In this video, Krista King from integralCALC Academy uses multiple examples, showing how to find the discontinuities in a multivariable function.

1. Partial Derivatives
2. Second Order Partial Derivatives
3. Equation of the Tangent Plane in Two Variables
4. Normal Line to the Surface
5. Linear Approximation in Two Variables
6. Linearization of a Multivariable Function
7. Differential of the Multivariable Function
8. Chain Rule for Partial Derivatives of Multivariable Functions
9. Chain Rule and Tree Diagrams of Multivariable Functions
10. Implicit Differentiation for Partial Derivatives of Multivariable Functions
11. Directional Derivatives
12. Gradient Vectors
13. Gradient Vectors and the Tangent Plane
14. Gradient Vectors and Maximum Rate of Change
15. Second Derivative Test: Two Variables
16. Local Extrema and Saddle Points of a Multivariable Function
17. Global Extrema in Two Variables
18. Extreme Value Theorem and Extrema in the Set D
19. Max Product of Three Real Numbers
20. Max Volume of a Rectangular Box Inscribed in a Sphere
21. Points on the Cone Closest to a Point
22. Lagrange Multipliers (Part I)
23. Lagrange Multipliers (Part II)
24. Lagrange Multipliers in Three Dimensions with Two Constraints
25. Midpoint Rule to Approximate Volume of a Double Integral
26. Riemann Sums to Approximate Volume of a Double Integral
27. Average Value of a Double Integral
28. Iterated Integrals
29. Double Integrals
30. Double Integrals of Type I and Type II Regions
31. Double Integrals to Find the Volume of the Solid
32. Double Integrals to Find Surface Area
33. Converting Iterated Integrals to Polar Coordinates
34. Converting Double Integrals to Polar Coordinates
35. Sketching the Region Given by a Double Polar Integral
36. Double Polar Integral to Find Area
37. Double Polar Integral to Find the Volume of the Solid
38. Double Integrals to Find Mass and Center of Mass of the Lamina
39. Midpoint Rule for Triple Integrals
40. Average Value of the Triple Integral
41. Triple Iterated Integrals
42. Triple Integrals
43. Triple Integrals to Find Volume of the Solid
44. Expressing a Triple Iterated Integral Six Ways
45. Mass and Center of Mass with Triple Integrals
46. Moments of Inertia with Triple Integrals
47. Cylindrical Coordinates
48. Converting Triple Integrals to Cylindrical Coordinates
49. Volume in Cylindrical Coordinates
50. Spherical Coordinates
51. Triple Integral in Spherical Coordinates to Find Volume
52. Jacobian of the Transformation (2x2)
53. Jacobian of the Transformation (3x3)
54. Plotting Points in Three Dimensions
55. Distance Formula for Three Variables
56. Equation of a Sphere, Plus Center and Radius
57. Describing a Region in 3D Space
58. Using Inequalities to Describe a Region in 3D Space
59. Finding a Vector From Two Points
60. Vector Addition and Combinations of Vectors
61. Sum of Two Vectors
62. Copying Vectors to Find Combinations of Vectors
63. Unit Vector in the Direction of the Given Vector
64. Angle Between a Vector and the x-axis
65. Magnitude and Angle of the Resultant Force
66. Dot Product of Two Vectors
67. Angle Between Two Vectors
68. Orthogonal, Parallel or Neither (Vectors)
69. Acute Angle Between the Lines (Vectors)
70. Acute Angles Between the Curves (Vectors)
71. Direction Cosines and Direction Angles (Vectors)
72. Scalar Equation of a Line
73. Scalar Equation of a Plane
74. Scalar and Vector Projections
75. Cross Product
76. Vector Orthogonal to the Plane
77. Volume of the Parallelepiped Determined by Vectors
78. Volume of the Parallelepiped with Adjacent Edges
79. Scalar Triple Product to Verify the Vectors are Coplanar
80. Vector and Parametric Equations of the Line
81. Parametric and Symmetric Equations of the Line
82. Symmetric Equations of a Line
83. Parallel, Intersecting, Skew and Perpendicular Lines
84. Equation of the Plane Using Vectors
85. Point of Intersection of a Line and a Plane
86. Parallel, Perpendicular, and Angle Between Planes
87. Parametric Equations for the Line of Intersection of Two Planes
88. Symmetric Equations for the Line of Intersection of Two Planes
89. Distance Between a Point and a Line (Vectors)
90. Distance Between a Point and a Plane (Vectors)
91. Distance Between Parallel Planes (Vectors)
92. Sketching the Quadric Surface
93. Reducing a Quadric Surface Equation to Standard Form
94. Domain of the Vector Function
95. Limit of the Vector Function
96. Sketching the Vector Equation
97. Projections of the Curve Onto the Coordinate Axes
98. Vector and Parametric Equations of the Line Segment
99. Vector Function for the Curve of Intersection of Two Surfaces
100. Derivative of the Vector Function
101. Unit Tangent Vector
102. Parametric Equations of the Tangent Line (Vectors)
103. Integral of the Vector Function
104. Green's Theorem: One Region
105. Green's Theorem: Two Regions
106. Linear Differential Equations
107. Circuits and Linear Differential Equations
108. Linear Differential Equation Initial Value Problem
109. Differential Equations
110. Change of Variable to Solve a Differential Equations
111. Separable Differential Equations Initial Value Problem
112. Mixing Problems with Separable Differential Equations
113. Euler's Method (Part I)
114. Euler's Method (Part II)
115. Euler's Method (Part III)
116. Sketching Direction Fields
117. Population Growth
118. Logistic Growth Model of a Population
119. Predator-Prey Systems
120. Second-Order Differential Equations
121. Equal Real Roots of Second-Order Homogeneous Differential Equations
122. Complex Conjugate Roots of Second-Order Homogeneous Differential Equations
123. Second-Order Differential Equations: Initial Value Problems (Example 1)
124. Boundary Value Problem, Second-Order Homogeneous Differential Equation, and Distinct Real Roots
125. Boundary Value Problem, Second-Order Homogeneous Differential Equation, and Complex Conjugate Roots
126. Second-Order Differential Equations: Working Backwards
127. Second-Order Non-Homogeneous Differential
128. Variation of Parameters for Differential Equations
129. Second-Order Non-Homogeneous Differential Equations: Initial Value Problem
130. Laplace Transforms Using the Definition
131. Laplace Transforms Using a Table
132. Initial Value Problems with Laplace Transforms
133. Laplace Transforms and Integration by Parts with Three Functions
134. Inverse Laplace Transform
135. Convolution Integral for Initial Value Problems
136. Exact Differential Equations
137. Lagrange Multipliers and Three Dimensions, One Constraint
138. Limit of the Multivariable Function
139. Minimum Distance Between the Point and the Plane
140. Precise Definition of the Limit for Multivariable Functions
141. Critical Points of Multivariable Functions
142. Discontinuities of a Multivariable Function
143. Domain of a Multivariable Function
144. Arc Length of a Vector Function
145. Area of the Surface
146. Tangential and Normal Components of the Acceleration Vector
147. Curl and Divergence
148. Curvature of the Vector Function
149. Independence of Path
150. Line Integral of a Curve
151. Line Integral of a Vector Function
152. Maximum Curvature of the Function
153. Normal and Osculating Planes
154. Parametric Representation of the Surface
155. Points on the Surface
156. Potential Function of a Conservative Vector Field
157. Potential Function of the Conservative Vector Field to Evaluate a Line Integral
158. Potential Function of the Conservative Vector Field, Three Dimensions
159. Re-parametrizing the Curve in Terms of Arc Length

In this course, Krista King from the integralCALC Academy covers a range of topics in Multivariable Calculus, including Vectors, Partial Derivatives, Multiple Integrals, and Differential Equations.