التفاضل والتكامل متعدد المتغيرات | Multivariable…
مِسبار · مقرر جامعي مجاني
Multivariable calculus
تعلم التفاضل والتكامل متعدد المتغيرات (Multivariable calculus) مجانًا عبر 5 وحدات و177 فيديو تعليميًا، بإجمالي نحو 24 ساعة، ضمن مكتبة مِسبار الجامعية.
Learn multivariable calculus—derivatives and integrals of multivariable functions, application problems, and more.
- 5 وحدات.
- 177 فيديو.
- نحو 24 ساعة مشاهدة.
- المستوى: college.
ابدأ مشاهدة المقرر داخل مكتبة مِسبار
التخصصات المرتبطة بالمقرر
- الهندسة الكهربائية (Electrical Engineering)
- هندسة الحاسوب (Computer Engineering)
- الهندسة الميكانيكية (Mechanical Engineering)
- الهندسة المدنية (Civil Engineering)
- الهندسة الكيميائية (Chemical Engineering)
- الهندسة الصناعية (Industrial Engineering)
- هندسة الطيران والفضاء (Aerospace Engineering)
- الذكاء الاصطناعي (Artificial Intelligence)
- علم البيانات (Data Science)
- الروبوتات (Robotics)
- الرياضيات (Mathematics)
- الفيزياء (Physics)
- العمارة (Architecture)
- تعليم الرياضيات (Mathematics Education)
وحدات ودروس المقرر
1. Thinking about multivariable functions
14 فيديو تعليمي.
موضوعات ودروس الوحدة
- Multivariable functions
- Representing points in 3d
- Introduction to 3d graphs
- Interpreting graphs with slices
- Contour plots
- Parametric curves
- Parametric surfaces
- Vector fields, introduction
- Fluid flow and vector fields
- 3d vector fields, introduction
- 3d vector field example
- Transformations, part 1
- Transformations, part 2
- Transformations, part 3
2. Derivatives of multivariable functions
59 فيديو تعليمي.
موضوعات ودروس الوحدة
- Partial derivatives, introduction
- Graphical understanding of partial derivatives
- Formal definition of partial derivatives
- Symmetry of second partial derivatives
- Gradient
- Gradient and graphs
- Gradient and contour maps
- Directional derivative
- Directional derivative, formal definition
- Directional derivatives and slope
- Why the gradient is the direction of steepest ascent
- Vector-valued functions intro
- Vector-valued functions differentiation
- Differential of a vector valued function
- Vector valued function derivative example
- Multivariable chain rule
- Multivariable chain rule intuition
- Vector form of the multivariable chain rule
- Multivariable chain rule and directional derivatives
- More formal treatment of multivariable chain rule
- Curvature intuition
- Curvature formula, part 1
- Curvature formula, part 2
- Curvature formula, part 3
- Curvature formula, part 4
- Curvature formula, part 5
- Curvature of a helix, part 1
- Curvature of a helix, part 2
- Curvature of a cycloid
- Computing the partial derivative of a vector-valued function
- Partial derivative of a parametric surface, part 1
- Partial derivative of a parametric surface, part 2
- Partial derivatives of vector fields
- Partial derivatives of vector fields, component by component
- Divergence intuition, part 1
- Divergence intuition, part 2
- Divergence formula, part 1
- Divergence formula, part 2
- Divergence example
- Divergence notation
- 2d curl intuition
- 2d curl formula
- 2d curl example
- 2d curl nuance
- Describing rotation in 3d with a vector
- 3d curl intuition, part 1
- 3d curl intuition, part 2
- 3d curl formula, part 1
- 3d curl formula, part 2
- 3d curl computation example
- Laplacian intuition
- Laplacian computation example
- Explicit Laplacian formula
- Harmonic Functions
- Jacobian prerequisite knowledge
- Local linearity for a multivariable function
- The Jacobian matrix
- Computing a Jacobian matrix
- The Jacobian Determinant
3. Applications of multivariable derivatives
26 فيديو تعليمي.
موضوعات ودروس الوحدة
- What is a tangent plane
- Controlling a plane in space
- Computing a tangent plane
- Local linearization
- What do quadratic approximations look like
- Quadratic approximation formula, part 1
- Quadratic approximation formula, part 2
- Quadratic approximation example
- The Hessian matrix
- Expressing a quadratic form with a matrix
- Vector form of multivariable quadratic approximation
- Multivariable maxima and minima
- Saddle points
- Warm up to the second partial derivative test
- Second partial derivative test
- Second partial derivative test intuition
- Second partial derivative test example, part 1
- Second partial derivative test example, part 2
- Constrained optimization introduction
- Lagrange multipliers, using tangency to solve constrained optimization
- Finishing the intro lagrange multiplier example
- Lagrange multiplier example, part 1
- Lagrange multiplier example, part 2
- The Lagrangian
- Meaning of the Lagrange multiplier
- Proof for the meaning of Lagrange multipliers
4. Integrating multivariable functions
42 فيديو تعليمي.
موضوعات ودروس الوحدة
- Introduction to the line integral
- Line integral example 1
- Line integral example 2 (part 1)
- Line integral example 2 (part 2)
- Line integrals and vector fields
- Using a line integral to find work
- Parametrization of a reverse path
- Scalar field line integral independent of path direction
- Vector field line integrals dependent on path direction
- Path independence for line integrals
- Closed curve line integrals of conservative vector fields
- Example of closed line integral of conservative field
- Second example of line integral of conservative vector field
- Double integral 1
- Double integrals 2
- Double integrals 3
- Double integrals 4
- Double integrals 5
- Double integrals 6
- Polar coordinates
- Triple integrals 1
- Triple integrals 2
- Triple integrals 3
- Parametrizing a surface, part 1
- Determining a position vector-valued function for a parametrization of two parameters
- Partial derivatives of vector-valued functions
- Introduction to the surface integral
- Example of calculating a surface integral part 1
- Example of calculating a surface integral part 2
- Example of calculating a surface integral part 3
- Surface integral example, part 1
- Surface integral example part 2
- Surface integral example part 3: The home stretch
- Surface integral ex2 part 1
- Surface integral ex2 part 2
- Surface integral ex3 part 1
- Surface integral ex3 part 2
- Surface integral ex3 part 3
- Surface integral ex3 part 4
- Conceptual understanding of flux
- Constructing a unit normal vector
- Vector representation of a surface integral
5. Green's, Stokes', and the divergence theorems
36 فيديو تعليمي.
موضوعات ودروس الوحدة
- Green's theorem proof (part 1)
- Green's theorem proof (part 2)
- Green's theorem example 1
- Green's theorem example 2
- Constructing a unit normal vector to a curve
- 2D divergence theorem
- Conceptual clarification for 2D divergence theorem
- Stokes' theorem intuition
- Green's and Stokes' theorem relationship
- Orienting boundary with surface
- Orientation and stokes
- Conditions for stokes theorem
- Stokes example part 1
- Stokes example part 2
- Stokes example part 3
- Stokes example part 4
- Evaluating line integral directly - part 1
- Evaluating line integral directly - part 2
- 3D divergence theorem intuition
- Divergence theorem example 1
- Explanation of example 1
- Stokes' theorem proof part 1
- Stokes' theorem proof part 2
- Stokes' theorem proof part 3
- Stokes' theorem proof part 4
- Stokes' theorem proof part 5
- Stokes' theorem proof part 6
- Stokes' theorem proof part 7
- Type I regions in three dimensions
- Type II regions in three dimensions
- Type III regions in three dimensions
- Divergence theorem proof (part 1)
- Divergence theorem proof (part 2)
- Divergence theorem proof (part 3)
- Divergence theorem proof (part 4)
- Divergence theorem proof (part 5)
مقررات مرتبطة
- حساب المثلثات | Trigonometry
- ما قبل التفاضل والتكامل | Precalculus
- الإحصاء والاحتمالات | Statistics & probability
- التفاضل والتكامل AP (AB) | AP®︎ Calculus AB
- التفاضل والتكامل AP (BC) | AP®︎ Calculus BC
- الإحصاء AP | AP®︎ Statistics
المصدر والحقوق
المحتوى الأصلي المرخص: أكاديمية خان. تقوم مِسبار بالفهرسة والتنظيم حسب التخصص، وتعرض الفيديوهات المرخصة غير التجارية داخل مكتبة مجانية مستقلة.