Engineering Mathematics 2 ( M2 )
October 12, 2020 2021-02-26 14:01Engineering Mathematics 2 ( M2 )
Engineering Mathematics 2 ( M2 )
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Unit One
First Order Differential Equations ( ODE )
- 1. Differential Equations – Introduction ( Watch Free )
- 2. Applications of Differential Equations – Newton’s Law of Cooling ( Watch Free )
- 3. Types of Differential Equations ( Watch Free )
- 4. Order and Degree of Differential Equations ( Watch Free )
- 5. Solutions and Types ( Watch Free )
- 6. Formation of Differential Equation Solution and Types
- 7. Example 1 – Formation of Differential Equations
- 8. Families of Plane Curves
- 9. Example – Families of Plane Curves
- 10. Differential Equation – First Order – First Degree
- 11. Example 1 – Variable Separable Method
- 12. Example 2 – Variable Separable Method
- 13. Equation reduced to Variable Separable form
- 14. Example 1 – Equation reduced to Variable Separable Form
- 15. Homogenius Differential Equations – Introduction
- 16. General Solution of Homogenous Differential Equations
- 17. Homogeneous Differential Equations – Example 1
- 18. Homogeneous Differential Equations – Example 2
- 19. Homogeneous Differential Equations – Example 3
- 20. Non-Homogeneous Differential Equations – Introduction
- 21. Non-Homogeneous Differential Equations – Example 1
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Unit Two
- 1. Exact Differential Equations – Introduction
- 2. Solving Exact Differential Equations
- 3. Exact Differential Equations – Example 1
- 4. Exact Differential Equations – Example 2
- 5. Exact Differential Equations – Example 3
- 6. Equations Reducible to Exact Equations
- 7. Inspection Method – Finding Integrating Factors
- 8. Finding Integrating Factors – Inspection Method – Example 1
- 9. Solving the Differential Equations
- 10. Solve Differential Equations using Operator Form
- 11. Complete Solution of Differential Equation
- 12. Solve Differential Equations
- 13. General Solution of Differential Equation by Auxillary Form
- 14. General Solution for Differential Equation
- 15. Solve Differential Equation
- 16. Solve Differential Equation Using Operator Form
- 17. Solving Differential Equation
- 18. Solving Differential Equation using Auxillary Form
- 19. Solving Differential Equation
- 20. Finding Particular Integral of a Differential Equation
- 21. Solve the Differential Equation
- 22. General Solution for Differential Equation
- 23. General Solution for Differential Equation – Example 2
- 24. General Solution for Differential Equation – Example 3
- 25. Particular Integral for Differential Equations
- 26. Differential Equations – Variation of Parameters
- 27. Differential Equations – Variation of Parameters – Example 2
- 28. Euler – Cauchy Equation – Introduction
- 29. General Solution for Differential Equation – Example 1
- 30. General Solution for Differential Equation – Example 2
- 31. General Solution for Differential Equation – Examplle 3
- 32. Legrande’s Linear Integral
- 33. Solve the Differential Equation
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Unit Three
- 1. Multiple Integrals
- 2. Double Integrals – Example 1
- 3. Evaluate Double Integral – Example 2
- 4. Evaluate Double Integral – Example 3
- 5. Evaluate Double Integral in Positive Quadrant
- 6. Evaluate Double Integral by Converting into Polar Co-Ordinates
- 7. Calculate the area between two circles
- 8. Volume of Double Integral
- 9. Applications of Double Integrals
- 10. Transformation of Co-Ordinates
- 11. Change of Order of Integration
- 12. Evaluate Double Integral by changing the order of Integration
- 13. Evaluate Double Integral by Changing the order of Integration – Example 2
- 14. Change of Variables from Cartesian to Spherical Polar Co-Ordinates
- 15. Change of Variables from Cartesian to Cylindrical Polar Co-Ordinates
- 16. Mass of Plane of Lamina
- 17. Evaluate Double Integral – Area bounded by Positive Quadrant of the circle
- 18. Evaluate Double Integral – Area bounded by Hyperbola
- 19. Evaluate Double Integral – Area bounded by Ellipse
- 20. Evaluate Double Integral – Polar Co-Ordinates
- 21. Triple Integrals – Introduction
- 22. Center of Gravity
- 23. Triple Integrals – Example 1
- 24. Triple Integrals – Example 2
- 25. Triple Integrals – Space Bound Problem
- 26. Triple Integrals – Change of Variables
- 27. Change of Variables from Cartesian to Cylinder
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Unit Four
Vector Differentiation
- 1. Vector Differential Operators – Introduction
- 2. Divergence of a Vector – Introduction
- 3. Example 1 – Divergence
- 4. Example 2 – Divergence
- 5. Summary
- 6. Example 3 – Divergence
- 7. Example 4 – Divergence
- 8. Example 5 – Divergence
- 9. Problem on Solenoidal Vector
- 10. Example 1 – Directional Derivative
- 11. Example 2 – Directional Derivative
- 12. Curl of a Vector
- 13. Problems on Irrotational Vector
- 14. Problems on Divergence and Curl
- 15. Irrotational Vector – Example
- 16. Vector Identities
- 17. Vector Identities – Example 2
- 18. Vector Identities – Example 3
- 19. Vector Identities – Example 4
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Unit Five
Vector Integration
- 1. Introduction to Vector Integration
- 2. Vector Integration – Introduction and Types
- 3. Problems on Vector Integration
- 4. Line Integral – Example
- 5. Problems on Vector Integration
- 6. Evaluation of Work Done – Example 1
- 7. Evaluation of Work Done – Example 2
- 8. Problems on Vector Integration
- 9. Evaluation of Work Done – Example 3
- 10. Evaluation of Work Done – Example 4