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18.01SC Single Variable Calculus

92 topics · 88 with MIT solutions · the full course →

  1. Introduction to Derivatives MIT solutionsMIT: Session 1: Introduction to Derivatives
  2. Examples of Derivatives MIT solutionsMIT: Session 2: Examples of Derivatives
  3. Derivative as Rate of Change MIT solutionsMIT: Session 3: Derivative as Rate of Change
  4. Limits and Continuity MIT solutionsMIT: Session 4: Limits and Continuity
  5. Discontinuity MIT solutionsMIT: Session 5: Discontinuity
  6. Calculating Derivatives MIT solutionsMIT: Session 6: Calculating Derivatives
  7. Derivatives of Sine and Cosine MIT solutionsMIT: Session 7: Derivatives of Sine and Cosine
  8. Limits of Sine and Cosine MIT solutionsMIT: Session 8: Limits of Sine and Cosine
  9. Product Rule MIT solutionsMIT: Session 9: Product Rule
  10. Quotient Rule MIT solutionsMIT: Session 10: Quotient Rule
  11. Chain Rule MIT solutionsMIT: Session 11: Chain Rule
  12. Higher Derivatives MIT solutionsMIT: Session 12: Higher Derivatives
  13. Implicit Differentiation MIT solutionsMIT: Session 13: Implicit Differentiation
  14. Examples of Implicit Differentiation MIT solutionsMIT: Session 14: Examples of Implicit Differentiation
  15. Implicit Differentiation and Inverse Functions MIT solutionsMIT: Session 15: Implicit Differentiation and Inverse Functions
  16. The Derivative of a^x MIT solutionsMIT: Session 16: The Derivative of aˣ
  17. The Exponential Function, its Derivative, and its Inverse MIT solutionsMIT: Session 17: The Exponential Function, its Derivative, and its Inverse
  18. Derivatives of other Exponential Functions MIT solutionsMIT: Session 18: Derivatives of other Exponential Functions
  19. An Interesting Limit Involving e MIT solutionsMIT: Session 19: An Interesting Limit Involving e
  20. Hyperbolic Trig Functions MIT solutionsMIT: Session 20: Hyperbolic Trig Functions
  21. Linear Approximation MIT solutionsMIT: Session 23: Linear Approximation
  22. Examples of Linear Approximation MIT solutionsMIT: Session 24: Examples of Linear Approximation
  23. Introduction to Quadratic Approximation MIT solutionsMIT: Session 25: Introduction to Quadratic Approximation
  24. Using Quadratic Approximations MIT solutionsMIT: Session 26: Using Quadratic Approximations
  25. Sketching Graphs I - Polynomials and Rational Functions MIT solutionsMIT: Session 27: Sketching Graphs I - Polynomials and Rational Functions
  26. Sketching Graphs II - General Strategies MIT solutionsMIT: Session 28: Sketching Graphs II - General Strategies
  27. Optimization Problems MIT solutionsMIT: Session 29: Optimization Problems; Session 30: Optimization Problems II
  28. Related Rates MIT solutionsMIT: Session 31: Related Rates
  29. Ring on a String MIT solutionsMIT: Session 32: Ring on a String
  30. Newton's Method MIT solutionsMIT: Session 33: Newton's Method
  31. Introduction to the Mean Value Theorem MIT solutionsMIT: Session 34: Introduction to the Mean Value Theorem
  32. Using the Mean Value Theorem MIT solutionsMIT: Session 35: Using the Mean Value Theorem
  33. Differentials MIT solutionsMIT: Session 36: Differentials
  34. Antiderivatives MIT solutionsMIT: Session 37: Antiderivatives
  35. Integration by Substitution MIT solutionsMIT: Session 38: Integration by Substitution
  36. Introduction to Differential Equations MIT solutionsMIT: Session 39: Introduction to Differential Equations
  37. Separation of Variables MIT solutionsMIT: Session 40: Separation of Variables
  38. Definite Integrals MIT solutionsMIT: Session 43: Definite Integrals
  39. Adding Areas of Rectangles MIT solutionsMIT: Session 44: Adding Areas of Rectangles
  40. Some Easy Integrals MIT solutionsMIT: Session 45: Some Easy Integrals
  41. Riemann Sums MIT solutionsMIT: Session 46: Riemann Sums
  42. Introduction of the Fundamental Theorem of Calculus MIT solutionsMIT: Session 47: Introduction of the Fundamental Theorem of Calculus
  43. The Fundamental Theorem of Calculus MIT solutionsMIT: Session 48: The Fundamental Theorem of Calculus
  44. Applications of the Fundamental Theorem of Calculus MIT solutionsMIT: Session 49: Applications of the Fundamental Theorem of Calculus
  45. Combining the Fundamental Theorem and the Mean Value Theorem MIT solutionsMIT: Session 50: Combining the Fundamental Theorem and the Mean Value Theorem
  46. The Second Fundamental Theorem of Calculus MIT solutionsMIT: Session 51: The Second Fundamental Theorem of Calculus
  47. Proving the Fundamental Theorem of Calculus MIT solutionsMIT: Session 52: Proving the Fundamental Theorem of Calculus
  48. New Functions From Old MIT solutionsMIT: Session 53: New Functions From Old
  49. The Second Fundamental Theorem and ln(x) MIT solutionsMIT: Session 54: The Second Fundamental Theorem and ln(x)
  50. Creating New Functions Using the Second Fundamental Theorem MIT solutionsMIT: Session 55: Creating New Functions Using the Second Fundamental Theorem
  51. Geometric Interpretation of Definite Integrals MIT solutionsMIT: Session 56: Geometric Interpretation of Definite Integrals
  52. How to Calculate Volumes MIT solutionsMIT: Session 57: How to Calculate Volumes
  53. Volume of a Sphere, Revolving About x-axis MIT solutionsMIT: Session 58: Volume of a Sphere, Revolving About x-axis
  54. Volume of a Parabaloid, Revolving About y-axis MIT solutionsMIT: Session 59: Volume of a Parabaloid, Revolving About y-axis
  55. Integrals and Averages MIT solutionsMIT: Session 60: Integrals and Averages
  56. Integrals and Weighted Averages MIT solutionsMIT: Session 61: Integrals and Weighted Averages
  57. Integrals and Probability MIT solutionsMIT: Session 62: Integrals and Probability
  58. Numerical Integration MIT solutionsMIT: Session 63: Numerical Integration
  59. Numerical Integration, Continued MIT solutionsMIT: Session 64: Numerical Integration, Continued
  60. Bell Curve, Conclusion MIT solutionsMIT: Session 65: Bell Curve, Conclusion
  61. Integral of sin^n(x) cos^m(x), Odd Exponents MIT solutionsMIT: Session 68: Integral of sinⁿ(x) cos^m(x), Odd Exponents
  62. Integral of sin^n(x) cos^m(x), Even Exponents MIT solutionsMIT: Session 69: Integral of sinⁿ(x) cos^m(x), Even Exponents
  63. Preview of Trig Substitution and Polar Coordinates MIT solutionsMIT: Session 70: Preview of Trig Substitution and Polar Coordinates
  64. Integrals Involving secant, cosecant and cotangent MIT solutionsMIT: Session 71: Integrals Involving secant, cosecant and cotangent
  65. Trig Substitution MIT solutionsMIT: Session 72: Trig Substitution
  66. Completing the Square MIT solutionsMIT: Session 73: Completing the Square
  67. Integration by Partial Fractions MIT solutionsMIT: Session 74: Integration by Partial Fractions
  68. Advanced Partial Fractions MIT solutionsMIT: Session 75: Advanced Partial Fractions
  69. Integration by Parts MIT solutionsMIT: Session 76: Integration by Parts
  70. Volume of a Wine Glass MIT solutionsMIT: Session 77: Volume of a Wine Glass
  71. Computing the Length of a Curve MIT solutionsMIT: Session 78: Computing the Length of a Curve
  72. Surface Area MIT solutionsMIT: Session 79: Surface Area
  73. Parametric Curves MIT solutionsMIT: Session 80: Parametric Curves
  74. Examples Using Parametrized Curves MIT solutionsMIT: Session 81: Examples Using Parametrized Curves
  75. Polar Coordinates MIT solutionsMIT: Session 82: Polar Coordinates
  76. Polar Coordinates, Continued MIT solutionsMIT: Session 83: Polar Coordinates, Continued
  77. Polar Coordinates and Graphing MIT solutionsMIT: Session 84: Polar Coordinates and Graphing
  78. L'Hospital's Rule MIT solutionsMIT: Session 87: L'Hospital's Rule
  79. Examples of L'Hospital's Rule MIT solutionsMIT: Session 88: Examples of L'Hospital's Rule
  80. L'Hospital's Rule and Rates of Growth MIT: Session 89: L'Hospital's Rule and Rates of Growth
  81. Advanced Examples of L'Hospital's Rule MIT solutionsMIT: Session 90: Advanced Examples of L'Hospital's Rule
  82. Improper Integrals MIT solutionsMIT: Session 91: Improper Integrals
  83. Integral Comparison MIT solutionsMIT: Session 92: Integral Comparison
  84. Indefinite Integrals and Singularities MIT: Session 93: Indefinite Integrals and Singularities
  85. Infinite Series MIT solutionsMIT: Session 94: Infinite Series
  86. Series Comparison MIT solutionsMIT: Session 95: Series Comparison
  87. Stacking Blocks MIT: Session 96: Stacking Blocks
  88. Power Series MIT solutionsMIT: Session 97: Power Series
  89. Taylor's Series MIT solutionsMIT: Session 98: Taylor's Series
  90. Taylor's Series, Continued MIT: Session 99: Taylor's Series, Continued
  91. Operations on Power Series MIT solutionsMIT: Session 100: Operations on Power Series
  92. Single Variable Calculus: Conclusion MIT solutionsMIT: Session 101: Conclusion

18.02SC Multivariable Calculus

101 topics · 91 with MIT solutions · the full course →

  1. Vectors MIT solutionsMIT: Session 1: Vectors
  2. Dot Products MIT solutionsMIT: Session 2: Dot Products
  3. Uses of the Dot Product: Lengths and Angles MIT solutionsMIT: Session 3: Uses of the Dot Product: Lengths and Angles
  4. Vector Components MIT solutionsMIT: Session 4: Vector Components
  5. Area and Determinants in 2D MIT solutionsMIT: Session 5: Area and Determinants in 2D
  6. Volumes and Determinants in Space MIT solutionsMIT: Session 6: Volumes and Determinants in Space
  7. Cross Products MIT solutionsMIT: Session 7: Cross Products
  8. Equations of Planes MIT solutionsMIT: Session 8: Equations of Planes
  9. Matrix Multiplication MIT solutionsMIT: Session 9: Matrix Multiplication
  10. Meaning of Matrix Multiplication MIT solutionsMIT: Session 10: Meaning of Matrix Multiplication
  11. Matrix Inverses MIT solutionsMIT: Session 11: Matrix Inverses
  12. Equations of Planes II MIT solutionsMIT: Session 12: Equations of Planes II
  13. Linear Systems and Planes MIT solutionsMIT: Session 13: Linear Systems and Planes
  14. Solutions to Square Systems MIT solutionsMIT: Session 14: Solutions to Square Systems
  15. Equations of Lines MIT solutionsMIT: Session 15: Equations of Lines
  16. Intersection of a Line and a Plane MIT solutionsMIT: Session 16: Intersection of a Line and a Plane
  17. General Parametric Equations; the Cycloid MIT solutionsMIT: Session 17: General Parametric Equations; the Cycloid
  18. Point (Cusp) on Cycloid MIT solutionsMIT: Session 18: Point (Cusp) on Cycloid
  19. Velocity and Acceleration MIT solutionsMIT: Session 19: Velocity and Acceleration
  20. Velocity and Arc Length MIT solutionsMIT: Session 20: Velocity and Arc Length
  21. Kepler's Second Law MIT solutionsMIT: Session 21: Kepler's Second Law
  22. Review of Topics MIT: Session 22: Review of Topics
  23. Review of Problems MIT: Session 23: Review of Problems
  24. Functions of Two Variables: Graphs MIT solutionsMIT: Session 24: Functions of Two Variables: Graphs
  25. Level Curves and Contour Plots MIT solutionsMIT: Session 25: Level Curves and Contour Plots
  26. Partial Derivatives MIT solutionsMIT: Session 26: Partial Derivatives
  27. Approximation Formula MIT solutionsMIT: Session 27: Approximation Formula
  28. Optimization Problems MIT solutionsMIT: Session 28: Optimization Problems
  29. Least Squares MIT solutionsMIT: Session 29: Least Squares
  30. Second Derivative Test MIT solutionsMIT: Session 30: Second Derivative Test
  31. Example MIT solutionsMIT: Session 31: Example
  32. Total Differentials and the Chain Rule MIT solutionsMIT: Session 32: Total Differentials and the Chain Rule
  33. Examples MIT solutionsMIT: Session 33: Examples
  34. The Chain Rule with More Variables MIT solutionsMIT: Session 34: The Chain Rule with More Variables
  35. Gradient: Definition, Perpendicular to Level Curves MIT solutionsMIT: Session 35: Gradient: Definition, Perpendicular to Level Curves
  36. Proof MIT solutionsMIT: Session 36: Proof
  37. Example MIT solutionsMIT: Session 37: Example
  38. Directional Derivatives MIT solutionsMIT: Session 38: Directional Derivatives
  39. Statement of Lagrange Multipliers and Example MIT solutionsMIT: Session 39: Statement of Lagrange Multipliers and Example
  40. Proof of Lagrange Multipliers MIT solutionsMIT: Session 40: Proof of Lagrange Multipliers
  41. Advanced Example MIT solutionsMIT: Session 41: Advanced Example
  42. Constrained Differentials MIT solutionsMIT: Session 42: Constrained Differentials
  43. Clearer Notation MIT solutionsMIT: Session 43: Clearer Notation
  44. Example MIT solutionsMIT: Session 44: Example
  45. Review of Topics MIT: Session 45: Review of Topics
  46. Review of Problems MIT: Session 46: Review of Problems
  47. Definition of Double Integration MIT solutionsMIT: Session 47: Definition of Double Integration
  48. Examples of Double Integration MIT solutionsMIT: Session 48: Examples of Double Integration
  49. Exchanging the Order of Integration MIT solutionsMIT: Session 49: Exchanging the Order of Integration
  50. Double Integrals in Polar Coordinates MIT solutionsMIT: Session 50: Double Integrals in Polar Coordinates
  51. Applications: Mass and Average Value MIT solutionsMIT: Session 51: Applications: Mass and Average Value
  52. Applications: Moment of Inertia MIT solutionsMIT: Session 52: Applications: Moment of Inertia
  53. Change of Variables MIT solutionsMIT: Session 53: Change of Variables
  54. Example: Polar Coordinates MIT solutionsMIT: Session 54: Example: Polar Coordinates
  55. Example MIT solutionsMIT: Session 55: Example
  56. Vector Fields MIT solutionsMIT: Session 56: Vector Fields
  57. Work and Line Integrals MIT solutionsMIT: Session 57: Work and Line Integrals
  58. Geometric Approach MIT solutionsMIT: Session 58: Geometric Approach
  59. Example: Line Integrals for Work MIT solutionsMIT: Session 59: Example: Line Integrals for Work
  60. Fundamental Theorem for Line Integrals MIT solutionsMIT: Session 60: Fundamental Theorem for Line Integrals
  61. Conservative Fields, Path Independence, Exact Differentials MIT solutionsMIT: Session 61: Conservative Fields, Path Independence, Exact Differentials
  62. Gradient Fields MIT solutionsMIT: Session 62: Gradient Fields
  63. Potential Functions MIT solutionsMIT: Session 63: Potential Functions
  64. Curl MIT solutionsMIT: Session 64: Curl
  65. Green's Theorem MIT solutionsMIT: Session 65: Green's Theorem
  66. Curl(F) = 0 Implies Conservative MIT solutionsMIT: Session 66: Curl(F) = 0 Implies Conservative
  67. Proof of Green's Theorem MIT solutionsMIT: Session 67: Proof of Green's Theorem
  68. Planimeter: Green's Theorem and Area MIT solutionsMIT: Session 68: Planimeter: Green's Theorem and Area
  69. Flux in 2D MIT solutionsMIT: Session 69: Flux in 2D
  70. Normal Form of Green's Theorem MIT solutionsMIT: Session 70: Normal Form of Green's Theorem
  71. Extended Green's Theorem: Boundaries with Multiple Pieces MIT solutionsMIT: Session 71: Extended Green's Theorem: Boundaries with Multiple Pieces
  72. Simply Connected Regions and Conservative Fields MIT solutionsMIT: Session 72: Simply Connected Regions and Conservative Fields
  73. Triple Integrals: Rectangular and Cylindrical Coordinates MIT solutionsMIT: Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates
  74. Applications and Examples MIT solutionsMIT: Session 75: Applications and Examples
  75. Spherical Coordinates MIT solutionsMIT: Session 76: Spherical Coordinates
  76. Triple Integrals in Spherical Coordinates MIT solutionsMIT: Session 77: Triple Integrals in Spherical Coordinates
  77. Applications: Gravitational Attraction MIT solutionsMIT: Session 78: Applications: Gravitational Attraction
  78. Vector Fields in Space MIT solutionsMIT: Session 79: Vector Fields in Space
  79. Flux Through a Surface MIT solutionsMIT: Session 80: Flux Through a Surface
  80. Calculating Flux; Finding ndS MIT solutionsMIT: Session 81: Calculating Flux; Finding ndS
  81. ndS for a Surface z = f(x, y) MIT solutionsMIT: Session 82: ndS for a Surface z = f(x, y)
  82. Other Ways to Find ndS MIT solutionsMIT: Session 83: Other Ways to Find ndS
  83. Divergence Theorem MIT solutionsMIT: Session 84: Divergence Theorem
  84. Physical Meaning of Flux; Del Notation MIT solutionsMIT: Session 85: Physical Meaning of Flux; Del Notation
  85. Proof of the Divergence Theorem MIT solutionsMIT: Session 86: Proof of the Divergence Theorem
  86. Diffusion Equation MIT solutionsMIT: Session 87: Diffusion Equation
  87. Line Integrals in Space MIT solutionsMIT: Session 88: Line Integrals in Space
  88. Gradient Fields and Potential Functions MIT solutionsMIT: Session 89: Gradient Fields and Potential Functions
  89. Curl in 3D MIT solutionsMIT: Session 90: Curl in 3D
  90. Stokes' Theorem MIT solutionsMIT: Session 91: Stokes' Theorem
  91. Proof of Stokes' Theorem MIT solutionsMIT: Session 92: Proof of Stokes' Theorem
  92. Example MIT solutionsMIT: Session 93: Example
  93. Simply Connected Regions; Topology MIT solutionsMIT: Session 94: Simply Connected Regions; Topology
  94. Stokes' Theorem and Surface Independence MIT solutionsMIT: Session 95: Stokes' Theorem and Surface Independence
  95. Summary of Multiple Integration MIT solutionsMIT: Session 96: Summary of Multiple Integration
  96. Curl and Physics MIT: Session 97: Curl and Physics
  97. Maxwell's Equations MIT: Session 98: Maxwell's Equations
  98. Unit 1 Review MIT: Session 99: Unit 1 Review
  99. Unit 2 Review MIT: Session 100: Unit 2 Review
  100. Unit 3 Review MIT: Session 101: Unit 3 Review
  101. Unit 4 Review MIT: Session 102: Unit 4 Review

18.03SC Differential Equations

36 topics · 35 with MIT solutions · the full course →

  1. Basic DE's and Separable Equations MIT solutionsMIT: Basic DE's and Separable Equations
  2. Geometric Methods MIT solutionsMIT: Geometric Methods
  3. Numerical Methods MIT solutionsMIT: Numerical Methods
  4. First Order Linear ODE's MIT solutionsMIT: First Order Linear ODE's
  5. Solution by Integrating Factors MIT solutionsMIT: Solution by Integrating Factors
  6. Complex Arithmetic and Exponentials MIT solutionsMIT: Complex Arithmetic and Exponentials
  7. Sinusoidal Functions MIT solutionsMIT: Sinusoidal Functions
  8. First Order Constant Coefficient Linear ODE's MIT solutionsMIT: First Order Constant Coefficient Linear ODE's
  9. Exponential Input; Gain and Phase Lag MIT solutionsMIT: Exponential Input; Gain and Phase Lag
  10. First Order Autonomous Differential Equations MIT solutionsMIT: First Order Autonomous Differential Equations
  11. Modes and the Characteristic Equation MIT solutionsMIT: Modes and the Characteristic Equation
  12. Damped Harmonic Oscillators MIT solutionsMIT: Damped Harmonic Oscillators
  13. Exponential Response MIT solutionsMIT: Exponential Response
  14. Gain and Phase Lag MIT solutionsMIT: Gain and Phase Lag
  15. Undetermined Coefficients MIT solutionsMIT: Undetermined Coefficients
  16. Linear Operators, Linear Time Invariance MIT solutionsMIT: Linear Operators, Linear Time Invariance
  17. Pure Resonance MIT solutionsMIT: Pure Resonance
  18. Frequency Response and Practical Resonance MIT solutionsMIT: Frequency Response and Practical Resonance
  19. Fourier Series: Basics MIT solutionsMIT: Fourier Series: Basics
  20. Operations on Fourier Series MIT solutionsMIT: Operations on Fourier Series
  21. ODE's with Periodic Input, Resonance MIT solutionsMIT: ODE's with Periodic Input, Resonance
  22. Step and Delta Functions: Integrals and Generalized Derivatives MIT solutionsMIT: Step and Delta Functions: Integrals and Generalized Derivatives
  23. Unit Step and Unit Impulse Response MIT solutionsMIT: Unit Step and Unit Impulse Response
  24. Convolution MIT solutionsMIT: Convolution
  25. Laplace Transform: Basics MIT solutionsMIT: Laplace Transform: Basics
  26. Partial Fractions and Inverse Laplace Transform MIT solutionsMIT: Partial Fractions and Inverse Laplace Transform
  27. Laplace Transform: Solving Initial Value Problems MIT solutionsMIT: Laplace Transform: Solving Initial Value Problems
  28. Transfer (System) and Weight Functions, Green's Formula MIT solutionsMIT: Transfer (System) and Weight Functions, Green's Formula
  29. Poles, Amplitude Response, Connection to ERF MIT solutionsMIT: Poles, Amplitude Response, Connection to ERF
  30. Linear Systems MIT solutionsMIT: Linear Systems
  31. Matrix Methods: Eigenvalues and Normal Modes MIT solutionsMIT: Matrix Methods: Eigenvalues and Normal Modes
  32. Qualitative Behavior: Phase Portraits MIT solutionsMIT: Qualitative Behavior: Phase Portraits
  33. Matrix Exponentials MIT solutionsMIT: Matrix Exponentials
  34. Nonlinear Systems MIT solutionsMIT: Nonlinear Systems
  35. Linearization Near Critical Points MIT solutionsMIT: Linearization Near Critical Points
  36. Limitations of the Linear: Limit Cycles and Chaos MIT: Limitations of the Linear: Limit Cycles and Chaos

18.06SC Linear Algebra

32 topics · 31 with MIT solutions · the full course →

  1. The Geometry of Linear Equations MIT solutionsMIT: The Geometry of Linear Equations
  2. An Overview of Key Ideas MIT: An Overview of Key Ideas
  3. Elimination with Matrices MIT solutionsMIT: Elimination with Matrices
  4. Multiplication and Inverse Matrices MIT solutionsMIT: Multiplication and Inverse Matrices
  5. Factorization into A = LU MIT solutionsMIT: Factorization into A = LU
  6. Transposes, Permutations, Vector Spaces MIT solutionsMIT: Transposes, Permutations, Vector Spaces
  7. Column Space and Nullspace MIT solutionsMIT: Column Space and Nullspace
  8. Solving Ax = 0: Pivot Variables, Special Solutions MIT solutionsMIT: Solving Ax = 0: Pivot Variables, Special Solutions
  9. Solving Ax = b: Row Reduced Form R MIT solutionsMIT: Solving Ax = b: Row Reduced Form R
  10. Independence, Basis and Dimension MIT solutionsMIT: Independence, Basis and Dimension
  11. The Four Fundamental Subspaces MIT solutionsMIT: The Four Fundamental Subspaces
  12. Matrix Spaces; Rank 1; Small World Graphs MIT solutionsMIT: Matrix Spaces; Rank 1; Small World Graphs
  13. Graphs, Networks, Incidence Matrices MIT solutionsMIT: Graphs, Networks, Incidence Matrices
  14. Orthogonal Vectors and Subspaces MIT solutionsMIT: Orthogonal Vectors and Subspaces
  15. Projections onto Subspaces MIT solutionsMIT: Projections onto Subspaces
  16. Projection Matrices and Least Squares MIT solutionsMIT: Projection Matrices and Least Squares
  17. Orthogonal Matrices and Gram-Schmidt MIT solutionsMIT: Orthogonal Matrices and Gram-Schmidt
  18. Properties of Determinants MIT solutionsMIT: Properties of Determinants
  19. Determinant Formulas and Cofactors MIT solutionsMIT: Determinant Formulas and Cofactors
  20. Cramer's Rule, Inverse Matrix and Volume MIT solutionsMIT: Cramer's Rule, Inverse Matrix and Volume
  21. Eigenvalues and Eigenvectors MIT solutionsMIT: Eigenvalues and Eigenvectors
  22. Diagonalization and Powers of A MIT solutionsMIT: Diagonalization and Powers of A
  23. Differential Equations and exp(At) MIT solutionsMIT: Differential Equations and exp(At)
  24. Markov Matrices; Fourier Series MIT solutionsMIT: Markov Matrices; Fourier Series
  25. Symmetric Matrices and Positive Definiteness MIT solutionsMIT: Symmetric Matrices and Positive Definiteness
  26. Complex Matrices; Fast Fourier Transform (FFT) MIT solutionsMIT: Complex Matrices; Fast Fourier Transform (FFT)
  27. Positive Definite Matrices and Minima MIT solutionsMIT: Positive Definite Matrices and Minima
  28. Similar Matrices and Jordan Form MIT solutionsMIT: Similar Matrices and Jordan Form
  29. Singular Value Decomposition MIT solutionsMIT: Singular Value Decomposition
  30. Linear Transformations and their Matrices MIT solutionsMIT: Linear Transformations and their Matrices
  31. Change of Basis; Image Compression MIT solutionsMIT: Change of Basis; Image Compression
  32. Left and Right Inverses; Pseudoinverse MIT solutionsMIT: Left and Right Inverses; Pseudoinverse

8.01SC Classical Mechanics

48 topics · 0 with MIT solutions · the full course →

  1. Vectors MIT: Lesson 0: Vectors [0.1 - 0.6]
  2. 1D Kinematics - Position and Velocity MIT: Lesson 1: 1D Kinematics - Position and Velocity [1.1-1.7]
  3. 1D Kinematics - Acceleration MIT: Lesson 2: 1D Kinematics - Acceleration [2.1-2.5]
  4. 2D Kinematics MIT: Lesson 3: 2D Kinematics [3.1-3.5]
  5. Week 1 Worked Examples MIT: Week 1 Worked Examples [PS.1.1-PS.1.5]
  6. Newton's Laws of Motion MIT: Lesson 4: Newton's Laws of Motion [4.1-4.4]
  7. Gravity MIT: Lesson 5: Gravity [5.1-5.3]
  8. Contact Forces MIT: Lesson 6: Contact Forces [6.1-6.2]
  9. Tension and Springs MIT: Lesson 7: Tension and Springs [7.1-7.4]
  10. Deep Dive: Friction MIT: Deep Dive: Friction [DD 1.1]
  11. Week 2 Worked Examples MIT: Week 2 Worked Examples [PS.2.1-PS.2.3]
  12. Circular Motion - Position and Velocity MIT: Lesson 8: Circular Motion - Position and Velocity [8.1-8.3]
  13. Uniform Circular Motion MIT: Lesson 9: Uniform Circular Motion [9.1-9.3]
  14. Circular Motion – Acceleration MIT: Lesson 10: Circular Motion – Acceleration [10.1-10.4]
  15. Newton's 2nd Law and Circular Motion MIT: Lesson 11: Newton's 2nd Law and Circular Motion [11.1-11.3]
  16. Worked Example - Orbital Circular Motion MIT: PS.3.1 Worked Example - Orbital Circular Motion
  17. Pulleys and Constraints MIT: Lesson 12: Pulleys and Constraints [12.1-12.5]
  18. Massive Rope MIT: Lesson 13: Massive Rope [13.1-13.6]
  19. Resistive Forces MIT: Lesson 14: Resistive Forces [14.1-14.3]
  20. Momentum and Impulse MIT: Lesson 15: Momentum and Impulse [15.1-15.5]
  21. Conservation of Momentum MIT: Lesson 16: Conservation of Momentum [16.1-16.2]
  22. Center of Mass and Motion MIT: Lesson 17: Center of Mass and Motion [17.1-17.7]
  23. Relative Velocity and Recoil MIT: Lesson 18: Relative Velocity and Recoil [18.1-18.4]
  24. Continuous Mass Transfer MIT: Lesson 19: Continuous Mass Transfer [19.1-19.7]
  25. Week 6 Worked Examples MIT: Week 6 Worked Examples [PS.6.1-PS.6.2]
  26. Kinetic Energy and Work in 1D MIT: Lesson 20: Kinetic Energy and Work in 1D [20.1-20.6]
  27. Kinetic Energy and Work in 2D and 3D MIT: Lesson 21: Kinetic Energy and Work in 2D and 3D [21.1-21.6]
  28. Conservative and Non-Conservative Forces MIT: Lesson 22: Conservative and Non-Conservative Forces [22.1-22.5]
  29. Worked Example - Collision and Sliding on a Rough Surface MIT: PS.7.1 Worked Example - Collision and Sliding on a Rough Surface
  30. Potential Energy MIT: Lesson 23: Potential Energy [23.1-23.5]
  31. Conservation of Energy MIT: Lesson 24: Conservation of Energy [24.1-24.4]
  32. Potential Energy Diagrams MIT: Lesson 25: Potential Energy Diagrams [25.1-25.3]
  33. Types of Collision MIT: Lesson 26: Types of Collision [26.1-26.3]
  34. Elastic Collisions MIT: Lesson 27: Elastic Collisions [27.1-27.6]
  35. Deep Dive: Center of Mass Reference Frame MIT: Deep Dive: Center of Mass Reference Frame [DD.2.1-DD.2.7]
  36. Introduction to Translation and Rotation MIT: 28.2 Introduction to Translation and Rotation
  37. Review of Angular Velocity and Acceleration MIT: 28.3 Review of Angular Velocity and Acceleration
  38. Moment of Inertia MIT: Lesson 29: Moment of Inertia [29.1-29.6]
  39. Torque MIT: Lesson 30: Torque [30.1-30.5]
  40. Rotational Dynamics MIT: Lesson 31: Rotational Dynamics [31.1-31.7]
  41. Blocks and Massive Pulley MIT: PS.10.1 Blocks and Massive Pulley
  42. Angular Momentum of a Point Particle MIT: Lesson 32: Angular Momentum of a Point Particle [32.1-32.4]
  43. Angular Momentum of a Rigid Body MIT: Lesson 33: Angular Momentum of a Rigid Body [33.1-33.5]
  44. Torque and Angular Impulse MIT: Lesson 34: Torque and Angular Impulse [34.1-34.5]
  45. Rolling Kinematics MIT: Lesson 35: Rolling Kinematics [35.1-35.5]
  46. Rolling Dynamics MIT: Lesson 36: Rolling Dynamics [36.1-36.5]
  47. Rolling Kinetic Energy & Angular Momentum MIT: Lesson 37: Rolling Kinetic Energy & Angular Momentum [37.1-37.4]
  48. Deep Dive: Gyroscopes MIT: Deep Dive: Gyroscopes [DD.3.1-DD.3.3]

6.041SC Probabilistic Systems Analysis and Applied Probability

20 topics · 20 with MIT solutions · the full course →

  1. Probability Models and Axioms MIT solutionsMIT: Lecture 1: Probability Models and Axioms
  2. Conditioning and Bayes' Rule MIT solutionsMIT: Lecture 2: Conditioning and Bayes' Rule
  3. Independence MIT solutionsMIT: Lecture 3: Independence
  4. Counting MIT solutionsMIT: Lecture 4: Counting
  5. Discrete Random Variables; Probability Mass Functions; Expectations MIT solutionsMIT: Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations
  6. Discrete Random Variable Examples; Joint PMFs MIT solutionsMIT: Lecture 6: Discrete Random Variable Examples; Joint PMFs
  7. Multiple Discrete Random Variables MIT solutionsMIT: Lecture 7: Multiple Discrete Random Variables
  8. Continuous Random Variables MIT solutionsMIT: Lecture 8: Continuous Random Variables
  9. Multiple Continuous Random Variables MIT solutionsMIT: Lecture 9: Multiple Continuous Random Variables
  10. Continuous Bayes' Rule; Derived Distributions MIT solutionsMIT: Lecture 10: Continuous Bayes' Rule; Derived Distributions
  11. Derived Distributions; Convolution; Covariance and Correlation MIT solutionsMIT: Lecture 11: Derived Distributions; Convolution; Covariance and Correlation
  12. Iterated Expectations; Sum of a Random Number of Random Variables MIT solutionsMIT: Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables
  13. Bernoulli Process MIT solutionsMIT: Lecture 13: Bernoulli Process
  14. Poisson Process MIT solutionsMIT: Lecture 14: Poisson Process - I; Lecture 15: Poisson Process - II
  15. Markov Chains MIT solutionsMIT: Lecture 16: Markov Chains - I; Lecture 17: Markov Chains - II; Lecture 18: Markov Chains - III
  16. Weak Law of Large Numbers MIT solutionsMIT: Lecture 19: Weak Law of Large Numbers
  17. Central Limit Theorem MIT solutionsMIT: Lecture 20: Central Limit Theorem
  18. Bayesian Statistical Inference MIT solutionsMIT: Lecture 21: Bayesian Statistical Inference - I; Lecture 22: Bayesian Statistical Inference - II
  19. Classical Statistical Inference - I MIT solutionsMIT: Lecture 23 Classical Statistical Inference - I
  20. Classical Inference MIT solutionsMIT: Lecture 24: Classical Inference - II; Lecture 25: Classical Inference - III

7.01SC Fundamentals of Biology

21 topics · 20 with MIT solutions · the full course →

  1. Types of Organisms, Cell Composition MIT solutionsMIT: Types of Organisms, Cell Composition
  2. Covalent Bonds, Hydrogen Bonds MIT solutionsMIT: Covalent Bonds, Hydrogen Bonds
  3. Macromolecules: Lipids, Carbohydrates, Nucleic Acid MIT solutionsMIT: Macromolecules: Lipids, Carbohydrates, Nucleic Acid
  4. Proteins, Levels of Structure, Non-Covalent Forces MIT solutionsMIT: Proteins, Levels of Structure, Non-Covalent Forces
  5. Biochemical Reactions, Enzymes, and ATP MIT solutionsMIT: Biochemical Reactions, Enzymes, and ATP
  6. Glycolysis, Respiration, and Fermentation MIT solutionsMIT: Glycolysis, Respiration, and Fermentation
  7. Photosynthesis MIT solutionsMIT: Photosynthesis
  8. DNA Structure, Classic Experiments MIT solutionsMIT: DNA Structure, Classic Experiments
  9. DNA Replication MIT solutionsMIT: DNA Replication
  10. Transcription, Translation MIT solutionsMIT: Transcription, Translation
  11. Alternative Approaches to Molecular Biology MIT solutionsMIT: Alternative Approaches to Molecular Biology
  12. Gene Regulation and the Lac Operon MIT solutionsMIT: Gene Regulation and the Lac Operon
  13. Mendel's Laws MIT solutionsMIT: Mendel's Laws
  14. Linkage and Recombination, Genetic Maps MIT solutionsMIT: Linkage and Recombination, Genetic Maps
  15. Pedigrees MIT solutionsMIT: Pedigrees
  16. Biochemical Genetics MIT solutionsMIT: Biochemical Genetics
  17. Development of Recombinant DNA MIT: Development of Recombinant DNA
  18. Basic Mechanics of Cloning: Restriction Enzymes & Cloning Vectors MIT solutionsMIT: Basic Mechanics of Cloning: Restriction Enzymes & Cloning Vectors
  19. Constructing and Screening a Recombinant DNA Library MIT solutionsMIT: Constructing and Screening a Recombinant DNA Library
  20. cDNA Libraries and Expression Libraries MIT solutionsMIT: cDNA Libraries and Expression Libraries
  21. Agarose Gel Electrophoresis, DNA Sequencing, PCR MIT solutionsMIT: Agarose Gel Electrophoresis, DNA Sequencing, PCR

3.091SC Introduction to Solid State Chemistry

35 topics · 33 with MIT solutions · the full course →

  1. Introduction to Solid State Chemistry MIT solutionsMIT: 1. Introduction to Solid State Chemistry
  2. The Periodic Table MIT solutionsMIT: 2. The Periodic Table
  3. Atomic Models: Rutherford & Bohr MIT solutionsMIT: 3. Atomic Models: Rutherford & Bohr
  4. Matter/Energy Interactions: Atomic Spectra MIT solutionsMIT: 4. Matter/Energy Interactions: Atomic Spectra
  5. Electron Shell Model & Quantum Numbers MIT solutionsMIT: 5. Electron Shell Model & Quantum Numbers
  6. Particle-Wave Duality MIT solutionsMIT: 6. Particle-Wave Duality
  7. The Aufbau Principle; Photoelectron Spectroscopy MIT: 7. The Aufbau Principle; Photoelectron Spectroscopy
  8. Ionic Crystals; Born-Haber Cycle MIT solutionsMIT: 8. Ionic Crystals; Born-Haber Cycle
  9. Drawing Lewis Structures MIT solutionsMIT: 9. Drawing Lewis Structures
  10. Hybridized & Molecular Orbitals; Paramagnetism MIT solutionsMIT: 10. Hybridized & Molecular Orbitals; Paramagnetism
  11. The Shapes of Molecules MIT solutionsMIT: 11. The Shapes of Molecules
  12. Intermolecular Forces MIT solutionsMIT: 12. Intermolecular Forces
  13. Band Theory of Solids MIT solutionsMIT: 13. Band Theory of Solids
  14. Semiconductors MIT solutionsMIT: 14. Semiconductors
  15. Introduction to Crystallography MIT solutionsMIT: 15. Introduction to Crystallography
  16. Crystallographic Notation & X-Rays MIT solutionsMIT: 16. Crystallographic Notation & X-Rays
  17. X-Ray Emission & Absorption MIT solutionsMIT: 17. X-Ray Emission & Absorption
  18. X-Ray Diffraction Techniques MIT solutionsMIT: 18. X-Ray Diffraction Techniques
  19. Point & Line Defects MIT solutionsMIT: 19. Point & Line Defects
  20. Line, Interface & Bulk Defects MIT solutionsMIT: 20. Line, Interface & Bulk Defects
  21. Introduction to Glasses MIT solutionsMIT: 21. Introduction to Glasses
  22. Engineering Glass Properties; Introduction to Kinetics MIT solutionsMIT: 22. Engineering Glass Properties; Introduction to Kinetics
  23. Reaction Rates MIT solutionsMIT: 23. Reaction Rates
  24. Diffusion MIT solutionsMIT: 24. Diffusion
  25. Introduction to Aqueous Solutions MIT solutionsMIT: 25. Introduction to Aqueous Solutions
  26. Acids & Bases MIT solutionsMIT: 26. Acids & Bases
  27. Introduction to Organic Chemistry MIT: 27. Introduction to Organic Chemistry
  28. Polymers: Structure & Composition MIT solutionsMIT: 28. Polymers: Structure & Composition
  29. Polymers: Synthesis, Properties & Applications MIT solutionsMIT: 29. Polymers: Synthesis, Properties & Applications
  30. Biochemistry: Amino Acids MIT solutionsMIT: 30. Biochemistry: Amino Acids
  31. Biochemistry: Protein Structure MIT solutionsMIT: 31. Biochemistry: Protein Structure
  32. Biochemistry: Lipids, Nucleic Acids & DNA MIT solutionsMIT: 32. Biochemistry: Lipids, Nucleic Acids & DNA
  33. Unary Phase Diagrams MIT solutionsMIT: 33. Unary Phase Diagrams
  34. Binary Phase Diagrams: Complete Solubility MIT solutionsMIT: 34. Binary Phase Diagrams: Complete Solubility
  35. Binary Phase Diagrams: Limited Solubility MIT solutionsMIT: 35. Binary Phase Diagrams: Limited Solubility

9.00SC Introduction to Psychology

21 topics · 0 with MIT solutions · the full course →

  1. Introduction to Psychology: Introduction MIT: Introduction
  2. Science & Research MIT: Science & Research
  3. Brain MIT: Brain I: Structure and Functions; Brain II: Methods of Research
  4. Vision MIT: Vision I; Vision II
  5. Consciousness MIT: Consciousness
  6. Attention MIT: Attention
  7. Memory I MIT: Memory I
  8. Learning MIT: Learning
  9. Memory II: Amnesia and Memory Systems MIT: Memory II: Amnesia and Memory Systems
  10. Language MIT: Language
  11. Thinking MIT: Thinking
  12. Intelligence MIT: Intelligence
  13. Emotion & Motivation MIT: Emotion & Motivation
  14. Personality MIT: Personality
  15. Child Development MIT: Child Development
  16. Adult Development MIT: Adult Development
  17. Stress MIT: Stress
  18. Psychopathology MIT: Psychopathology I; Psychopathology II
  19. Social Psychology I MIT: Social Psychology I
  20. Social Psychology II MIT: Social Psychology II
  21. Conclusions: Evolutionary Psychology, Happiness MIT: Conclusions: Evolutionary Psychology, Happiness

14.01SC Principles of Microeconomics

20 topics · 18 with MIT solutions · the full course →

  1. Introduction to Microeconomics MIT solutionsMIT: Introduction to Microeconomics
  2. Applying Supply and Demand MIT solutionsMIT: Applying Supply and Demand
  3. Elasticity MIT solutionsMIT: Elasticity
  4. Preferences and Utility MIT solutionsMIT: Preferences and Utility
  5. Budget Constraints MIT solutionsMIT: Budget Constraints
  6. Deriving Demand Curves MIT solutionsMIT: Deriving Demand Curves
  7. Introduction to Producer Theory MIT solutionsMIT: Introduction to Producer Theory
  8. Productivity and Costs MIT solutionsMIT: Productivity and Costs
  9. Competition MIT solutionsMIT: Competition I; Competition II; Competition III
  10. Principles of Welfare Economics MIT solutionsMIT: Principles of Welfare Economics
  11. Monopoly MIT solutionsMIT: Monopoly I; Monopoly II
  12. Oligopoly MIT solutionsMIT: Oligopoly I; Oligopoly II
  13. Factor Markets MIT solutionsMIT: Factor Markets
  14. International Trade MIT solutionsMIT: International Trade
  15. Uncertainty MIT solutionsMIT: Uncertainty
  16. Capital Supply and Markets MIT solutionsMIT: Capital Supply and Markets I; Capital Supply and Markets II
  17. Equity and Efficiency MIT solutionsMIT: Equity and Efficiency
  18. Government Redistribution Policy MIT solutionsMIT: Government Redistribution Policy
  19. U.S. Social Insurance Programs MIT: U.S. Social Insurance Programs
  20. Healthcare Economics MIT: Healthcare Economics

2.003SC Engineering Dynamics

12 topics · 10 with MIT solutions · the full course →

  1. Newton's Laws, Vectors, and Reference Frames MIT solutionsMIT: Newton's Laws, Vectors, and Reference Frames
  2. Velocity, Acceleration, and Rotational Motion MIT solutionsMIT: Velocity, Acceleration, and Rotational Motion
  3. Angular Momentum and Torque MIT solutionsMIT: Angular Momentum and Torque
  4. Free Body Diagrams and Fictitious Forces MIT solutionsMIT: Free Body Diagrams and Fictitious Forces
  5. Angular Momentum and Rotating Masses MIT: Angular Momentum and Rotating Masses
  6. Angular Momentum and Motion of Rotating Rigid Bodies MIT solutionsMIT: Angular Momentum and Motion of Rotating Rigid Bodies
  7. Finding Equations of Motion for Rigid Body Rotation MIT solutionsMIT: Finding Equations of Motion for Rigid Body Rotation
  8. Lagrange Equations MIT solutionsMIT: Lagrange Equations; Lagrange Equations Continued
  9. Mechanical Vibration MIT solutionsMIT: Mechanical Vibration
  10. Reducing Problem Vibration and Intro to Multi-DOF Vibration MIT: Reducing Problem Vibration and Intro to Multi-DOF Vibration
  11. Vibration of Multi-Degree-of-Freedom Systems MIT solutionsMIT: Vibration of Multi-Degree-of-Freedom Systems
  12. Vibration Analysis by Mode Superposition MIT solutionsMIT: Vibration Analysis by Mode Superposition

5.07SC Biological Chemistry I

11 topics · 3 with MIT solutions · the full course →

  1. What is Biochemistry? MIT solutionsMIT: Session 1: What is Biochemistry?
  2. Enzyme Kinetics and Enzyme Inhibition MIT solutionsMIT: Session 4: Enzyme Kinetics and Enzyme Inhibition
  3. Biochemical Transformations III MIT solutionsMIT: Session 7: Biochemical Transformations III
  4. Glycolysis and Early Stages of Respiration MIT: Session 9: Glycolysis and Early Stages of Respiration
  5. Maintenance of Redox Neutrality MIT: Session 11: Maintenance of Redox Neutrality
  6. Respiration: Proton Pumps and ATP Synthesis MIT: Session 13: Respiration: Proton Pumps and ATP Synthesis
  7. Lipid Catabolism: Fatty Acid Beta-Oxidation MIT: Session 14: Lipid Catabolism: Fatty Acid Beta-Oxidation
  8. Fatty Acid and Lipid Biosynthesis MIT: Session 17: Fatty Acid and Lipid Biosynthesis
  9. Carbohydrate Biosynthesis I: Glycogen Synthesis MIT: Session 18: Carbohydrate Biosynthesis I: Glycogen Synthesis
  10. Carbohydrate Biosynthesis III: Pentose Phosphate Pathway MIT: Session 20: Carbohydrate Biosynthesis III: Pentose Phosphate Pathway
  11. Regulation of Metabolism MIT: Session 21: Regulation of Metabolism