Mathematics (All Of It)

Chapters

1. 01Introduction to Mathematics06:44
2. 02Addition and Subtraction of Small Numbers08:39
3. 03Multiplication and Division of Small Numbers06:20
4. 04Understanding Fractions, Improper Fractions, and Mixed Numbers06:13
5. 05Large Whole Numbers: Place Values and Estimating04:29
6. 06Decimals: Notation and Operations04:21
7. 07Working With Percentages03:36
8. 08Converting Between Fractions, Decimals, and Percentages05:21
9. 09Addition and Subtraction of Large Numbers05:57
10. 10The Distributive Property for Arithmetic03:19
11. 11Multiplication of Large Numbers06:28
12. 12Division of Large Numbers: Long Division05:41
13. 13Negative Numbers05:27
14. 14Understanding Exponents and Their Operations08:42
15. 15Order of Arithmetic Operations: PEMDAS04:22
16. 16Divisibility, Prime Numbers, and Prime Factorization05:54
17. 17Least Common Multiple (LCM)05:40
18. 18Greatest Common Factor (GCF)04:46
19. 19Addition and Subtraction of Fractions04:07
20. 20Multiplication and Division of Fractions05:06
21. 21Analyzing Sets of Data: Range, Mean, Median, and Mode05:46
22. 22Introduction to Algebra: Using Variables04:04
23. 23Basic Number Properties for Algebra05:16
24. 24Algebraic Equations and Their Solutions04:52
25. 25Algebraic Equations With Variables on Both Sides06:46
26. 26Algebraic Word Problems05:38
27. 27Solving Algebraic Inequalities05:43
28. 28Square Roots, Cube Roots, and Other Roots09:02
29. 29Simplifying Expressions With Roots and Exponents08:23
30. 30Solving Algebraic Equations With Roots and Exponents05:46
31. 31Introduction to Polynomials05:13
32. 32Adding and Subtracting Polynomials05:32
33. 33Multiplying Binomials by the FOIL Method06:25
34. 34Solving Quadratics by Factoring09:37
35. 35Solving Quadratics by Completing the Square07:32
36. 36Solving Quadratics by Using the Quadratic Formula06:55
37. 37Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test09:22
38. 38Manipulating Rational Expressions: Simplification and Operations09:30
39. 39Graphing in Algebra: Ordered Pairs and the Coordinate Plane06:56
40. 40Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts06:52
41. 41Graphing Lines in Slope-Intercept Form (y = mx + b)05:06
42. 42Graphing Lines in Standard Form (ax + by = c)05:33
43. 43Graphing Parallel and Perpendicular Lines04:47
44. 44Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination10:21
45. 45Absolute Values: Defining, Calculating, and Graphing05:10
46. 46What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational09:00
47. 47Introduction to Geometry: Ancient Greece and the Pythagoreans04:00
48. 48Basic Euclidean Geometry: Points, Lines, and Planes04:19
49. 49Types of Angles and Angle Relationships07:24
50. 50Types of Triangles in Euclidean Geometry05:25
51. 51Proving Triangle Congruence and Similarity05:08
52. 52Special Lines in Triangles: Bisectors, Medians, and Altitudes06:20
53. 53The Triangle Midsegment Theorem03:08
54. 54The Pythagorean Theorem05:02
55. 55Types of Quadrilaterals and Other Polygons06:17
56. 56Calculating the Perimeter of Polygons05:08
57. 57Circles: Radius, Diameter, Chords, Circumference, and Sectors04:58
58. 58Calculating the Area of Shapes06:39
59. 59Proving the Pythagorean Theorem03:34
60. 60Three-Dimensional Shapes Part 1: Types, Calculating Surface Area07:32
61. 61Three-Dimensional Shapes Part 2: Calculating Volume06:17
62. 62Back to Algebra: What are Functions?07:23
63. 63Manipulating Functions Algebraically and Evaluating Composite Functions05:29
64. 64Graphing Algebraic Functions: Domain and Range, Maxima and Minima05:54
65. 65Transforming Algebraic Functions: Shifting, Stretching, and Reflecting07:52
66. 66Continuous, Discontinuous, and Piecewise Functions05:18
67. 67Inverse Functions06:29
68. 68The Distance Formula: Finding the Distance Between Two Points03:38
69. 69Graphing Conic Sections Part 1: Circles07:46
70. 70Graphing Conic Sections Part 2: Ellipses06:33
71. 71Graphing Conic Sections Part 3: Parabolas in Standard Form08:30
72. 72Graphing Conic Sections Part 4: Hyperbolas05:58
73. 73Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros09:15
74. 74Graphing Rational Functions and Their Asymptotes07:24
75. 75Solving and Graphing Polynomial and Rational Inequalities07:34
76. 76Evaluating and Graphing Exponential Functions05:59
77. 77Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions08:10
78. 78Logarithms Part 2: Base Ten Logs, Natural Logs, and the Change-Of-Base Property06:26
79. 79Logarithms Part 3: Properties of Logs, Expanding Logarithmic Expressions07:06
80. 80Solving Exponential and Logarithmic Equations07:08
81. 81Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem08:35
82. 82Set Theory: Types of Sets, Unions and Intersections06:22
83. 83Sequences, Factorials, and Summation Notation11:12
84. 84Theoretical Probability, Permutations and Combinations15:52
85. 85Introduction to Trigonometry: Angles and Radians06:27
86. 86Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent07:18
87. 87The Easiest Way to Memorize the Trigonometric Unit Circle09:48
88. 88Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities05:25
89. 89Graphing Trigonometric Functions11:40
90. 90Inverse Trigonometric Functions06:54
91. 91Verifying Trigonometric Identities09:14
92. 92Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod09:29
93. 93Solving Trigonometric Equations08:28
94. 94The Law of Sines05:14
95. 95The Law of Cosines04:38
96. 96Polar Coordinates and Graphing Polar Equations10:46
97. 97Parametric Equations04:36
98. 98Introduction to Calculus: The Greeks, Newton, and Leibniz08:40
99. 99Understanding Differentiation Part 1: The Slope of a Tangent Line05:29
100. 100Understanding Differentiation Part 2: Rates of Change05:31
101. 101Limits and Limit Laws in Calculus12:49
102. 102What is a Derivative? Deriving the Power Rule10:05
103. 103Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule11:53
104. 104Derivatives of Trigonometric Functions07:57
105. 105Derivatives of Composite Functions: The Chain Rule12:29
106. 106Derivatives of Logarithmic and Exponential Functions08:41
107. 107Implicit Differentiation11:45
108. 108Higher Derivatives and Their Applications07:29
109. 109Related Rates in Calculus08:53
110. 110Finding Local Maxima and Minima by Differentiation06:17
111. 111Graphing Functions and Their Derivatives13:06
112. 112Optimization Problems in Calculus10:55
113. 113Understanding Limits and L'Hospital's Rule09:12
114. 114What is Integration? Finding the Area Under a Curve08:18
115. 115The Fundamental Theorem of Calculus: Redefining Integration09:38
116. 116Properties of Integrals and Evaluating Definite Integrals09:48
117. 117Evaluating Indefinite Integrals10:44
118. 118Evaluating Integrals With Trigonometric Functions07:32
119. 119Integration Using The Substitution Rule10:40
120. 120Integration By Parts13:17
121. 121Integration By Trigonometric Substitution15:55
122. 122Advanced Strategy for Integration in Calculus16:13
123. 123Evaluating Improper Integrals12:24
124. 124Finding the Area Between Two Curves by Integration07:52
125. 125Calculating the Volume of a Solid of Revolution by Integration11:20
126. 126Calculating Volume by Cylindrical Shells07:40
127. 127The Mean Value Theorem For Integrals: Average Value of a Function07:24
128. 128Convergence and Divergence: The Return of Sequences and Series09:40
129. 129Estimating Sums Using the Integral Test and Comparison Test09:56
130. 130Alternating Series, Types of Convergence, and the Ratio Test12:08
131. 131Power Series06:48
132. 132Taylor and Maclaurin Series09:34
133. 133Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses07:34
134. 134Three-Dimensional Coordinates and the Right-Hand Rule06:41
135. 135Introduction to Vectors and Their Operations10:17
136. 136The Vector Dot Product06:59
137. 137Introduction to Linear Algebra: Systems of Linear Equations10:46
138. 138Understanding Matrices and Matrix Notation05:26
139. 139Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination10:36
140. 140Types of Matrices and Matrix Addition06:46
141. 141Matrix Multiplication and Associated Properties06:22
142. 142Evaluating the Determinant of a Matrix07:09
143. 143The Vector Cross Product06:46
144. 144Inverse Matrices and Their Properties12:00
145. 145Solving Systems Using Cramer's Rule07:43
146. 146Understanding Vector Spaces08:41
147. 147Subspaces and Span05:50
148. 148Linear Independence12:56
149. 149Basis and Dimension10:06
150. 150Change of Basis09:34
151. 151Linear Transformations on Vector Spaces09:11
152. 152Image and Kernel05:35
153. 153Orthogonality and Orthonormality11:48
154. 154The Gram-Schmidt Process10:07
155. 155Finding Eigenvalues and Eigenvectors17:10
156. 156Diagonalization08:43
157. 157Complex, Hermitian, and Unitary Matrices09:00
158. 158Further Matrix Decompositions: LU, Cholesky, QR, and SVD10:10
159. 159Double and Triple Integrals15:29
160. 160Partial Derivatives and the Gradient of a Function10:57
161. 161Vector Fields, Divergence, and Curl15:36
162. 162Evaluating Line Integrals12:54
163. 163Green's Theorem06:37
164. 164Evaluating Surface Integrals12:24
165. 165Stokes's Theorem08:11
166. 166The Divergence Theorem06:31
167. 167Introduction to Differential Equations04:34
168. 168Classification of Differential Equations07:33
169. 169Separable First-Order Differential Equations07:05
170. 170Linear First-Order Differential Equations04:46
171. 171Exact First-Order Differential Equations08:45
172. 172Homogeneous Differential Equations and Bernoulli Differential Equations10:20
173. 173Linear Second-Order Differential Equations Part 1: Homogeneous Case10:20
174. 174Linear Second-Order Differential Equations Part 2: Non-Homogeneous Differential Equations10:18
175. 175Special Second-Order Differential Equations: Cauchy-Euler, Nonlinear, and More09:37
176. 176Numerical Methods for Solving Differential Equations08:30
177. 177Power Series Solutions Part 1: Leibniz Method10:33
178. 178Power Series Solutions Part 2: Frobenius Method09:24
179. 179Systems of Differential Equations Part 1: Modeling and Elimination07:50
180. 180Systems of Differential Equations Part 2: Matrices and Stability11:50
181. 181Laplace Transforms Part 1: Solving Differential Equations07:58
182. 182Laplace Transforms Part 2: Convolutions and LTI Systems14:59
183. 183Difference Equations and Z-Transforms10:34
184. 184Introduction to Partial Differential Equations: Classification and Differential Operators10:56
185. 185Quasi-Linear First-Order Partial Differential Equations: Lagrange’s Method08:14
186. 186Laplace’s Equation: Separation of Variables11:04
187. 187Fourier Series and Transforms Part 1: Concepts in Frequency Analysis11:02
188. 188Fourier Series and Transforms Part 2: Power Spectra and K-Space06:38
189. 189The Wave Equation Part 1: Vibrations in 1D10:15
190. 190The Wave Equation Part 2: Multidimensional Waves and Dispersion08:20
191. 191The Diffusion Equation Part 1: Separation of Variables06:52
192. 192The Diffusion Equation Part 2: Dimensional Analysis and Self-Similarity10:59
193. 193The Diffusion Equation Part 3: Green’s Functions08:42

About this course

Stop hating math! Learn math with Professor Dave and you'll love it as much as ice cream. In this series we go from arithmetic all the way to differential equations, so no matter what your level of ability, there's something here for you. See if you can watch them all!