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Calculus 3 (multivariable calculus), part 2 of 2.
BY
Udemy
Develop a thorough understanding of calculus 3 fundamentals, including multivariate calculus, vector calculus, and ...Read more
Online
₹ 3099
Quick Facts
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Medium of instructions
English
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Mode of learning
Self study
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Mode of Delivery
Video and Text Based
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Course overview
Calculus 3 (multivariable calculus), part 2 of 2 online certifications is developed by Hania Uscka-Wehlou, Ph.D., Mathematics Professor, in collaboration with Martin Wehlou, Certified Editor at MITM and delivered by Udemy, which is aimed at students who want to master the essential concepts and principles of calculus 3. To make their learning process more efficient, students who want to enroll in Calculus 3 (multivariable calculus), part 2 of 2 online courses must first complete "Calculus 3 (multivariable calculus), part 1 of 2" course.
Calculus 3 (multivariable calculus), part 2 of 2 online classes provides more than 44.5 hours of explanatory video-based lectures they were accompanied by 305 downloadable resources which discuss various topics of mathematics like divergence, domains, gradient, graphing, vector calculus, integrals, line integrals, flux integrals, direct substitution, inverse substitution. By the end of this course, students will have acquired the knowledge of the core theories related to calculus 3, including Green's theorem, Fubini's theorem, Stokes' theorem, and Gauss' theorem.
The highlights
- Certificate of completion
- Self-paced course
- 44.5 hours of pre-recorded video content
- 305 downloadable resources
Program offerings
- Online course
- Learning resources. 30-day money-back guarantee
- Unlimited access
- Accessible on mobile devices and tv
Course and certificate fees
Fees information
₹ 3,099
certificate availability
Yes
certificate providing authority
Udemy
What you will learn
Mathematical skill
After completing Calculus 3 (multivariable calculus), part 2 of the 2 certification course, students will gather the knowledge of the basic and advanced principles associated with calculus 3 including multivariate calculus. Students will explore numerous tactics and methodologies related to vector calculus, integrals, domains, gradients, divergence, curls, and vector fields, among other topics in calculus 3. Students will learn about the strategies for computing line integrals and flux integrals, as well as graphing functions, direct substitution, and inverse substitution. Students will also study Fubini's theorem, Stokes' theorem, Green's theorem, and Gauss' theorem, which are all related to calculus 3.
The syllabus
Introduction to the course
Repetition (Riemann integrals, sets in the plane, curves)
- Riemann integrals repetition 1
- Riemann integrals repetition 2
- Riemann integrals repetition 3
- Riemann integrals repetition 4
- Riemann integrals repetition 5
- Curves part 1 general
- Curves part 2, arc length
- Sets in the plane
Double integrals
- Double integrals, notation and applications
- APR
- Double integrals, definition on APR
- Double integrals, definition on compact domains
- Multiple integrals generally
- Properties of double integrals
- Double integrals by inspection 1
- Odd functions
- Integration by inspection 2
- Integration by inspection, Problem 1
- Integration by inspection, Problem 2
- Integration by inspection, Problem 3
- Integration by inspection, Problem 4
- Integration by iteration, Fubini on APR
- Fubini on APR, Problem 1
- Fubini on APR, Problem 2
- Fubini on APR, Problem 3
- Fubini on APR, rule for products
- Fubini on APR, Problem 4
- Fubini on APR: an example where order matters
- X- and Y-simple sets
- Integration by iteration, Fubini on X- and Y-simple sets
- Fubini general problem 1
- Fubini general problem 2
- Fubini general problem 3
- Fubini general problem 4
- Fubini general problem 5
- Fubini general problem 6
- Fubini general problem 7
- Fubini general problem 8
Change of variables in double integrals
- Why change of variables, comparison
- Jacobian and the change in area element after substitution
- One formula for both substitutions
- Inverse substitution
- Direct substitution
- Change of variables, problem 3
- Change of variables, problem 4
- Change of variables, problem 5
- Change of variables, problem 6
- Change of variables, problem 7
- Double integrals, wrap-up
Improper integrals
- Improper integrals, repetition Calc 2
- Improper double integrals
- Calc 3 helps Calc 2, problem 1
- Improper integrals, problem 2
- Improper integrals, problem 3
- Improper integrals, problem 4
- Improper integrals, problem 5
- Improper integrals, problem 6
- Mean value theorem
- Mean value theorem, example 1
- Mean value theorem, example 2
Triple integrals
- Triple integrals: notation, definition and properties
- Integration by inspection
- Fubini
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Area and volume in different ways
- Volume of a tetrahedron
Change of variables in triple integrals
- Change of variables in triple integrals
- Change of variables, problem 1
- Change of variables, problem 2
- Change of variables, problem 3
- Change of variables, problem 4
- Change of variables, problem 5
- Change of variables, wrap-up
Applications of multiple integrals
- Applications of multiple integrals, area and volume
- Applications of multiple integrals, mass
- Applications of multiple integrals, mass centre, centroid
- Applications of multiple integrals, surface area
- Surface area, problem 1
- Surface area, problem 2
- Surface area, problem 3
- Surface area, problem 4
Vector fields
- Different kinds of functions and their visualisation
- Vector fields, some examples
- Vector fields, definition, notation, plot and domain
- Streamlines
- Streamlines problem 1
- Streamlines problem 2
- Streamlines problem 3
- Streamlines problem 4
- Streamlines problem 5
- Streamlines problem 6
Conservative vector fields
- Is each vector field a gradient to some function? Computations.
- Is each vector field a gradient to some function? Geometry.
- Conservative vector fields and equipotential lines
- Schwarz' theorem, a repetition
- Hessian vs Jacobian
- The necessary conditions for conservative vector fields
- Example 1: electrostatic field
- Example 2: gravitational field
- Conservative vector fields and their potentials, problem 1
- Conservative vector fields and their potentials, problem 2
- Conservative vector fields and their potentials, problem 3
- Conservative vector fields and their potentials, problem 4
Line integrals of functions
- Line integrals, notation
- Line integrals of functions, applications and properties
- Line integrals of functions, problem 1
- Line integrals of functions, problem 2
- Line integrals of functions, problem 3
- Line integrals of functions, problem 4
Line integrals of vector fields
- Line integrals of vector fields, notation, definition and application
- Line integrals of vector fields, properties
- Line integrals of vector fields, problem 1 from definition
- Line integrals of vector fields, problem 2 from definition
- Line integrals of vector fields, problem 3 from definition
- Line integrals of vector fields, differential formula
- Line integrals of vector fields, differential fomula, problem 4
- Fundamental theorem for conservative vector fields
- Path independence of line integrals
- Path independence, problem 5
- Path independence, problem 6
- Path independence, problem 7
- Path independence, problem 8
- Path independence, problem 9
- Line integrals of vector fields, wrap-up
Surfaces
- Why surfaces and what they are
- Different ways of defining surfaces
- Boundary of a surface; closed and composite surfaces
- Normal vector and orientation of a surface
- Normal vectors to some important surfaces
- Surface element, both for surfaces defined as graphs and parametric surfaces
Surface integrals
- Surface integrals: notation
- Surface integrals of functions: definition and applications
- Surface integrals of functions: computations and properties
- Surface integrals of functions, problem 1
- Surface integrals of functions, problem 2
- Surface integrals of functions, problem 3
- Surface integrals of functions, problem 4
Oriented surfaces and flux integrals
- Orientation of a surface which agrees with orientation of its boundary
- Flux integrals: notation, definition, computations and applications
- Flux integrals: properties
- Flux integrals, problem 1
- Flux integrals, problem 2
- Flux integrals, problem 3
Gradient, divergence and curl
- Derivatives: gradient, rotation (curl), divergence
- Curl, an interpretation: irrotational vector fields
- Rotation (curl) of a 3D vector field, an example
- Divergence, an interpretation; solenoidal vector fields
- Product rules for gradient, divergence and curl
- Product rule for gradient
- Product rule for divergence
- Product rule for curl
- Curl of each vector field is solenoidal; vector potentials
- Conservative vector fields are irrotational
- Laplacian
Green's theorem in the plane
- Green's theorem: our third fundamental theorem
- Green's theorem: formulation of the theorem
- Green's theorem: proof
- Green's theorem: three common issues and how to handle them
- Green's theorem: problem 1
- Green's theorem: problem 2
- Green's theorem: problem 3
- Green's theorem: problem 4
- Green's theorem: problem 5
- Magnetic field and enclosing singularities
- Necessary and sufficient condition for (plane) conservative vector fields
- Area with help of Green's theorem
Gauss' theorem (Divergence theorem) in 3-space
- Gauss' theorem: our fourth fundamental theorem
- Gauss' theorem: formulation of the theorem
- Gauss' theorem: proof
- Gauss' theorem: three common issues and how to handle them
- Gauss' theorem: problem 1
- Gauss' theorem: problem 2
- Gauss' theorem: problem 3
- Gauss' theorem: problem 4
- An example where Gauss' theorem cannot be applied
- Volume of a cone
Stokes' theorem
- Stokes' theorem: our fifth fundamental theorem
- Stokes' theorem: formulation
- Stokes' theorem: proof
- Stokes' theorem: how to use it
- Stokes' theorem: how it helps; example 1
- Stokes' theorem: verification on an example (example 2)
- Stokes' theorem: example 3
- Stokes' theorem: surface independence, example 4
- Stokes' theorem: surface integral of curl over closed surfaces, regular domains
- Simply connected sets in space
- Necessary and sufficient condition for conservative vector fields
- Stokes' theorem, problem 1
- Stokes' theorem, problem 2
- Stokes' theorem, problem 3
- Stokes' theorem, problem 4
- Stokes' theorem, problem 5
- Stokes' theorem, problem 6
- Stokes' theorem for computations of surface integrals, vector potentials
Wrap-up Multivariable calculus / Calculus 3, part 2 of 2
- Calculus 3, wrap-up
- Final words
Instructors
Ms Hania Uscka Wehlou
Teacher in mathematics
Udemy
Ph.D
Mr Martin Wehlou
Editor
Freelancer
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