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共 15 学时 | 总时长：05:47:13 | 2056 人感兴趣

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高等数学、物理学

空间解析几何与向量分析 00:23:56

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微分学与积分学（包括极限、导数、微分、不定积分、定积分等） 00:25:58

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常微分方程 00:20:22

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线性代数 00:22:55

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热学（气体状态方程、热力学定律、熵等） 00:27:54

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波动学（机械波的产生和传播、简谐波表达式等） 00:25:44

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[ DB ] CONNECT:[ UseTime:0.008862s ] mysql:host=rm-2zem7n9463wy062amco.mysql.rds.aliyuncs.com;port=3306;dbname=new_xuexiwang;charset=utf8mb4
[ SQL ] SHOW COLUMNS FROM `website` [ RunTime:0.006368s ]
[ SQL ] SELECT * FROM `website` WHERE `id` = 1 LIMIT 1 [ RunTime:0.005390s ]
[ SQL ] SHOW COLUMNS FROM `website_navigation` [ RunTime:0.006057s ]
[ SQL ] SELECT * FROM `website_navigation` WHERE `site_id` = 1 AND `link` = 'course' LIMIT 1 [ RunTime:0.005620s ]
[ SQL ] SHOW COLUMNS FROM `model_course` [ RunTime:0.006118s ]
[ SQL ] SELECT `a`.`title`,`b`.`keywords`,`b`.`description` FROM `model_course` `a` INNER JOIN `course` `b` ON `a`.`course_id`=`b`.`id` WHERE `a`.`id` = '18' LIMIT 1 [ RunTime:0.005380s ]
[ SQL ] SELECT `id`,`pid`,`name`,`model_id`,`url`,`image`,`link`,`type` FROM `website_navigation` WHERE `site_id` = 1 AND `status` = 1 ORDER BY `weigh` ASC [ RunTime:0.005433s ]
[ SQL ] SELECT `a`.`description`,`b`.`id`,`b`.`title`,`b`.`type`,`b`.`image`,`b`.`pr_guiding`,`b`.`pr_selling`,`b`.`level`,`b`.`views`,`b`.`course_id` FROM `model_course` `b` INNER JOIN `course` `a` ON `a`.`id`=`b`.`course_id` WHERE `b`.`id` = '18' LIMIT 1 [ RunTime:0.005376s ]
[ SQL ] SHOW COLUMNS FROM `course_type` [ RunTime:0.006141s ]
[ SQL ] SELECT `id`,`name` FROM `course_type` WHERE `id` IN (13) [ RunTime:0.005317s ]
[ SQL ] SHOW COLUMNS FROM `course_sections` [ RunTime:0.006165s ]
[ SQL ] SELECT node_type, COUNT(*) as count, SUM(seconds) as total_seconds FROM `course_sections` WHERE `course_id` = 78 GROUP BY `node_type` [ RunTime:0.005480s ]
[ SQL ] UPDATE `model_course` SET `views`=`views`+1 WHERE `id` = 18 [ RunTime:0.006254s ]
[ SQL ] SELECT * FROM `course_sections` WHERE `course_id` = 78 ORDER BY `weigh` ASC LIMIT 120 [ RunTime:0.005521s ]
[ SQL ] SELECT `vid` FROM `course_sections` WHERE `id` = 3680 AND `node_type` = 2 LIMIT 1 [ RunTime:0.005452s ]
[ SQL ] SELECT `vid` FROM `course_sections` WHERE `id` = 3681 AND `node_type` = 2 LIMIT 1 [ RunTime:0.005369s ]
[ SQL ] SELECT `vid` FROM `course_sections` WHERE `id` = 3682 AND `node_type` = 2 LIMIT 1 [ RunTime:0.005393s ]

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