Calculus 2

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About Course

This Calculus course includes several techniques of integration, improper integrals, antiderivatives, application of the definite integral, differential equations, and approximations using Taylor polynomials and series. This course is required for engineering, physics, and mathematics majors.

This course contains a series of video tutorials that are broken up into various levels. Each video builds upon the previous one. Level I videos lay out the theoretical framework to successfully tackle problems covered in the next videos.

These videos can be used as a stand-alone course or as a supplement to your current course.

This course is for anyone who wants to fortify their understanding of calculus II

 

Who this course is for:

  • College Students
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What Will You Learn?

  • Fortify your understanding of Calculus II.

Course Content

Calculus 2

  • 01 – Introduction
    00:00
  • 02 – Vectors
    00:00
  • 03 – The Cartesian coordinate system
    00:00
  • 04 – The dot product
    00:00
  • 05 – The dot product – continued
    00:00
  • 06 – The cross product
    00:00
  • 07 – The triple product
    00:00
  • 08 – The equation of a plane
    00:00
  • 09 – Planes – continued
    00:00
  • 10 – The equation of a line
    00:00
  • 11 – Lines – continued
    00:00
  • 12 – Lines – continued
    00:00
  • 13 – Lines and planes
    00:00
  • 14 – Surfaces
    00:00
  • 15 – Surfaces – continued
    00:00
  • 16 – Surfaces – continued
    00:00
  • 17 – Curves
    00:00
  • 18 – Topology
    00:00
  • 19 – Sequences
    00:00
  • 20 – Functions and graphs
    00:00
  • 21 – Level curves
    00:00
  • 22 – Level surfaces
    00:00
  • 23 – Limits
    00:00
  • 24 – Properties of limits
    00:00
  • 25 – Limits along curves
    00:00
  • 26 – Limits and polar coordinates
    00:00
  • 27 – Iterated limits
    00:00
  • 28 – Continuity
    00:00
  • 29 – The intermediate value theorem
    00:00
  • 30 – Tangents to curves
    00:00
  • 31 – Partial derivatives
    00:00
  • 32 – Calculating partial derivatives
    00:00
  • 33 – The tangent plane
    00:00
  • 34 – Differentiability
    00:00
  • 35 – Differentiability – continued
    00:00
  • 36 – Differentiability, continuity and partial derivatives
    00:00
  • 37 – Directional derivatives
    00:00
  • 38 – The gradient
    00:00
  • 39 – The chain rule
    00:00
  • 40 – Higher order derivatives
    00:00
  • 41 – The Taylor polynomial
    00:00
  • 42 – The implicit function theorem
    00:00
  • 43 – The implicit function theorem – continued
    00:00
  • 44 – Proof of the implicit function theorem
    00:00
  • 45 – The gradient is perpendicular to level surfaces
    00:00
  • 46 – The implicit function theorem for systems of equations
    00:00
  • 47 – The inverse function theorem
    00:00
  • 48 – Minima and maxima
    00:00
  • 49 – Classification of critical points
    00:00
  • 50 – Exterma subject to constraints
    00:00
  • 51 – The method of Lagrange multipliers
    00:00
  • 52 – A two variable example of Lagrange multipliers
    00:00
  • 53 – A three variable example of Lagrange multipliers
    00:00
  • 54 – Proof of the Lagrange multipliers theorem
    00:00
  • 55 – Lagrange multipliers for several constraints
    00:00
  • 56 – Double integrals
    00:00
  • 57 – Properties of double integrals
    00:00
  • 58 – Iterated integrals
    00:00
  • 59 – Simple domains
    00:00
  • 60 – Double integrals on simple domains
    00:00
  • 61 – Examples of iterated integrals
    00:00
  • 62 – Changing order of integration
    00:00
  • 63 – Change of variables
    00:00
  • 64 – Examples of changing variables
    00:00
  • 65 – Examples of changing variables – continued
    00:00
  • 66 – The requirement that J is not 0
    00:00
  • 67 – The geometric meaning of J
    00:00
  • 68 – A cool example
    00:00
  • 69 – Triple integrals
    00:00
  • 70 – Triple integrals over simple domains
    00:00
  • 71 – Cylindrical coordinates
    00:00
  • 72 – Spherical coordinates
    00:00
  • 73 – One more example of changing variables
    00:00
  • 74 – The length of a curve
    00:00
  • 75 – Line integrals of scalar functions
    00:00
  • 76 – Line integrals of vector fields
    00:00
  • 77 – Green’s theorem
    00:00
  • 78 – Finding area with Green’s theorem
    00:00
  • 79 – Evaluating line integrals with Green’s theorem
    00:00
  • 80 – Conservative fields
    00:00
  • 81 – Simply connected domains
    00:00
  • 82 – Conservative fields in simply connected domains
    00:00
  • 83 – Conservative fields in simply connected domains – examples
    00:00
  • 84 – Surfaces
    00:00
  • 85 – Area of a surface
    00:00
  • 86 – Surface integrals of scalar functions
    00:00
  • 87 – Surface integrals of vector fields
    00:00
  • 88 – Surface integrals of vector fields – example
    00:00
  • 89 – The divergence
    00:00
  • 90 – The divergence theorem (Gauss)
    00:00
  • 91 – More on the divergence
    00:00
  • 92 – The curl
    00:00
  • 93 – Stokes’ theorem
    00:00
  • 94 – Using Stokes’ theorem
    00:00
  • 95 – Using Stokes’ theorem – continued
    00:00
  • 96 – Conservative fields in 3 dimensions
    00:00
  • 97 – An example of a conservative field
    00:00
  • 98 – More on the curl
    00:00
  • 99 – A review problem
    00:00
  • 100 – A review problem – continued
    00:00

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