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3","description":"

🌟🌟🌟🌟🌟 \"Thorough and well explained.\"\n

🌟🌟🌟🌟🌟 \"The instructor is amazing at explaining the concepts and working through them. I wish the instructor taught all of math.\"\n

The curriculum includes:\n

Three-dimensional coordinate systems\n\t
1. Plotting points in three dimensions
2. Distance between points in three dimensions
3. Center, radius, and equation of the sphere
4. Describing a region in three-dimensional space
5. Using inequalities to describe the region
Sketching graphs and level curves\n\t
1. Sketching graphs of multivariable functions
2. Matching the function with the graph and level curves
Lines and planes\n\t
1. Vector and parametric equations of a line
2. Parametric and symmetric equations of a line
3. Symmetric equations of a line
4. Parallel, intersecting, skew and perpendicular lines
5. Equation of a plane
6. Intersection of a line and a plane
7. Parallel, perpendicular and angle between planes
8. Parametric equations for the line of intersection of two planes
9. Symmetric equations for the line of intersection of two planes
10. Distance between a point and a line
11. Distance between a point and a plane
12. Distance between parallel planes
Cylinders and quadric surfaces\n\t
1. Reducing equations to standard form
2. Sketching the surface
3. Traces to sketch and identify the surface
Limits and continuity\n\t
1. Domains
2. Limits
3. Precise definition of the limit
4. Discontinuities
Partial derivatives\n\t
1. Partial derivatives in two variables
2. Partial derivatives in three or more variables
3. Second order and higher order partial derivatives
Differentials\n\t
1. Differential of a multivariable function
Chain rule\n\t
1. Chain rule for multivariable functions
2. Chain rule and tree diagrams
Implicit differentiation
1. Implicit differentiation for multivariable functions
Directional derivatives\n\t
1. In the direction of the vector
2. In the direction of the angle
Linear approximation and linearization\n\t
1. Linear approximation
2. Linearization
Gradient vectors\n\t
1. Gradient vectors
2. Gradient vectors and the tangent plane
3. Maximum rate of change and its direction
Tangent planes and normal lines\n\t
1. Equation of the tangent plane
2. Normal line to the surface
Optimization\n\t
1. Critical points
2. Second derivative test
3. Local extrema and saddle points
4. Global extrema
5. Extreme value theorem, extrema in the set D
Applied optimization\n\t
1. Maximum product of three real numbers
2. Maximum volume of a rectangular box inscribed in a sphere
3. Minimum distance between the point and the plane
4. Points on the cone closest to the given point
Lagrange multipliers\n\t
1. Two dimensions and one constraint
2. Three dimensions and one constraint
3. Three dimensions and two constraints
Approximating double integrals\n\t
1. With rectangles
2. Midpoint rule
3. Riemann sums
Double integrals\n\t
1. Average value over the region
2. Double integrals and iterated integrals
3. Type I regions and type II regions (type 1 and type 2)
4. Surface area
5. Volume of the solid
6. Changing the order of integration
Double polar integrals\n\t
1. Changing iterated integrals to polar coordinates
2. Changing double integrals to polar coordinates
3. Sketching area in polar coordinates
4. Area in polar coordinates
5. Volume in polar coordinates
Applications of double integrals\n\t
1. Mass and center of mass of the lamina
2. Moments of inertia and radii of gyration
Approximating triple integrals\n\t
1. Midpoint rule
Triple integrals\n\t
1. Iterated triple integrals and triple integrals
2. Average value over the region
3. Volume of the solid
4. Expressing the integral six ways
5. Type I regions, type II regions, and type III regions (type 1, type 2 and type 3)
Triple integrals in cylindrical coordinates\n\t
1. Cylindrical coordinates
2. Changing triple integrals to cylindrical coordinates
3. Volume of the solid
Triple integrals in spherical coordinates\n\t
1. Spherical coordinates
2. Changing triple integrals to spherical coordinates
3. Volume of the solid
Change of variables\n\t
1. Jacobian of the transformation in two variables
2. Jacobian of the transformation in three variables
3. Evaluating double integrals
4. Equations of the transformation
5. Image of the set under the transformation
Applications of triple integrals\n\t
1. Mass and center of mass of the lamina
2. Moments of inertia
Introduction to vectors\n\t
1. Vector from two points
2. Combinations of vectors
3. Sum of two vectors
4. Copying vectors and using them to find combinations
5. Unit vector in the direction of the given vector
6. Angle between a vector and the x-axis
7. Magnitude and angle of the resultant force
Dot products\n\t
1. Dot product of two vectors
2. Angle between two vectors
3. Orthogonal, parallel, or neither
4. Acute angle between the lines
5. Acute angle between the curves
6. Direction cosines and direction angles
7. Scalar equation of a line
8. Scalar equation of a plane
9. Scalar and vector projections
Cross products\n\t
1. Cross product of two vectors
2. Vector orthogonal to the plane
3. Volume of the parallelepiped given vectors
4. Volume of the parallelepiped given adjacent edges
5. Scalar triple product for coplanar vectors
Vector functions and space curves\n\t
1. Domain of the vector function
2. Limit of the vector function
3. Sketching the vector equation
4. Projections of the curve
5. Vector and parametric equations of a line segment
6. Vector function for the curve of intersection of two surfaces
Derivatives and integrals of vector functions\n\t
1. Derivative of a vector function
2. Unit tangent vector
3. Parametric equations of the tangent line
4. Integral of a vector function
Arc length and curvature\n\t
1. Arc length
2. Reparametrizing the curve
3. Unit tangent vectors and unit normal vectors
4. Curvature
5. Maximum curvature
6. Normal and osculating planes
Velocity and acceleration\n\t
1. Velocity and acceleration vectors
2. Velocity, acceleration and speed, given position
3. Velocity and position given acceleration and initial conditions
4. Tangential components and normal components of acceleration
Line integrals\n\t
1. Line integral of a curve
2. Line integral of a vector function
3. Conservative vector fields
4. Potential function of a conservative vector field
5. Independence of path
6. Work done by the force field
7. Open, connected, and simply-connected regions
Green's theorem\n\t
1. Green's theorem with one region
2. Green's theorem with two regions
Curl and divergence\n\t
1. Curl and divergence of a vector field
2. Potential function of a conservative vector field
Parametric surfaces and areas\n\t
1. Points on the surface
2. Surface of the vector equation
3. Parametric representation of the surface
4. Tangent plane to the parametric surface
5. Area of the surface
Surface integrals\n\t
1. Surface integrals
Stokes' and divergence theorem\n\t
1. Stokes theorem
2. Divergence theorem

About the Author
\n

Krista King is a math tutor, online educator, and the creator of KristaKingMath.com. Her YouTube channel has more than 43.5 million views, and her online courses have helped more than 244,000 students.\n

\"Krista is very very quick to respond. I've had a few questions and I usually didn't have to wait much longer than a day to get an answer. Not only that, but she obviously spent time answering to make sure I understood the content.\" - Morgan Gray\n

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By signing up for the Calculus 3 course, you'll gain access to:\n

Calculus 3, and every other Krista King Math course
Step-by-step videos
Course notes and flashcards
Practice quizzes
Bonus practice workbooks
Comprehensive formula sheets
Summary study sheets
Practice final exams

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