Calculus 2
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 standalone 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
Course Content
Calculus 2

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