Mô tả

HOW BECOME A CALCULUS 3 MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:

This 526-lesson course includes video and text explanations of everything from Calculus 3, and it includes 161 quizzes (with solutions!) and an additional 40 workbooks with extra practice problems, to help you test your understanding along the way. Become a Calculus 3 Master is organized into the following sections:

  • Partial Derivatives

  • Multiple Integrals

  • Vectors



AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.



HERE'S WHAT SOME STUDENTS OF BECOME A CALCULUS 3 MASTER HAVE TOLD ME:

  • “Krista is an excellent teacher and her course is comprehensive. She is a clear communicator, makes complex calculus topics easily understandable, and uses video tools expertly.” - John

  • “One of the best instructors that I have ever learned from. She has a way of explaining topics so clearly that they become fairly easy. I took her calculus 2 course because I had a hard time understanding my teacher. I finished the class with a B+ mostly because I watched her videos, read the outline that she provides and practiced problems in the book.” - Desarael B.

  • “I have taken all 3 of her classes and sadly she doesn't have anymore. I honestly feel like more people including teachers should take notes on how she goes about teaching these difficult concepts. I flew through this class, not because it is easy, but because she makes it so easy to grasp everything. I am honestly bummed that this is the last leg of my journey with this incredible teacher. If people were half as good as she is at teaching there would be a lot more people in STEM. P.S. I am writing this review 2 months since completing her Calc 3 and have since gone on to take Partial Differentials, Linear Algebra, and Analysis. There would be absolutely no way I would've been able to learn this much in so little time without her. She gave me such a strong grasp on math and how to approach problems that I feel I have the tools to really explore so much more. Without her I'm sure I would still be learning derivatives. I would recommend this class to anyone going to college, in college, or out of college. These classes are some of the best reference materials you'll ever have. The only thing I do wish is to have some quizzes at least for the ODE's to really cement an understanding of the math. Already miss learning from you Krista! Thanks for everything you've helped me learn.” - Morgan G.

  • “This is the PERFECT GRE MATH SUBJECT TEST review for Calc III and DE. Thank you!!” - Carter R.



YOU'LL ALSO GET:

  • Lifetime access to Become a Calculus 3 Master

  • Friendly support in the Q&A section

  • Udemy Certificate of Completion available for download

  • 30-day money back guarantee


Enroll today!

I can't wait for you to get started on mastering calculus 3.

- Krista :)



Bạn sẽ học được gì

Partial Derivatives, including higher order partial derivatives, multivariable chain rule and implicit differentiation

Multiple Integrals, including approximating double and triple integrals, finding volume, and changing the order of integration

Vectors, including derivatives and integrals of vector functions, arc length and curvature, and line and surface integrals

Yêu cầu

  • You should have a decent foundation (but it doesn't have to be perfect! :D) in Algebra.
  • If you have some experience with Trigonometry and Precalculus, that will definitely be helpful, but it's not absolutely necessary.
  • A good foundation in Calculus 1 (derivatives) and Calculus 2 (integrals) is required for this course.

Nội dung khoá học

41 sections

Getting started

4 lectures
What we'll learn in this course
02:58
How to get the most out of this course
01:26
Download the formula sheet
00:19
The EVERYTHING download
00:24

Partial Derivatives - Three-dimensional coordinate systems

15 lectures
Introduction to three-dimensional coordinate systems
00:20
Plotting points in three dimensions
00:00
Plotting points in three dimensions
10:47
Plotting points in three dimensions
3 questions
Distance between points in three dimensions
00:00
Distance between points in three dimensions
10:16
Distance between points in three dimensions
3 questions
Center, radius, and equation of the sphere
00:00
Center, radius, and equation of the sphere
09:57
Center, radius, and equation of the sphere
3 questions
Describing a region in three-dimensional space
05:06
Describing a region in three-dimensional space
3 questions
Using inequalities to describe the region
05:48
Using inequalities to describe the region
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Sketching graphs and level curves

4 lectures
Introduction to sketching graphs and level curves
00:21
Sketching level curves of multivariable functions
18:00
Sketching level curves of multivariable functions
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Lines and planes

33 lectures
Introduction to lines and planes
00:20
Vector, parametric and symmetric equations of a line
00:00
Vector and parametric equations of a line
06:42
Vector and parametric equations of a line
3 questions
Parametric and symmetric equations of a line
08:38
Parametric and symmetric equations of a line
3 questions
Symmetric equations of a line
02:58
Symmetric equations of a line
3 questions
Parallel, intersecting, skew, and perpendicular lines
Processing..
Parallel, intersecting, skew, and perpendicular lines
10:32
Parallel, intersecting, skew, and perpendicular lines
3 questions
Equation of a plane
00:00
Equation of a plane
08:00
Equation of a plane
3 questions
Intersection of a line and a plane
00:00
Intersection of a line and a plane
04:13
Intersection of a line and a plane
3 questions
Parallel, perpendicular and angle between planes
00:00
Parallel, perpendicular and angle between planes
09:22
Parallel, perpendicular and angle between planes
3 questions
Parametric equations for the line of intersection of two planes
00:00
Parametric equations for the line of intersection of two planes
12:29
Parametric equations for the line of intersection of two planes
3 questions
Symmetric equations for the line of intersection of two planes
Processing..
Symmetric equations for the line of intersection of two planes
10:43
Symmetric equations for the line of intersection of two planes
3 questions
Distance between a point and a line
08:46
Distance between a point and a line
3 questions
Distance between a point and a plane
07:11
Distance between a point and a plane
3 questions
Distance between parallel planes
08:27
Distance between parallel planes
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Cylinders and quadric surfaces

7 lectures
Introduction to cylinders and quadric surfaces
00:21
Reference chart for cylinders and quadric surfaces
00:04
Reducing equations to standard form
15:02
Reducing equations to standard form
3 questions
Sketching the surface
07:59
Sketching the surface
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Limits and continuity

12 lectures
Introduction to limits and continuity
00:20
Domain of a multivariable function
05:36
Domain of a multivariable function
3 questions
Limit of a multivariable function
06:43
Limit of a multivariable function
2 questions
Precise definition of the limit for multivariable functions
34:19
Precise definition of the limit for multivariable functions
3 questions
Discontinuities of multivariable functions
04:07
Discontinuities of multivariable functions
3 questions
Compositions of multivariable functions
09:08
Compositions of multivariable functions
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Partial derivatives

11 lectures
Introduction to partial derivatives
00:20
Partial derivatives in two variables
00:00
Partial derivatives in two variables
07:25
Partial derivatives in two variables
3 questions
Partial derivatives in three or more variables
00:00
Partial derivatives in three or more variables
05:27
Partial derivatives in three or more variables
3 questions
Higher order partial derivatives
00:00
Higher order partial derivatives
05:57
Higher order partial derivatives
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Differentials

5 lectures
Introduction to differentials
00:20
Differential of a multivariable function
00:00
Differential of a multivariable function
04:24
Differential of a multivariable function
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Chain rule

6 lectures
Introduction to chain rule
00:20
Chain rule for multivariable functions
00:00
Chain rule for multivariable functions
18:04
Chain rule for multivariable functions, tree diagram
09:31
Chain rule for multivariable functions and tree diagrams
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Implicit differentiation

5 lectures
Introduction to implicit differentiation
00:20
Implicit differentiation for multivariable functions
00:00
Implicit differentiation for multivariable functions
08:14
Implicit differentiation for multivariable functions
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Directional derivatives

7 lectures
Introduction to directional derivatives
00:20
Directional derivatives in the direction of the vector
00:00
Directional derivatives in the direction of the vector
05:54
Directional derivatives in the direction of the vector
3 questions
Directional derivatives in the direction of the angle
07:43
Directional derivatives in the direction of the angle
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Linear approximation and linearization

7 lectures
Introduction to linear approximation and linearization
00:21
Linear approximation in two variables
00:00
Linear approximation in two variables
06:35
Linear approximation in two variables
3 questions
Linearization of a multivariable function
06:45
Linearization of a multivariable function
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Gradient vectors

10 lectures
Introduction to gradient vectors
00:20
Gradient vectors
00:00
Gradient vectors
03:50
Gradient vectors
3 questions
Gradient vectors and the tangent plane
00:00
Gradient vectors and the tangent plane
07:15
Gradient vectors and the tangent plane
3 questions
Maximum rate of change and its direction
05:57
Maximum rate of change and its direction
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Tangent planes and normal lines

8 lectures
Introduction to tangent planes and normal lines
00:21
Equation of the tangent plane
00:00
Equation of the tangent plane
05:22
Equation of the tangent plane
3 questions
Normal line to the surface
00:00
Normal line to the surface
11:15
Normal line to the surface
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Optimization

13 lectures
Introduction to optimization
00:20
Critical points
05:24
Critical points
3 questions
Second derivative test
00:00
Second derivative test
08:52
Second derivative test
3 questions
Local extrema and saddle points
11:18
Local extrema and saddle points
3 questions
Global extrema
06:54
Global extrema
3 questions
Extreme value theorem
18:40
Extreme value theorem
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Applied optimization

7 lectures
Introduction to applied optimization
00:20
Maximum product of three real numbers
13:09
Maximum volume of a rectangular box inscribed in a sphere
15:21
Minimum distance from the point to the plane
04:39
Points on the cone closest to the given point
08:42
Applied optimization
3 questions
BONUS! Extra practice problems. :)
00:26

Partial Derivatives - Lagrange multipliers

9 lectures
Introduction to lagrange multipliers
00:20
Lagrange multipliers
00:00
Two dimensions, one constraint
08:54
Two dimensions, one constraint
3 questions
Three dimensions, one constraint
11:56
Three dimensions, one constraint
3 questions
Three dimensions, two constraints
14:53
Three dimensions, two constraints
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Approximating double integrals

9 lectures
Introduction to approximating double integrals
00:20
Approximating double integrals with rectangles
19:56
Approximating double integrals with rectangles
3 questions
Midpoint rule for double integrals
00:00
Midpoint rule for double integrals
09:15
Midpoint rule for double integrals
3 questions
Riemann sums for double integrals
08:32
Riemann sums for double integrals
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Double integrals

21 lectures
Introduction to double integrals
00:20
Average value
00:00
Average value
06:41
Average value
3 questions
Iterated and double integrals
00:00
Iterated integrals
23:29
Iterated integrals
3 questions
Double integrals
07:15
Double integrals
3 questions
Type I and II regions
00:00
Type I and II regions
11:16
Type I and II regions
3 questions
Finding surface area
00:00
Finding surface area
10:52
Finding surface area
3 questions
Finding volume
00:00
Finding volume
08:30
Finding volume
3 questions
Changing the order of integration
17:24
Changing the order of integration
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Double integrals in polar coordinates

16 lectures
Introduction to double integrals in polar coordinates
00:21
Changing iterated and double integrals to polar coordinates
00:00
Changing iterated integrals to polar coordinates
10:33
Changing iterated integrals to polar coordinates
3 questions
Changing double integrals to polar coordinates
12:33
Changing double integrals to polar coordinates
3 questions
Sketching area
00:00
Sketching area
05:35
Sketching area
3 questions
Finding area
00:00
Finding area
12:01
Finding area
3 questions
Finding volume
00:00
Finding volume
12:16
Finding volume
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Applications of double integrals

4 lectures
Introduction to applications of double integrals
00:21
Double integrals to find mass and center of mass
11:53
Double integrals to find mass and center of mass
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Approximating triple integrals

5 lectures
Introduction to approximating triple integrals
00:20
Midpoint rule for triple integrals
Processing..
Midpoint rule for triple integrals
10:55
Midpoint rule for triple integrals
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Triple integrals

15 lectures
Introduction to triple integrals
00:20
Iterated and triple integrals
00:00
Iterated integrals
10:28
Iterated integrals
3 questions
Triple integrals
13:34
Average value
00:00
Average value
06:30
Average value
3 questions
Finding volume
00:00
Finding volume
13:57
Finding volume
3 questions
Expressing the integral six ways
Processing..
Expressing the integral six ways
17:28
Expressing the integral six ways
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Triple integrals in cylindrical coordinates

11 lectures
Introduction to triple integrals in cylindrical coordinates
00:21
Cylindrical coordinates
Processing..
Cylindrical coordinates
03:55
Cylindrical coordinates
3 questions
Changing triple integrals to cylindrical coordinates
00:00
Changing triple integrals to cylindrical coordinates
23:31
Changing triple integrals to cylindrical coordinates
3 questions
Finding volume
Processing..
Finding volume
12:14
Finding volume
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Triple integrals in spherical coordinates

10 lectures
Introduction to triple integrals in spherical coordinates
00:21
Spherical coordinates
00:00
Spherical coordinates
05:23
Spherical coordinates
3 questions
Changing triple integrals to spherical coordinates
17:56
Changing triple integrals to spherical coordinates
3 questions
Finding volume
00:00
Finding volume
14:16
Finding volume
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Change of variables

8 lectures
Introduction to change of variables
00:20
Jacobian for two variables
00:00
Jacobian for two variables
06:00
Jacobian for two variables
3 questions
Jacobian for three variables
00:00
Jacobian for three variables
10:31
Jacobian for three variables
3 questions
BONUS! Extra practice problems. :)
00:26

Multiple Integrals - Applications of triple integrals

6 lectures
Introduction to applications of triple integrals
00:21
Triple integrals to find mass and center of mass
10:38
Triple integrals to find mass and center of mass
3 questions
Moments of inertia
08:03
Moments of inertia
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Introduction to vectors

19 lectures
Introduction to vectors
00:20
Vector from two points
05:03
Vector from two points
3 questions
Combinations of vectors
00:00
Combinations of vectors
07:43
Combinations of vectors
3 questions
Sum of two vectors
00:00
Sum of two vectors
05:31
Sum of two vectors
3 questions
Copying vectors and using them to find combinations
09:36
Copying vectors and using them to find combinations
3 questions
Unit vector in the direction of the given vector
05:28
Unit vector in the direction of the given vector
3 questions
Angle between a vector and the x-axis
08:04
Angle between a vector and the x-axis
3 questions
Magnitude and angle of the resultant force
00:00
Magnitude and angle of the resultant force
12:53
Magnitude and angle of the resultant force
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Dot products

29 lectures
Introduction to dot products
00:20
Dot product of two vectors
00:00
Dot product of two vectors
03:22
Dot product of two vectors
3 questions
Angle between two vectors
00:00
Angle between two vectors
05:21
Angle between two vectors
3 questions
Orthogonal, parallel or neither
00:00
Orthogonal, parallel or neither
06:51
Orthogonal, parallel or neither
3 questions
Acute angle between the lines
00:00
Acute angle between the lines
08:52
Acute angle between the lines
3 questions
Acute angles between the curves
00:00
Acute angles between the curves
16:58
Acute angles between the curves
3 questions
Direction cosines and direction angles
Processing..
Direction cosines and direction angles
07:59
Direction cosines and direction angles
3 questions
Scalar equation of a line
00:00
Scalar equation of a line
02:56
Scalar equation of a line
3 questions
Scalar equation of a plane
00:00
Scalar equation of a plane
03:49
Scalar equation of a plane
3 questions
Scalar and vector projections
00:00
Scalar and vector projections
07:33
Scalar and vector projections
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Cross products

17 lectures
Introduction to cross products
00:20
Cross product of two vectors
00:00
Cross product of two vectors
05:38
Cross product of two vectors
3 questions
Vector orthogonal to the plane
00:00
Vector orthogonal to the plane
09:03
Vector orthogonal to the plane
3 questions
Volume of the parallelepiped from vectors
00:00
Volume of the parallelepiped from vectors
06:57
Volume of the parallelepiped from vectors
3 questions
Volume of the parallelepiped from adjacent edges
00:00
Volume of the parallelepiped from adjacent edges
08:12
Volume of the parallelepiped from adjacent edges
3 questions
Scalar triple product to prove vectors are coplanar
00:00
Scalar triple product to prove vectors are coplanar
08:52
Scalar triple product to prove vectors are coplanar
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Vector functions and space curves

19 lectures
Introduction to vector functions and space curves
00:21
Domain of a vector function
00:00
Domain of a vector function
05:10
Domain of a vector function
3 questions
Limit of a vector function
00:00
Limit of a vector function
05:52
Limit of a vector function
3 questions
Sketching the vector equation
10:56
Sketching the vector equation
3 questions
Projections of the curve
00:00
Projections of the curve
16:28
Projections of the curve
3 questions
Vector and parametric equations of a line segment
00:00
Vector and parametric equations of a line segment
05:00
Vector and parametric equations of a line segment
3 questions
Vector function for the curve of intersection of two surfaces
00:00
Vector function for the curve of intersection of two surfaces
05:37
Vector function for the curve of intersection of two surfaces
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Derivatives and integrals of vector functions

14 lectures
Introduction to derivatives and integrals of vector functions
00:21
Derivative of a vector function
Processing..
Derivative of a vector function
07:58
Derivative of a vector function
3 questions
Unit tangent vector
00:00
Unit tangent vector
06:23
Unit tangent vector
3 questions
Parametric equations of the tangent line
00:00
Parametric equations of the tangent line
08:17
Parametric equations of the tangent line
3 questions
Integral of a vector function
00:00
Integral of a vector function
09:00
Integral of a vector function
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Arc length and curvature

20 lectures
Introduction to arc length and curvature
00:21
Arc length of a vector function
00:00
Arc length of a vector function
09:39
Arc length of a vector function
3 questions
Reparametrizing the curve
00:00
Reparametrizing the curve
07:56
Reparametrizing the curve
3 questions
Unit tangent and unit normal vectors
00:00
Unit tangent and unit normal vectors
08:49
Unit tangent and unit normal vectors
3 questions
Curvature
00:00
Curvature
11:45
Curvature
3 questions
Maximum curvature
00:00
Maximum curvature
13:07
Maximum curvature
3 questions
Normal and osculating planes
00:00
Normal and osculating planes
23:22
Normal and osculating planes
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Velocity and acceleration

13 lectures
Introduction to velocity and acceleration
00:20
Velocity and acceleration vectors
00:00
Velocity and acceleration vectors
05:38
Velocity and acceleration vectors
3 questions
Velocity, acceleration and speed, given position
00:00
Velocity, acceleration and speed, given position
04:54
Velocity, acceleration and speed, given position
3 questions
Velocity and position given acceleration and initial conditions
07:54
Velocity and position given acceleration and initial conditions
3 questions
Tangential and normal components of acceleration
00:00
Tangential and normal components of acceleration
13:54
Tangential and normal components of acceleration
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Line integrals

19 lectures
Introduction to line integrals
00:20
Line integrals
00:00
Line integral of a curve
16:29
Line integral of a curve
3 questions
Line integral of a vector function
10:38
Line integral of a vector function
3 questions
Conservative vector fields
00:00
Potential function of a conservative vector field
12:57
Potential function of a conservative vector field
3 questions
Potential function of a conservative vector field to evaluate a line integral
13:32
Potential function of a conservative vector field to evaluate a line integral
3 questions
Independence of path
Processing..
Independence of path
15:48
Independence of path
3 questions
Work done by the force field
13:00
Work done by the force field
3 questions
Open, connected, and simply-connected
07:41
Open, connected, and simply-connected
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Green's Theorem

8 lectures
Introduction to Green's Theorem
00:20
Green's Theorem for one region
00:00
Green's Theorem for one region
08:15
Green's Theorem for one region
3 questions
Green's Theorem for two regions
00:00
Green's Theorem for two regions
13:24
Green's Theorem for two regions
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Curl and divergence

6 lectures
Introduction to curl and divergence
00:20
Curl and divergence of a vector field
12:20
Curl and divergence of a vector field
3 questions
Potential function of a conservative vector field, three dimensions
17:33
Potential function of a conservative vector field, three dimensions
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Parametric surfaces and areas

12 lectures
Introduction to parametric surfaces and areas
00:21
Points on the surface
07:20
Points on the surface
3 questions
Surface of the vector equation
10:21
Surface of the vector equation
3 questions
Parametric representation of the surface
08:28
Parametric representation of the surface
3 questions
Tangent plane to the parametric surface
10:08
Tangent plane to the parametric surface
3 questions
Area of a surface
11:42
Area of a surface
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Surface integrals

4 lectures
Introduction to surface integrals
00:20
Surface integrals
08:24
Surface integrals
3 questions
BONUS! Extra practice problems. :)
00:26

Vectors - Stokes' and divergence theorem

7 lectures
Introduction to stokes' and divergence theorem
00:21
Stokes' theorem
19:19
Stokes' theorem
3 questions
Divergence theorem
17:05
Divergence theorem for surface integrals
3 questions
Divergence theorem and flux
3 questions
BONUS! Extra practice problems. :)
00:26

Final exam and wrap-up

4 lectures
Practice final exam #1 (optional)
00:35
Practice final exam #2 (optional)
00:35
Calculus 3 final exam
00:31
Wrap-up
00:19

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