Fundamentals of Mathematics in Medical Research: Theory and Cases

Functions of Several Variables

Author(s): Carlos Polanco * .

Pp: 10-17 (8)

DOI: 10.2174/9789815223132124010006

* (Excluding Mailing and Handling)

Abstract

This chapter reviews the real-valued functions on space, with fully solved examples that show the application and usefulness of their components to deal with practical problems. Then, we see the types of functions that the reader will often find in academic and research activities. Later, another family of functions called Vector-Valued Functions is defined and its usefulness in solving application problems is shown with examples. Finally, both types of functions are generalized for higher-dimension spaces.

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      • 16. app/Models/Subject.php:238
      • 17. app/Http/Controllers/ChapterController.php:1434
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 11. app/Models/ContentAccess.php:647
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      840μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3741 and `b`.`banner_from_date` <= 1740514075 and `b`.`banner_to_date` >= 1740514075 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.51msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3741
      • 3: 1740514075
      • 4: 1740514075
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='a75054dec8563f67b21c09b727801567'
      290μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
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        _flash
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        PHPDEBUGBAR_STACK_DATA
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        path_info
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        status_code
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        status_text
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        format
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        content_type
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        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
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        request_cookies
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        response_headers
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 20:07:55GET/chapter/22835112182