[OCW Scholar] Multivariable Calculus

원문 링크 http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/

 

MIT Open Courseware 에서 제공하는 무료 multivariate calculus 동영상 강좌 입니다.

[출처 : MIT OpenCourseware ]

Multivariate calculus 강의는 http://ocw.mit.edu/courses/audio-video-courses/#mathematics 에서 확인해 보면

2개가 올라와 있는데요, 2 강좌 모두 동영상은 동일합니다.

		18.02SC	Multivariable Calculus	Fall 2010
		18.02	Multivariable Calculus	Fall 2007

 

다만 18.02SC 는 OCW Scholar 를 받을 수 있도록 구성되어 있습니다.
( OCW Scholoar에 대한 더 자세한 설명은 여기로 )

 

강의 구성이 보다 체계적이고 완전하며 (끝까지 종강됨), 제공되는 자료가 잘 정리 되어 있습니다.

• Lecture Videos recorded on the MIT campus

• Recitation Videos with problem-solving tips
• Examples of solutions to sample problems
• Problem for you to solve, with solutions
• Exams with solutions
• Interactive Java Applets ("Mathlets") to reinforce key concepts
• An Online Study Group

이 강의 동영상 전체는 무료로 다운로드 받을 수 있습니다.
게다가 iTunesU 에서도 받을 수 있으므로 iPhone, iPod, iPad 사용자는 편하게 다운받아 보실 수 있습니다.

[출처 : MIT OpenCourseware ]

Download the complete lectures from this course:

iTunes U
Internet Archive

각 단원별로 Recitation Video를 보면 보다 쉬운 내용으로 설명하는 동영상을 볼 수 있습니다.
이 동영상만을 보고 싶다면 iTunesU 에서 검색해서 전체를 다운받을 수 있습니다.

Download the complete lectures from this course:

iTunes U
Internet Archive

[출처 : MIT OpenCourseware ]

다음은 각 단원 목차 및 내용입니다.

Course Outline

Unit 1: Vectors and Matrices

Part A: Vectors, Determinants, and Planes

» Session 1: Vectors
» Session 2: Dot Products
» Session 3: Uses of the Dot Product: Lengths and Angles
» Session 4: Vector Components
» Session 5: Area and Determinants in 2D
» Session 6: Volumes and Determinants in Space
» Session 7: Cross Products
» Session 8: Equations of Planes
» Problem Set 1

Part B: Matrices and Systems of Equations

» Session 9: Matrix Multiplication
» Session 10: Meaning of Matrix Multiplication
» Session 11: Matrix Inverses
» Session 12: Equations of Planes II
» Session 13: Linear Systems and Planes
» Session 14: Solutions to Square Systems
» Problem Set 2

Part C: Parametric Equations for Curves

» Session 15: Equations of Lines
» Session 16: Intersection of a Line and a Plane
» Session 17: General Parametric Equations; the Cycloid
» Session 18: Point (Cusp) on Cycloid
» Session 19: Velocity and Acceleration
» Session 20: Velocity and Arc Length
» Session 21: Kepler's Second Law
» Problem Set 3

Exam 1

» Practice Exam
» Session 22: Review of Topics
» Session 23: Review of Problems
» Exam

Unit 2: Partial Derivatives

Part A: Functions of Two Variables, Tangent Approximation and Optimization

» Session 24: Functions of Two Variables: Graphs
» Session 25: Level Curves and Contour Plots
» Session 26: Partial Derivatives
» Session 27: Approximation Formula
» Session 28: Optimization Problems
» Session 29: Least Squares
» Session 30: Second Derivative Test
» Session 31: Example
» Problem Set 4

Part B: Chain Rule, Gradient and Directional Derivatives

» Session 32: Total Differentials and the Chain Rule
» Session 33: Examples
» Session 34: The Chain Rule with More Variables
» Session 35: Gradient: Definition, Perpendicular to Level Curves
» Session 36: Proof
» Session 37: Example
» Session 38: Directional Derivatives
» Problem Set 5

Part C: Lagrange Multipliers and Constrained Differentials

» Session 39: Statement of Lagrange Multipliers and Example
» Session 40: Proof of Lagrange Multipliers
» Session 41: Advanced Example
» Session 42: Constrained Differentials
» Session 43: Clearer Notation
» Session 44: Example
» Problem Set 6

Exam 2

» Practice Exam
» Session 45: Review of Topics
» Session 46: Review of Problems
» Exam Materials

 

Unit 3: Double Integrals and Line Integrals in the Plane

Part A: Double Integrals

» Session 47: Definition of Double Integration
» Session 48: Examples of Double Integration
» Session 49: Exchanging the Order of Integration
» Session 50: Double Integrals in Polar Coordinates
» Session 51: Applications: Mass and Average Value
» Session 52: Applications: Moment of Inertia
» Session 53: Change of Variables
» Session 54: Example: Polar Coordinates
» Session 55: Example
» Problem Set 7

Part B: Vector Fields and Line Integrals

» Session 56: Vector Fields
» Session 57: Work and Line Integrals
» Session 58: Geometric Approach
» Session 59: Example: Line Integrals for Work
» Session 60: Fundamental Theorem for Line Integrals
» Session 61: Conservative Fields, Path Independence, Exact Differentials
» Session 62: Gradient Fields
» Session 63: Potential Functions
» Session 64: Curl
» Problem Set 8

Part C: Green's Theorem

» Session 65: Green's Theorem
» Session 66: Curl(F) = 0 Implies Conservative
» Session 67: Proof of Green's Theorem
» Session 68: Planimeter: Green's Theorem and Area
» Session 69: Flux in 2D
» Session 70: Normal Form of Green's Theorem
» Session 71: Extended Green's Theorem: Boundaries with Multiple Pieces
» Session 72: Simply Connected Regions and Conservative
» Problem Set 9

Exam 3

» Practice Exam
» Session 73: Exam Review
» Exam

 

Unit 4: Triple Integrals and Surface Integrals in 3-Space

Part A: Triple Integrals

» Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates
» Session 75: Applications and Examples
» Session 76: Spherical Coordinates
» Session 77: Triple Integrals in Spherical Coordinates
» Session 78: Applications: Gravitational Attraction
» Problem Set 10

Part B: Flux and the Divergence Theorem

» Session 79: Vector Fields in Space
» Session 80: Flux Through a Surface
» Session 81: Calculating Flux; Finding ndS
» Session 82: ndS for a Surface z = f(x, y)
» Session 83: Other Ways to Find ndS
» Session 84: Divergence Theorem
» Session 85: Physical Meaning of Flux; Del Notation
» Session 86: Proof of the Divergence Theorem
» Session 87: Diffusion Equation
» Problem Set 11

Part C: Line Integrals and Stokes' Theorem

» Session 88: Line Integrals in Space
» Session 89: Gradient Fields and Potential Functions
» Session 90: Curl in 3D
» Session 91: Stokes' Theorem
» Session 92: Proof of Stokes' Theorem
» Session 93: Example
» Session 94: Simply Connected Regions; Topology
» Session 95: Stokes' Theorem and Surface Independence
» Session 96: Summary of Multiple Integration
» Problem Set 12

 Exam 4

» Practice Exam
» Exam

Physics Applications

» Session 97: Curl and Physics
» Session 98: Maxwell's Equations

 

Practice Final Exam

Review

» Session 99: Unit 1 Review
» Session 100: Unit 2 Review
» Session 101: Unit 3 Review
» Session 102: Unit 4 Review

Final Exam