Home »Mathematics »The University of New South Wales » Engineering Mathematics



Engineering Mathematics

The University of New South Wales Course , Prof. Chris Tisdell       Subscribe to feed

Lights off      

Lecture 28: Evaluating challenging integrals via differentiation: Leibniz rule

Embed
Download:   MP4, FLV and 3GP 1681 views

SEE: Guide to Download The University of New South Wales Video Lecture

Lecture Details :

I discuss and solve a challenging integral. The method involves differentiation and then the solution of the resultant differential equation. The so-called Leibniz rule for differentiating integrals is applied during the process. Such an example is seen in 2nd-year university mathematics.

Course Description :

Topics covered will include important aspects of applied mathematics used in engineering, such as: multivariable calculus; vector calculus; differential equations; Laplace transforms; Fourier series.

Other Resources :


Other Mathematics Courses

» check out the complete list of Mathematics lectures          

 

Mathematics Lecture Notes

 

Comments

Post your Comments

  1. Vector Revision: Chris Tisdell UNSW Sydney
  2. Intro to curves and vector functions: Chris Tisdell UNSW Sydney
  3. Limits of vector functions: Chris Tisdell UNSW Sydney
  4. Calculus of vector functions - 1 variable. Chris Tisdell UNSW Sydney
  5. Calculus of vector functions tutorial: Chris Tisdell UNSW Sydney
  6. Vector functions of one variable tutorial. Chris Tisdell UNSW Sydney
  7. Vector functions tutorial. Chris Tisdell UNSW Sydney
  8. Intro to functions of two variables: Chris Tisdell UNSW Sydney
  9. Partial derivatives. Chris Tisdell UNSW Sydney
  10. 2 variable functions: graphs + limits tutorial. Chris Tisdell UNSW Sydney
  11. Multivariable chain rule and differentiability: Chris Tisdell UNSW Sydney
  12. Chain rule: partial derivative of $arctan (y/x)$ w.r.t. $x$
  13. Chain rule: identity involving partial derivatives
  14. Chain rule & partial derivatives
  15. Partial derivatives and PDEs tutorial
  16. Multivariable chain rule tutorial. Chris Tisdell UNSW Sydney
  17. Gradient and directional derivative. Chris Tisdell UNSW Sydney
  18. Gradient of a function.
  19. Tutorial on gradient and tangent plane. Chris Tisdell UNSW Sydney
  20. Directional derivative of $f(x,y)$
  21. Gradient & directional derivative tutorial. Chris Tisdell UNSW Sydney
  22. Tangent plane approximation and error estimation. Chris Tisdell UNSW Sydney
  23. Partial derivatives and error estimation
  24. Multivariable Taylor Polynomials. Chris Tisdell UNSW Sydney
  25. Taylor polynomials: functions of two variables
  26. Differentiation under integral signs: Leibniz rule. Chris Tisdell UNSW Sydney
  27. Leibniz' rule: Integration via differentiation under integral sign
  28. Evaluating challenging integrals via differentiation: Leibniz rule
  29. Critical points of functions. Chris Tisdell UNSW Sydney
  30. Second derivative test: two variables. Chris Tisdell UNSW Sydney
  31. How to find critical points of functions
  32. Critical points + 2nd derivative test: Multivariable calculus
  33. Critical points + 2nd derivative test: Multivariable calculus
  34. How to find and classify critical points of functions
  35. Lagrange multipliers. Chris Tisdell UNSW Sydney.
  36. Lagrange multipliers: Extreme values of a function subject to a constraint
  37. Lagrange multipliers example
  38. Lagrange multiplier example: Minimizing a function subject to a constraint
  39. 2nd derivative test, max / min and Lagrange multipliers tutorial. Chris Tisdell UNSW Sydney
  40. Lagrange multipliers: 2 constraints. Chris Tisdell UNSW Sydney
  41. Intro to vector fields. Chris Tisdell UNSW Sydney
  42. What is the divergence? Chris Tisdell UNSW Sydney
  43. Divergence + Vector fields. Chris Tisdell UNSW Sydney
  44. Divergence of a vector field: Vector Calculus
  45. What is the curl? Chris Tisdell UNSW Sydney
  46. Curl of a vector field (ex. no.1): Vector Calculus
  47. Curl of a vector field (ex. no.2): Vector calculus
  48. Line integrals. Chris Tisdell UNSW Sydney
  49. Integration over curves. Chris Tisdell UNSW Sydney
  50. Path integral (scalar line integral) from vector calculus