edX

Overview

Computational thinking is becoming widely recognized as a skill necessary for every educated person in a technologically advanced society. 

We will focus on just a subset of computational thinking which concerns creating models of the physical world – something that engineers frequently need to do.  Because of that choice, this course covers many topics normally viewed as within the domain of mathematics such as algebra and calculus, but the solution procedures are algorithmic rather than symbolic.

The major themes of the course are:
  • Representation -- How do you encode information about the world in a computer?  How do your choices in representation affect the ease with which you can solve problems?
  • Decomposition -- How do you break a large and diverse problem into many simpler parts?
  • Discretization -- How do you break up space and time into a large number of relatively small pieces?  What are the alternative ways of doing this?  What are the consequences of discretization procedures for accuracy and speed?
  • Verification -- How do you build confidence in the results of a model?

Syllabus

What is Computational Thinking? (representation, discretization, error, decomposition, verification)

Interpolation (building simple surrogates for more complex functions)

Integration (processes for numerical quadrature)

Randomness (generating and using pseudorandom variables in models)

Differentiation (numerical derivatives)

Solving equations (Gaussian elimination for linear systems, Newton-Raphson for non-linear systems)

Taught by

Daniel Frey and Ali Talebinejad

Computational Thinking for Modeling and Simulation
Go to course

Computational Thinking for Modeling and Simulation

Brought by: edX

  • edX
  • Free
  • English
  • Certificate Not Available
  • Certain days
  • intermediate
  • English
8.1.2PHP Version639msRequest Duration2MBMemory UsageGET en/courses/{slug}Route
    • Booting (404ms)
    • Application (233ms)
    • 1 x Booting (63.29%)
      404.22ms
      1 x Application (36.46%)
      232.85ms
      14 templates were rendered
      • public.courses.show (resources/views/public/courses/show.blade.php)3bladefile
        Params
        0
        course
        1
        links
        2
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.courses.partials.details (resources/views/public/courses/partials/details.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.layouts.main (resources/views/public/layouts/main.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.meta (resources/views/public/layouts/partials/meta.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.navbar (resources/views/public/layouts/partials/navbar.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.links (resources/views/public/auth/profile/partials/links.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.layouts.partials.flash-session (resources/views/public/layouts/partials/flash-session.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      uri
      GET en/courses/{slug}
      middleware
      web, localize:en
      controller
      App\Http\Controllers\CourseController@show
      as
      en.courses.show
      namespace
      prefix
      /en
      where
      file
      app/Http/Controllers/CourseController.php:17-35
      7 statements were executed7.36ms
      • select * from `courses` where `slug_en` = 'computational-thinking-for-modeling-and-simulation' limit 1
        5.43ms/app/Http/Controllers/CourseController.php:20corspedia
        Metadata
        Bindings
        • 0. computational-thinking-for-modeling-and-simulation
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:20
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `courses` set `visitors` = `visitors` + 1, `courses`.`updated_at` = '2025-07-06 08:19:43' where `id` = 544
        800μs/app/Http/Controllers/CourseController.php:21corspedia
        Metadata
        Bindings
        • 0. 2025-07-06 08:19:43
        • 1. 544
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:21
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `topic_id`, `slug_en`, `slug_ar` from `subjects` where `subjects`.`id` in (1)
        240μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `slug_en`, `slug_ar` from `topics` where `topics`.`id` in (1)
        190μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 25. /app/Http/Controllers/CourseController.php:23
        • 26. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 27. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 28. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `institutions` where `institutions`.`id` in (3) and `institutions`.`deleted_at` is null
        220μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `providers` where `providers`.`id` in (1) and `providers`.`deleted_at` is null
        210μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `html_files` where `html_files`.`id` = 538 limit 1
        270μs/app/Models/Course.php:84corspedia
        Metadata
        Bindings
        • 0. 538
        Backtrace
        • 21. /app/Models/Course.php:84
        • 28. view::public.courses.show:29
        • 30. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:125
        • 31. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 32. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
      App\Models\HtmlFile
      1
      App\Models\Provider
      1
      App\Models\Institution
      1
      App\Models\Topic
      1
      App\Models\Subject
      1
      App\Models\Course
      1
        _token
        x6bAULjtG0SzyDlYQgxgIYyF8dzEm98fzc5ubJx4
        locale
        en
        _previous
        array:1 [ "url" => "https://www.corspedia.com/en/courses/computational-thinking-for-modeling-and-s...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /en/courses/computational-thinking-for-modeling-and-simulation
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:24 [ "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.172" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.172" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "cf-ray" => array:1 [ 0 => "95adadc1b92aab90-YYZ" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "host" => array:1 [ 0 => "www.corspedia.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:50 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.172" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.172" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_CF_RAY" => "95adadc1b92aab90-YYZ" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_HOST" => "www.corspedia.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "corspedia.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "141.95.147.152" "REMOTE_USER" => "" "REMOTE_PORT" => "55602" "REMOTE_ADDR" => "172.69.130.250" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/2.0" "DOCUMENT_ROOT" => "/var/www/corspedia/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/en/courses/computational-thinking-for-modeling-and-simulation" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/corspedia/public/index.php" "PATH_INFO" => "" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1751789983.2563 "REQUEST_TIME" => 1751789983 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Sun, 06 Jul 2025 08:19:43 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjdsK09MZVBxdHBYMUUzMnRneGMxbmc9PSIsInZhbHVlIjoiTk9XeUdVMGtSZW5KQm8vWEJGbVA3dCtxaDNYMTk2eldUZXJQZzQ2dHJCTCtaRFdQZm1kbUFrRGltVHQzWEFtSk9oUUZUNHZHWlliVE9PTFJpWnVvc202SWEvbE9ITVI2SkVnaWo1TUU1dVZiQy8vaDhtM01XMDdtQXI0MVJnZlYiLCJtYWMiOiIwMmYwMTZhOTFhMDIxODU5YjYyMzI0MWYxZDM1MGYzODc4YzgwYzExZTZmZGNhMDRhOTcwZjBmNDdhNjc1NzE5IiwidGFnIjoiIn0%3D; expires=Sun, 06 Jul 2025 10:19:43 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IjdsK09MZVBxdHBYMUUzMnRneGMxbmc9PSIsInZhbHVlIjoiTk9XeUdVMGtSZW5KQm8vWEJGbVA3dCtxaDNYMTk2eldUZXJQZzQ2dHJCTCtaRFdQZm1kbUFrRGltVHQzWEFtSk9oUUZUN" 1 => "laravel_session=eyJpdiI6InVJVVlaOFRsNWZkUFpUVXpNUWhYQUE9PSIsInZhbHVlIjoiaU5vb0g0bnhZU0tuY3NZNVg5b1hxb3BrREdzRFFGMFoyWGI2RDA5YWlaNWVXSjFSbFpTeWFsUWhXdVpYZXFieXBjL2NocjRBSW1YMXkxMFNXNHI5V3V1QlNkd3laK2hsK1hhcXc2OFBvc2p4bjJMVnlwMjJoNG1zN1QvekpPckciLCJtYWMiOiJjNDBlNDA4MjUyZWI3OGFjYzFjZDVjMmIyNmIzZDE3ZGZmYmRiZmI4Zjk2MzQ5ZTliYjk1YzM5NTFhMzM4NjNlIiwidGFnIjoiIn0%3D; expires=Sun, 06 Jul 2025 10:19:43 GMT; Max-Age=7200; path=/; httponly; samesite=laxlaravel_session=eyJpdiI6InVJVVlaOFRsNWZkUFpUVXpNUWhYQUE9PSIsInZhbHVlIjoiaU5vb0g0bnhZU0tuY3NZNVg5b1hxb3BrREdzRFFGMFoyWGI2RDA5YWlaNWVXSjFSbFpTeWFsUWhXdVpYZXFieXBj" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjdsK09MZVBxdHBYMUUzMnRneGMxbmc9PSIsInZhbHVlIjoiTk9XeUdVMGtSZW5KQm8vWEJGbVA3dCtxaDNYMTk2eldUZXJQZzQ2dHJCTCtaRFdQZm1kbUFrRGltVHQzWEFtSk9oUUZUNHZHWlliVE9PTFJpWnVvc202SWEvbE9ITVI2SkVnaWo1TUU1dVZiQy8vaDhtM01XMDdtQXI0MVJnZlYiLCJtYWMiOiIwMmYwMTZhOTFhMDIxODU5YjYyMzI0MWYxZDM1MGYzODc4YzgwYzExZTZmZGNhMDRhOTcwZjBmNDdhNjc1NzE5IiwidGFnIjoiIn0%3D; expires=Sun, 06-Jul-2025 10:19:43 GMT; path=/XSRF-TOKEN=eyJpdiI6IjdsK09MZVBxdHBYMUUzMnRneGMxbmc9PSIsInZhbHVlIjoiTk9XeUdVMGtSZW5KQm8vWEJGbVA3dCtxaDNYMTk2eldUZXJQZzQ2dHJCTCtaRFdQZm1kbUFrRGltVHQzWEFtSk9oUUZUN" 1 => "laravel_session=eyJpdiI6InVJVVlaOFRsNWZkUFpUVXpNUWhYQUE9PSIsInZhbHVlIjoiaU5vb0g0bnhZU0tuY3NZNVg5b1hxb3BrREdzRFFGMFoyWGI2RDA5YWlaNWVXSjFSbFpTeWFsUWhXdVpYZXFieXBjL2NocjRBSW1YMXkxMFNXNHI5V3V1QlNkd3laK2hsK1hhcXc2OFBvc2p4bjJMVnlwMjJoNG1zN1QvekpPckciLCJtYWMiOiJjNDBlNDA4MjUyZWI3OGFjYzFjZDVjMmIyNmIzZDE3ZGZmYmRiZmI4Zjk2MzQ5ZTliYjk1YzM5NTFhMzM4NjNlIiwidGFnIjoiIn0%3D; expires=Sun, 06-Jul-2025 10:19:43 GMT; path=/; httponlylaravel_session=eyJpdiI6InVJVVlaOFRsNWZkUFpUVXpNUWhYQUE9PSIsInZhbHVlIjoiaU5vb0g0bnhZU0tuY3NZNVg5b1hxb3BrREdzRFFGMFoyWGI2RDA5YWlaNWVXSjFSbFpTeWFsUWhXdVpYZXFieXBj" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "x6bAULjtG0SzyDlYQgxgIYyF8dzEm98fzc5ubJx4" "locale" => "en" "_previous" => array:1 [ "url" => "https://www.corspedia.com/en/courses/computational-thinking-for-modeling-and-simulation" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]