Engineering Mathematics - II (BMATE201) EE & EC

Complete Engineering mathematics-II for Electrical & Electronics Engineering Stream

Math Inova

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What you will learn

  • Important Formulae and Procedures

  • Derivations

  • Engineering relevance of critical concepts

  • Model Question Paper Problems

BMATE201: Mathematics-II for Electrical & Electronics engineering stream of Visvesvaraya Technological University (VTU). The curriculum incepts with vector calculus which is highly useful for applications in antenna design. This is followed by vector space and linear transformation which is a power tool especially for communication, signal processing and circuit analysis. Third topic happens to be Laplace transforms which is fundamental to applications based on frequency domain representation and control engineering. Finally, we have numerical methods which are highly necessitated in the era of digitization be it solving polynomial or differential equations.

play
Understanding the Concept of Gradient
Preview

Understanding the Concept of Divergence

Understanding the concept of Curl

Gradient, Divergence & Curl - Formula and Procedure
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Gradient, Divergence & Curl - Problems: (Problem 1 - Gradient)
Preview

Gradient, Divergence & Curl - Problems: (Problem 2 - Gradient)

Gradient, Divergence & Curl - Problems: (Problem 3 - Divergence)

Gradient, Divergence & Curl - Problems: (Problem 4 - Divergence)

Gradient, Divergence & Curl - Problems: (Problem 5 - Divergence & Curl)

Gradient, Divergence & Curl - Problems: (Problem 6 - Curl)

Gradient, Divergence & Curl - Problems: (Problem 7 - Curl)

Gradient, Divergence & Curl - Problems: (Problem 8 - Directional Derivative)

Gradient, Divergence & Curl - Problems: (Problem 9 - Directional Derivative)

Gradient, Divergence & Curl - Problems: (Problem 10 - Gradient)

Gradient, Divergence & Curl - Problems: (Problem 11 - Gradient)

Gradient, Divergence & Curl - Problems: (Problem 11 - Curl of a Gradient)

Gradient, Divergence & Curl - Problems: (Problem 11 - Divergence of a Curl)
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Introduction to Line Integral (For Work done)
Preview

Line Integral - Problems: (Problem 1)

Line Integral - Problems: (Problem 2)

Line Integral - Problems: (Problem 3)

Important Observations for Problems 2 & 3

Line Integral - Problems: (Problem 4)

Line Integral - Problems: (Problem 5)

Introduction to Stoke's Theorem

Introduction to Green's Theorem

Green & Stoke's Theorem - Problems: (Problem 1 - Stoke's Theorem)

Green & Stoke's Theorem - Problems: (Problem 1 (verification) - Stoke's Theorem)

Green & Stoke's Theorem - Problems: (Problem 2 - Stoke's Theorem - Using Line Integral)

Green & Stoke's Theorem - Problems: (Problem 3 - Stoke's Theorem - Using Double Integral)

Green & Stoke's Theorem - Problems: (Problem 4 - Stoke's Theorem)

Green & Stoke's Theorem - Problems: (Problem 5 - Green's Theorem)

Green & Stoke's Theorem - Problems: (Problem 6 - Green's Theorem)

Green & Stoke's Theorem - Problems: (Problem 7 (Area Bounded by ellipse) - Green's Theorem)

Green & Stoke's Theorem - Problems: (Problem 8 (Area Bounded by 2 parabolas) - Green's Theorem)

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Understanding Linearly Dependent and Independent Vectors/Sets
Preview

Linear Independence and Dependence for a 3D vector set/Matrix

Understanding the Idea of Vector Space and Subspace

Understanding Basis, Linear span and Dimension
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Problem 1
Preview

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6
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Introduction to Linear Transformation
Preview

Visualizing Linear Transformation

Understanding Rank & Nullity

Numerical Understanding of Nullity - Square Matrix

Numerical Understanding of Nullity - Rectangular Matrix

Inner Product and Orthogonality

Rotation as a linear Transformation - Self Study Topic

Reflection as a linear Transformation - Self Study Topic

Problem 1

Problem 2

Problem 3
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Problem 4 - Based on Rank and Null Space
Preview

Problem 5 - Understanding left Null Space

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Learning Map & Key Takeaways
Preview

Understanding Laplace Transform - Symbolism

Difference between Laplace & Fourier Transforms

Understanding the Role of the exponential function in the laplace integral - Part 1

Understanding the Role of the exponential function in the laplace integral - Part 2

Understanding Transfer Function
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Engineering Applications of Laplace Transform: (Application - Pitching of a Satellite)
Preview

Engineering Applications of Laplace Transform: (Practical Example - Second Order System)

Important formula and standard results to remember

Important Properties of Laplace Transforms
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Laplace Transforms - Problems: (Problem 1 - sin(at) and cos(at))
Preview

Laplace Transforms - Problems: (Problem 1 - sin(at) and cos(at): Physical Interpretation)

Laplace Transforms - Problems: (Problem 2 - sinh(at) and cosh(at))

Laplace Transforms - Problems: (Problem 3)

Laplace Transforms - Problems: (Problem 4)

Laplace Transforms - Problems: (Problem 5)

Laplace Transforms - Problems: (Problem 6)

Laplace Transforms - Problems: (Problem 7)

Laplace Transforms - Problems: (Problem 8)

Introduction to Gamma functions

Finding the Laplace Transform

Relevance of Gaussian Function

Gamma Function - Problem

Laplace Transforms - Problems: (Problem 9)

Laplace Transforms - Problems: (Problem 10)

Laplace Transforms - Problems: (Problem 11)

Laplace Transforms - Problems: (Problem 12)

Laplace Transforms - Problems: (Problem 13)

Laplace Transforms - Problems: (Problem 14)

Laplace Transforms - Problems: (Problem 15)

Laplace Transforms - Problems: (Problem 16)

Understanding Region of Convergence (ROC)

Example - ROC

Properties of Laplace Transforms: (Linearity)

Properties of Laplace Transforms: (Scaling)
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Properties of Laplace Transforms: (Frequency Shifting)
Preview

Properties of Laplace Transforms: (Time Shifting)

Properties of Laplace Transforms: (Differentiation in Frequency Domain)

Properties of Laplace Transforms: (Differentiation in Time Domain)

Properties of Laplace Transforms: (Integration in Frequency Domain)

Properties of Laplace Transforms: (Integration in Time Domain)

Introduction to Laplace Transform of Periodic Functions

Deriving Formula for Laplace Transform for Periodic Functions

Laplace Transfroms of Special Functions: (Square Wave)

Laplace Transfroms of Special Functions: (Saw-Tooth Wave)

Laplace Transforms of Special Functions: (Triangular wave - Part 1)

Laplace Transfroms of Special Functions: (Triangular Wave - Part 2)

Laplace Transfroms of Special Functions: (Full-Rectified Wave)

Laplace Transforms of Special Functions: (Half Rectified Wave)

Laplace Transforms of Special Functions - Problems: (Problem 1 (By Euler Definition) - [sin⁡ωt]

Laplace Transforms of Special Functions - Problems: (Problem 1 (By Integration by parts) - [sin⁡ωt]

Laplace Transforms of Special Functions - Problems: (Problem 1 (By time shift) - [sin⁡ωt ]

Introduction to Heavy Side Function

Computing Standard Results - Laplace Transforms of Heavy Side Function

Computing the Laplace Transform of a function multiplied by a Heavy Side Function

Construction of a Pulse using Heavy Side Function

Heavy Side Function - Problems: (Problem 1)

Heavy Side Function - Problems: (Problem 2)

Heavy Side Function - Problems: (Problem 3)

Introduction to Laplace Transform of Unit Impulse Function

Introduction to Inverse Laplace Transforms

Inverse Laplace Transforms - Understanding Method by Inspection

Inverse laplace Transforms - Problems: (Problem 1 - By completing the Square)

Rule for finding Inverse Laplace Transform for "Log and Inverse trignometric functions"

Inverse laplace Transforms - Problems: (Problem 2 - By Differentiation)

Inverse laplace Transforms - Problems: (Problem 3 - By Differentiation & Completing the squares)

Inverse laplace Transforms - Problems: (Problem 4 - By Partial Fraction)

Inverse laplace Transforms - Problems: (Problem 5 - By Partial Fraction)

Introduction to Convolution Theorem
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Physical Interpretation of Convolution Theorem
Preview

Convolution Theorem - Problems: (Problem 1)

Convolution Theorem - Problems: (Problem 2)

Convolution Theorem - Problems: (Problem 3)

Introduction of solution of Ordinary Differential Equations using Laplace Transforms

Differential Equations - Laplace Transforms Problems: (Problem 1)

Differential Equations - Laplace Transforms Problems: (Problem 2)

Differential Equations - Laplace Transforms Problems: (Problem 3)

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Understanding the Newton-Raphson Method
Preview

Newton-Raphson Method - Problems: (Problem 1)

Newton-Raphson Method - Problems: (Problem 2)

Newton-Raphson Method - Problems: (Problem 3)
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Newton-Raphson Method - Problems: (Problem 4)
Preview

Newton-Raphson Method - Problems: (Problem 5)

Newton-Raphson Method - Problems: (Problem 1) Using Scientific Calculator

Newton-Raphson Method - Problems: (Problem 2) Using Scientific Calculator

Newton-Raphson Method - Problems: (Problem 3) Using Scientific Calculator

Newton-Raphson Method - Problems: (Problem 4) Using Scientific Calculator

Newton-Raphson Method - Problems: (Problem 5) Using Scientific Calculator

Understanding the Regula-Falsi Method

Regula-Falsi - Problems: (Problem 1)
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Regula-Falsi - Problems: (Problem 2)
Preview

Regula-Falsi - Problems: (Problem 3)

Regula-Falsi - Problems: (Problem 1) Using Scientific Calculator

Regula-Falsi - Problems: (Problem 2) Using Scientific Calculator

Regula-Falsi - Problems: (Problem 3) Using Scientific Calculator

Introduction to Finite Differences
play
Application of Finite Differences
Preview

Formulae for Backward, Forward and Divided Differences

Newton's Forward and Backward Difference - Problems: (Problem 1)

Newton's Forward and Backward Difference - Problems: (Problem 2)

Newton's Forward and Backward Difference - Problems: (Problem 3)

Newton's Forward and Backward Difference - Problems: (Problem 4)

Newton's Forward and Backward Difference - Problems: (Problem 5)

Newton's Divided Difference - Problems: (Problem 1)

Newton's Divided Difference - Problems: (Problem 2)

Understanding Lagrange's Interpolation

Lagrange's Interpolation - Problems: (Problem 1)

Lagrange's Interpolation - Problems: (Problem 2)

Introduction to Numerical Integration

Numerical Integration - Problems: (Problem 1)
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Numerical Integration - Problems: (Problem 2)
Preview

Numerical Integration - Problems: (Problem 3)

Numerical Integration - Problems: (Problem 4)

Numerical Integration - Problems: (Problem 5)

Numerical Integration - Problems: (Problem 6)

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Introduction to Numerical Solution of Differential Equations of First Order and First Degree
Preview

Intution of Taylor's Formulae

Taylor's Series Method - Problems: (Problem 1)

Taylor's Series Method - Problems: (Problem 2)

Taylor's Series Method - Problems: (Problem 3)
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Taylor's Series Method - Problems: (Problem 4)
Preview

Taylor's Series Method - Problems: (Problem 5)

Taylor's Series Method - Problems: (Problem 6 - Practical Example)

Intution of Formulae for Numerical Solution of First order DE's

Runge-Kutta Method - Problems: (Problem 1)

Runge-Kutta Method - Problems: (Problem 2)

Runge-Kutta Method - Problems: (Problem 3)

Modified Euler Method - Problems: (Problem 1)

Modified Euler Method - Problems: (Problem 2)

Modified Euler Method - Problems: (Problem 3)
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Milne's Predictor-Corrector Method - Problems: (Problem 1)
Preview

Milne's Predictor-Corrector Method - Problems: (Problem 2)
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Math Inova
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      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 1
      2.31msvlms_beta_onlinehelper.php#933
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 1
      Backtrace
      • 15. app/Helper/helper.php:933
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:259
      • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select `id` from `courses` where `private_mode` != 1 and (not `course_view_type` = 3 or `is_standalone_course` = 1) and `user_id` = 4780
      3.66msvlms_beta_onlineCourseController.php#207
      Bindings
      • 0: 1
      • 1: 3
      • 2: 1
      • 3: 4780
      Backtrace
      • 13. app/Http/Controllers/Frontend/CourseController.php:207
      • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:259
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select count(*) as aggregate from `enrollments` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695)
      57.38msvlms_beta_onlineCourseController.php#209
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      Backtrace
      • 15. app/Http/Controllers/Frontend/CourseController.php:209
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:259
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select count(*) as aggregate from `enrollments` where `course_id` = 1170
      58.06msvlms_beta_onlineCourseController.php#214
      Bindings
      • 0: 1170
      Backtrace
      • 15. app/Http/Controllers/Frontend/CourseController.php:214
      • 16. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 17. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 18. vendor/laravel/framework/src/Illuminate/Routing/Route.php:259
      • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `instructors` where `instructors`.`id` = 441 and `instructors`.`deleted_at` is null limit 1
      2.58msvlms_beta_onlinecourse-details.blade.php#19
      Bindings
      • 0: 441
      Backtrace
      • 20. view::frontend.course.course-details:19
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 25. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `users` where `users`.`id` = 4780 and `users`.`deleted_at` is null limit 1
      2.26msvlms_beta_onlinecourse-details.blade.php#20
      Bindings
      • 0: 4780
      Backtrace
      • 20. view::frontend.course.course-details:20
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 25. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select `ranking_levels`.*, `user_badges`.`user_id` as `pivot_user_id`, `user_badges`.`ranking_level_id` as `pivot_ranking_level_id` from `ranking_levels` inner join `user_badges` on `ranking_levels`.`id` = `user_badges`.`ranking_level_id` where `user_badges`.`user_id` = 4780
      3.56msvlms_beta_onlinecourse-details.blade.php#20
      Bindings
      • 0: 4780
      Backtrace
      • 19. view::frontend.course.course-details:20
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_instructor` where `course_instructor`.`course_id` = 1170 and `course_instructor`.`course_id` is not null and `course_instructor`.`deleted_at` is null
      4.73msvlms_beta_onlinecourse-details.blade.php#70
      Bindings
      • 0: 1170
      Backtrace
      • 19. view::frontend.course.course-details:70
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `learn_key_points` where `learn_key_points`.`course_id` = 1170 and `learn_key_points`.`course_id` is not null
      7.94msvlms_beta_onlinepartial-overview-tab.blade.php#3
      Bindings
      • 0: 1170
      Backtrace
      • 19. view::frontend.course.partial.partial-overview-tab:3
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lessons` where `course_lessons`.`course_id` = 1170 and `course_lessons`.`course_id` is not null
      22.48msvlms_beta_onlinepartial-curriculum-tab.blade.php#4
      Bindings
      • 0: 1170
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:4
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`lesson_id` = 9685 and `course_lectures`.`lesson_id` is not null
      190msvlms_beta_onlinepartial-curriculum-tab.blade.php#21
      Bindings
      • 0: 9685
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:21
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`lesson_id` = 9687 and `course_lectures`.`lesson_id` is not null
      215msvlms_beta_onlinepartial-curriculum-tab.blade.php#21
      Bindings
      • 0: 9687
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:21
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`lesson_id` = 9688 and `course_lectures`.`lesson_id` is not null
      182msvlms_beta_onlinepartial-curriculum-tab.blade.php#21
      Bindings
      • 0: 9688
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:21
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`lesson_id` = 9689 and `course_lectures`.`lesson_id` is not null
      225msvlms_beta_onlinepartial-curriculum-tab.blade.php#21
      Bindings
      • 0: 9689
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:21
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`lesson_id` = 9690 and `course_lectures`.`lesson_id` is not null
      222msvlms_beta_onlinepartial-curriculum-tab.blade.php#21
      Bindings
      • 0: 9690
      Backtrace
      • 19. view::frontend.course.partial.partial-curriculum-tab:21
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `users` where `users`.`id` = 4780 and `users`.`deleted_at` is null limit 1
      2.72msvlms_beta_onlinepartial-instructor-tab.blade.php#11
      Bindings
      • 0: 4780
      Backtrace
      • 20. view::frontend.course.partial.partial-instructor-tab:11
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 25. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `instructors` where `instructors`.`user_id` = 4780 and `instructors`.`user_id` is not null and `instructors`.`deleted_at` is null limit 1
      4.47msvlms_beta_onlinepartial-instructor-tab.blade.php#42
      Bindings
      • 0: 4780
      Backtrace
      • 21. view::frontend.course.partial.partial-instructor-tab:42
      • 23. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 26. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `courses` where `courses`.`instructor_id` = 441 and `courses`.`instructor_id` is not null
      10.39msvlms_beta_onlinepartial-instructor-tab.blade.php#42
      Bindings
      • 0: 441
      Backtrace
      • 20. view::frontend.course.partial.partial-instructor-tab:42
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 25. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `enrollments` where `enrollments`.`owner_user_id` = 4780 and `enrollments`.`owner_user_id` is not null
      165msvlms_beta_onlinepartial-instructor-tab.blade.php#43
      Bindings
      • 0: 4780
      Backtrace
      • 19. view::frontend.course.partial.partial-instructor-tab:43
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select `id` from `courses` where `user_id` = 4780
      4.44msvlms_beta_onlinehelper.php#927
      Bindings
      • 0: 4780
      Backtrace
      • 13. app/Helper/helper.php:927
      • 16. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 17. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 19. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 5
      2.26msvlms_beta_onlinehelper.php#929
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 5
      Backtrace
      • 15. app/Helper/helper.php:929
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 4
      1.81msvlms_beta_onlinehelper.php#930
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 4
      Backtrace
      • 15. app/Helper/helper.php:930
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 3
      1.83msvlms_beta_onlinehelper.php#931
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 3
      Backtrace
      • 15. app/Helper/helper.php:931
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 2
      1.68msvlms_beta_onlinehelper.php#932
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 2
      Backtrace
      • 15. app/Helper/helper.php:932
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select count(*) as aggregate from `reviews` where `course_id` in (698, 837, 841, 1141, 1170, 1179, 1192, 1544, 1565, 1628, 1629, 1630, 1631, 1634, 1635, 1695) and `rating` = 1
      1.74msvlms_beta_onlinehelper.php#933
      Bindings
      • 0: 698
      • 1: 837
      • 2: 841
      • 3: 1141
      • 4: 1170
      • 5: 1179
      • 6: 1192
      • 7: 1544
      • 8: 1565
      • 9: 1628
      • 10: 1629
      • 11: 1630
      • 12: 1631
      • 13: 1634
      • 14: 1635
      • 15: 1695
      • 16: 1
      Backtrace
      • 15. app/Helper/helper.php:933
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select `ranking_levels`.*, `user_badges`.`user_id` as `pivot_user_id`, `user_badges`.`ranking_level_id` as `pivot_ranking_level_id` from `ranking_levels` inner join `user_badges` on `ranking_levels`.`id` = `user_badges`.`ranking_level_id` where `user_badges`.`user_id` = 4780
      2.59msvlms_beta_onlinepartial-instructor-tab.blade.php#55
      Bindings
      • 0: 4780
      Backtrace
      • 19. view::frontend.course.partial.partial-instructor-tab:55
      • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 24. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `promotion_courses` where `promotion_courses`.`course_id` = 1170 and `promotion_courses`.`course_id` is not null limit 1
      1.58msvlms_beta_onlinecourse-details.blade.php#107
      Bindings
      • 0: 1170
      Backtrace
      • 20. view::frontend.course.course-details:107
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 23. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 24. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 25. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `currencies` where `current_currency` = 'on' limit 1
      1.49msvlms_beta_onlinehelper.php#173
      Bindings
      • 0: on
      Backtrace
      • 15. app/Helper/helper.php:173
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `currencies` where `current_currency` = 'on' limit 1
      1.38msvlms_beta_onlinehelper.php#133
      Bindings
      • 0: on
      Backtrace
      • 15. app/Helper/helper.php:133
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • 21. vendor/laravel/framework/src/Illuminate/View/View.php:195
    • select * from `course_lectures` where `course_lectures`.`course_id` = 1170 and `course_lectures`.`course_id` is not null
      144msvlms_beta_onlineCourse.php#213
      Bindings
      • 0: 1170
      Backtrace
      • 19. app/Models/Course.php:213
      • 25. view::frontend.course.course-details:169
      • 27. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • 28. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 29. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
    • select * from `difficulty_levels` where `difficulty_levels`.`id` = 2 limit 1
      1.84msvlms_beta_onlinecourse-details.blade.php#181
      Bindings
      • 0: 2
      Backtrace
      • 20. view::frontend.course.course-details:181
      • 22. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
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