Taylor Polynomials: Functions of Two Variables 
Taylor Polynomials: Functions of Two Variables
by UNSW / Christopher Tisdell
Video Lecture 42 of 88
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Views: 1,650
Date Added: July 26, 2011

Lecture Description

This video lecture, part of the series Vector Calculus by Prof. Christopher Tisdell, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

- The CosmoLearning Team

Course Index

  1. Applications of Double integrals
  2. Path Integrals: How to Integrate Over Curves
  3. What is a Vector Field?
  4. What is the Divergence?
  5. What is the Curl?
  6. What is a Line Integral?
  7. Applications of Line Integrals
  8. Fundamental Theorem of Line Integrals
  9. What is Green's Theorem?
  10. Green's Theorem
  11. Parametrised Surfaces
  12. What is a Surface Integral? (Part I)
  13. More On Surface Integrals
  14. Surface Integrals and Vector Fields
  15. Divergence Theorem of Gauss
  16. How to Solve PDEs via Separation of Variables and Fourier Series
  17. Vector Revision
  18. Intro to Curves and Vector Functions
  19. Limits of Vector Functions
  20. Calculus of Vector Functions: One Variable
  21. Calculus of Vector Functions Tutorial
  22. Vector Functions Tutorial
  23. Intro to Functions of Two Variables
  24. Limits of Functions of Two Variables
  25. Partial Derivatives
  26. Partial Derivatives and PDEs Tutorial
  27. Multivariable Functions: Graphs and Limits
  28. Multivariable Chain Rule and Differentiability
  29. Chain Rule: Partial Derivative of $\arctan (y/x)$ w.r.t. $x$
  30. Chain Rule & Partial Derivatives
  31. Chain Rule: Identity Involving Partial Derivatives
  32. Multivariable Chain Rule
  33. Leibniz' Rule: Integration via Differentiation Under Integral Sign
  34. Evaluating Challenging Integrals via Differentiation: Leibniz Rule
  35. Gradient and Directional Derivative
  36. Gradient and Directional Derivative
  37. Directional dDerivative of $f(x,y)$
  38. Tangent Plane Approximation and Error Estimation
  39. Gradient and Tangent Plane
  40. Partial Derivatives and Error Estimation
  41. Multivariable Taylor Polynomials
  42. Taylor Polynomials: Functions of Two Variables
  43. Multivariable Calculus: Limits, Chain Rule and Arc Length
  44. Critical Points of Functions
  45. How to Find Critical Points of Functions
  46. How to Find Critical Points of Functions
  47. Second Derivative Test: Two Variables
  48. Multivariable Calculus: Critical Points and Second Derivative Test
  49. How to Find and Classify Critical Points of Functions
  50. Lagrange Multipliers
  51. Lagrange Multipliers: Two Constraints
  52. Lagrange Multipliers: Extreme Values of a Function Subject to a Constraint
  53. Lagrange Multipliers Example
  54. Lagrange multiplier Example: Minimizing a Function Subject to a Constraint
  55. Second Derivative Test, Max/Min and Lagrange Multipliers
  56. Intro to Jacobian Matrix and Differentiability
  57. Jacobian Chain Rule and Inverse Function Theorem
  58. Intro to Double Integrals
  59. Double Integrals Over General Regions
  60. Double Integrals: Volume Between Two Surfaces
  61. Double Integrals: Volume of a Tetrahedron
  62. Double Integral
  63. Double Integrals and Area
  64. Double Integrals in Polar Co-ordinates
  65. Reversing Order in Double Integrals
  66. Double Integrals: Reversing the Order of Integration
  67. Applications of Double Integrals
  68. Double Integrals and Polar Co-ordinates
  69. Double Integrals
  70. Centroid and Double Integral
  71. Center of Mass, Double Integrals and Polar Co-ordinates
  72. Triple Integral
  73. Triple integrals in Cylindrical and Spherical Coordinates
  74. Triple integrals & Center of Mass
  75. Change of Variables in Double Integrals
  76. Path Integral (Scalar Line Integral) From Vector Calculus
  77. Line Integral Example in 3D-Space
  78. Line Integral From Vector Calculus Over a Closed Curve
  79. Line Integral Example From Vector Calculus
  80. Divergence of a Vector Field
  81. Curl of a Vector Field (ex. no.1)
  82. Curl of a Vector Field (ex. no.2)
  83. Divergence Theorem of Gauss
  84. Intro to Fourier Series and How to Calculate Them
  85. How to Compute a Fourier Series: An Example
  86. What are Fourier Series?
  87. Fourier Series
  88. Fourier Series and Differential Equations

Course Description

In this course, Prof. Chris Tisdell gives 88 video lectures on Vector Calculus. This is a series of lectures for "Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009 and Session 1, 2011. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences. There is an emphasis on examples and also on proofs. Dr Chris Tisdell is Senior Lecturer in Applied Mathematics.


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