Higher Mathematics for Science, Technology and Engineering

Partial Fractions

Author(s): S. G. Ahmed

Pp: 226-256 (31)

DOI: 10.2174/9781681082813116010007

* (Excluding Mailing and Handling)

Abstract

Partial fractions encountered within theoretical and applied problems. Also, the partial fractions are good mathematical tools when solving complicated integrals. The main usage of the partial fractions can be considered as a simplified mathematical tool.


Keywords: Fraction decomposition, rational fractions

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      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 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` = 2002 and `b`.`banner_from_date` <= 1740526056 and `b`.`banner_to_date` >= 1740526056 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.02msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2002
      • 3: 1740526056
      • 4: 1740526056
      • 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='7390e2a3bd82682a3828b11ce8f06f74'
      240μsalphaeurekaselec_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\Keywords
    2Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        deRfLIj733IWzOI4t0beEXs5UU4ndoU8feaAIpId
        uc_cart_id
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        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/9330" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/9330
        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:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6ImJKaHZsL1oyclBZQko3Rk5RN1R1NFE9PSIsInZhbHVlIjoiLzYzd21HQ1V2M3hSQTEvZVFNalBqQ2tnT1ZISGkvTHl0amVxUzFHb1BxND0iLCJtYWMiOiIzNmJiYWVhNjVmNDlkM2U3Mzc5MTVjODIwZmM0ZTYwMWE3NTkwM2E2M2ExNDg3NzZiMzM3ZGU2M2NiNjU4Yzk0IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6ImJKaHZsL1oyclBZQko3Rk5RN1R1NFE9PSIsInZhbHVlIjoiLzYzd21HQ1V2M3hSQTEvZVFNalBqQ2tnT1ZISGkvTHl0amVxUzFHb1BxND0iLCJtYWMiOiIzNmJiYWVhNjVmNDlk" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "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 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
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        response_headers
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 23:27:36GET/chapter/9330112184