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Mathematics - All of It

Mathematics - All of It

Professor Dave Explains via YouTube Direct link

The Gram-Schmidt Process

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The Gram-Schmidt Process

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Mathematics - All of It

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  1. 1 Introduction to Mathematics
  2. 2 Addition and Subtraction of Small Numbers
  3. 3 Multiplication and Division of Small Numbers
  4. 4 Understanding Fractions, Improper Fractions, and Mixed Numbers
  5. 5 Large Whole Numbers: Place Values and Estimating
  6. 6 Decimals: Notation and Operations
  7. 7 Working With Percentages
  8. 8 Converting Between Fractions, Decimals, and Percentages
  9. 9 Addition and Subtraction of Large Numbers
  10. 10 The Distributive Property for Arithmetic
  11. 11 Multiplication of Large Numbers
  12. 12 Division of Large Numbers: Long Division
  13. 13 Negative Numbers
  14. 14 Understanding Exponents and Their Operations
  15. 15 Order of Arithmetic Operations: PEMDAS
  16. 16 Divisibility, Prime Numbers, and Prime Factorization
  17. 17 Least Common Multiple (LCM)
  18. 18 Greatest Common Factor (GCF)
  19. 19 Addition and Subtraction of Fractions
  20. 20 Multiplication and Division of Fractions
  21. 21 Analyzing Sets of Data: Range, Mean, Median, and Mode
  22. 22 Introduction to Algebra: Using Variables
  23. 23 Basic Number Properties for Algebra
  24. 24 Algebraic Equations and Their Solutions
  25. 25 Algebraic Equations With Variables on Both Sides
  26. 26 Algebraic Word Problems
  27. 27 Solving Algebraic Inequalities
  28. 28 Square Roots, Cube Roots, and Other Roots
  29. 29 Simplifying Expressions With Roots and Exponents
  30. 30 Solving Algebraic Equations With Roots and Exponents
  31. 31 Introduction to Polynomials
  32. 32 Adding and Subtracting Polynomials
  33. 33 Multiplying Binomials by the FOIL Method
  34. 34 Solving Quadratics by Factoring
  35. 35 Solving Quadratics by Completing the Square
  36. 36 Solving Quadratics by Using the Quadratic Formula
  37. 37 Solving Higher Degree Polynomials by Synthetic Division and the Rational Roots Test
  38. 38 Manipulating Rational Expressions: Simplification and Operations
  39. 39 Graphing in Algebra: Ordered Pairs and the Coordinate Plane
  40. 40 Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts
  41. 41 Graphing Lines in Slope-Intercept Form (y = mx + b)
  42. 42 Graphing Lines in Standard Form (ax + by = c)
  43. 43 Graphing Parallel and Perpendicular Lines
  44. 44 Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination
  45. 45 Absolute Values: Defining, Calculating, and Graphing
  46. 46 What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
  47. 47 Introduction to Geometry: Ancient Greece and the Pythagoreans
  48. 48 Basic Euclidean Geometry: Points, Lines, and Planes
  49. 49 Types of Angles and Angle Relationships
  50. 50 Types of Triangles in Euclidean Geometry
  51. 51 Proving Triangle Congruence and Similarity
  52. 52 Special Lines in Triangles: Bisectors, Medians, and Altitudes
  53. 53 The Triangle Midsegment Theorem
  54. 54 The Pythagorean Theorem
  55. 55 Types of Quadrilaterals and Other Polygons
  56. 56 Calculating the Perimeter of Polygons
  57. 57 Circles: Radius, Diameter, Chords, Circumference, and Sectors
  58. 58 Calculating the Area of Shapes
  59. 59 Proving the Pythagorean Theorem
  60. 60 Three-Dimensional Shapes Part 1: Types, Calculating Surface Area
  61. 61 Three-Dimensional Shapes Part 2: Calculating Volume
  62. 62 Back to Algebra: What are Functions?
  63. 63 Manipulating Functions Algebraically and Evaluating Composite Functions
  64. 64 Graphing Algebraic Functions: Domain and Range, Maxima and Minima
  65. 65 Transforming Algebraic Functions: Shifting, Stretching, and Reflecting
  66. 66 Continuous, Discontinuous, and Piecewise Functions
  67. 67 Inverse Functions
  68. 68 The Distance Formula: Finding the Distance Between Two Points
  69. 69 Graphing Conic Sections Part 1: Circles
  70. 70 Graphing Conic Sections Part 2: Ellipses
  71. 71 Graphing Conic Sections Part 3: Parabolas in Standard Form
  72. 72 Graphing Conic Sections Part 4: Hyperbolas
  73. 73 Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros
  74. 74 Graphing Rational Functions and Their Asymptotes
  75. 75 Solving and Graphing Polynomial and Rational Inequalities
  76. 76 Evaluating and Graphing Exponential Functions
  77. 77 Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions
  78. 78 Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property
  79. 79 Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions
  80. 80 Solving Exponential and Logarithmic Equations
  81. 81 Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem
  82. 82 Set Theory: Types of Sets, Unions and Intersections
  83. 83 Sequences, Factorials, and Summation Notation
  84. 84 Theoretical Probability, Permutations and Combinations
  85. 85 Introduction to Trigonometry: Angles and Radians
  86. 86 Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent
  87. 87 The Easiest Way to Memorize the Trigonometric Unit Circle
  88. 88 Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities
  89. 89 Graphing Trigonometric Functions
  90. 90 Inverse Trigonometric Functions
  91. 91 Verifying Trigonometric Identities
  92. 92 Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod
  93. 93 Solving Trigonometric Equations
  94. 94 The Law of Sines
  95. 95 The Law of Cosines
  96. 96 Polar Coordinates and Graphing Polar Equations
  97. 97 Parametric Equations
  98. 98 Introduction to Calculus: The Greeks, Newton, and Leibniz
  99. 99 Understanding Differentiation Part 1: The Slope of a Tangent Line
  100. 100 Understanding Differentiation Part 2: Rates of Change
  101. 101 Limits and Limit Laws in Calculus
  102. 102 What is a Derivative? Deriving the Power Rule
  103. 103 Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule
  104. 104 Derivatives of Trigonometric Functions
  105. 105 Derivatives of Composite Functions: The Chain Rule
  106. 106 Derivatives of Logarithmic and Exponential Functions
  107. 107 Implicit Differentiation
  108. 108 Higher Derivatives and Their Applications
  109. 109 Related Rates in Calculus
  110. 110 Finding Local Maxima and Minima by Differentiation
  111. 111 Graphing Functions and Their Derivatives
  112. 112 Optimization Problems in Calculus
  113. 113 Understanding Limits and L'Hospital's Rule
  114. 114 What is Integration? Finding the Area Under a Curve
  115. 115 The Fundamental Theorem of Calculus: Redefining Integration
  116. 116 Properties of Integrals and Evaluating Definite Integrals
  117. 117 Evaluating Indefinite Integrals
  118. 118 Evaluating Integrals With Trigonometric Functions
  119. 119 Integration Using The Substitution Rule
  120. 120 Integration By Parts
  121. 121 Integration by Trigonometric Substitution
  122. 122 Advanced Strategy for Integration in Calculus
  123. 123 Evaluating Improper Integrals
  124. 124 Finding the Area Between Two Curves by Integration
  125. 125 Calculating the Volume of a Solid of Revolution by Integration
  126. 126 Calculating Volume by Cylindrical Shells
  127. 127 The Mean Value Theorem For Integrals: Average Value of a Function
  128. 128 Convergence and Divergence: The Return of Sequences and Series
  129. 129 Estimating Sums Using the Integral Test and Comparison Test
  130. 130 Alternating Series, Types of Convergence, and The Ratio Test
  131. 131 Power Series
  132. 132 Taylor and Maclaurin Series
  133. 133 Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses
  134. 134 Three-Dimensional Coordinates and the Right-Hand Rule
  135. 135 Introduction to Vectors and Their Operations
  136. 136 The Vector Dot Product
  137. 137 Introduction to Linear Algebra: Systems of Linear Equations
  138. 138 Understanding Matrices and Matrix Notation
  139. 139 Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination
  140. 140 Types of Matrices and Matrix Addition
  141. 141 Matrix Multiplication and Associated Properties
  142. 142 Evaluating the Determinant of a Matrix
  143. 143 The Vector Cross Product
  144. 144 Inverse Matrices and Their Properties
  145. 145 Solving Systems Using Cramer's Rule
  146. 146 Understanding Vector Spaces
  147. 147 Subspaces and Span
  148. 148 Linear Independence
  149. 149 Basis and Dimension
  150. 150 Change of Basis
  151. 151 Linear Transformations on Vector Spaces
  152. 152 Image and Kernel
  153. 153 Orthogonality and Orthonormality
  154. 154 The Gram-Schmidt Process
  155. 155 Finding Eigenvalues and Eigenvectors
  156. 156 Diagonalization
  157. 157 Complex, Hermitian, and Unitary Matrices
  158. 158 Double and Triple Integrals
  159. 159 Partial Derivatives and the Gradient of a Function
  160. 160 Vector Fields, Divergence, and Curl
  161. 161 Evaluating Line Integrals
  162. 162 Green's Theorem
  163. 163 Evaluating Surface Integrals
  164. 164 Stokes's Theorem
  165. 165 The Divergence Theorem

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