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Matematika
Table of Contents
Part 1: Sets and numbers
1. Sets
2. Types Of Numbers
3. Natural Numbers
4. Integers
5. Modulo Operator
6. Real Numbers
7. Properties Of Real Numbers
8. Absolute Value
9. Intervals
10. Supremum and Infimum
11.
12. Binomial Coefficient
Part 2: Algebraic structures
13.
14. Rings
15. Fields
16. Vector Spaces
Part 3: Powers radicals and logarithms
17.
18. Radicals
19. Logarithms
Part 4: Complex numbers
20. Complex Numbers
21. Operations with Complex Numbers
22. Complex Numbers in Trigonometric Form
23.
24. De Moivre’s Theorem
25. Roots of Unity
Part 5: Trigonometry
26. Unit Circle
27. Sine and Cosine
28. Tangent and Cotangent
29. Secant and Cosecant
30. Arcsine and Arccosine
31. Arctangent and Arccotangent
32. Hyperbolic Sine and Cosine
33. Hyperbolic Tangent and Cotangent
34.
35. Trigonometric Identities
36. Pythagorean Identity
37.
38. Reduction Formulas and Reference Angles
39. The Law of Sines
40. The Law of Cosines
Part 6: Polynomials
41.
42. Monomials
43. Binomials
44. Trinomials
45. Adding and Subtracting Polynomials
46. Polynomial Division
47. The Synthetic Division Method
48. Roots of a Polynomial
49. Binomial Theorem
50.
51.
52. Notable Products
53. Partial Fraction Decomposition
Part 7: Equations
54. Equations
55.
56. Linear Equations
57.
58.
59. Factoring Quadratic Equations
60. Incomplete Quadratic Equations
61. The Geometric Interpretation of Quadratic Equations
62. Loss of Roots
63.
64.
65. Trinomial Equations
66. Rational Equations
67. Irrational Equations
68. Absolute Value Equations
69.
70. Logarithmic Equations
71. Homogeneous Trigonometric Equations
72.
73. Equations with Parameters
74. Linear Equations with Parameters
75. Quadratic Equations with Parameters
Part 8: Inequalities
76. Linear Inequalities
77. Quadratic Inequalities
78. Sign Analysis in Inequalities
79. Rational Inequalities
80. Irrational Inequalities
81.
82. Logarithmic Inequalities
83. Trigonometric Inequalities
84. Systems of Inequalities
Part 9: Lines planes and conic sections
85. Lines
86.
87. Polar Coordinates
88. Parabola
89.
90. Ellipse
91. Hyperbola
Part 10: Vectors and matrices
92. Vectors and Matrices
93. Vectors and Matrices
94. Vectors and Matrices
95.
96. Vectors and Matrices
97. Vectors and Matrices
98. Vectors and Matrices
99. Vectors and Matrices
Part 11: Linear systems
100. Systems of Linear Equations
101. Cramer’s Rule
102. Gaussian Elimination
Part 12: Sequences
103. Principle of Mathematical Induction
104. Sequences
105. Convergent and Divergent Sequences
106.
107. Arithmetic Sequence
108. Geometric Sequence
109. Cauchy Sequence
110.
111. Sequences of Functions
Part 13: Series
112. Series
113. Cauchy’s Convergence Criterion for Series
114.
115.
116.
117. Integral Test for Series Convergence
118. Root Test for Series Convergence
119. Leibniz’s Criterion
120. Function Series
121. Power Series
122. Taylor Series
123. Fourier Series
Part 14: Functions
124. Functions
125. Determining the Domain of a Function
126. Even and Odd Functions
127.
128. Convexity and Concavity of Functions
129. Composite Functions
130.
131. Continuous Functions
132. Uniform Continuity
133. Discontinuities of Real Functions
134. Analyzing the Graphs of Functions
135.
136. Rational Functions
137. Logarithmic Function
138.
139.
140.
141. Sine Function
142. Cosine Function
143. Tangent Function
144. Cotangent Function
145. Secant Function
146. Cosecant Function
147.
148. Sigmoid Function
Part 15: Limits
149. Limits
150. Algebra of Limits
151. Squeeze Theorem
152. Remarkable Limits
153. Asymptotes
154.
155. Little-o Notation
156. Big O Notation
Part 16: Derivatives
157. Difference Quotient
158. Derivatives
159. Derivative of a Composite Function
160. Non-Differentiable Points
161. Differential of a Function
162. Derivative of Composite Power Functions
163. Maximum, Minimum, and Inflection Points
164. Partial Derivatives
Part 17: Differential calculus theorems
165.
166. Fermat’s Theorem
167.
168. Lagrange’s Theorem
169. Cauchy’s Theorem
170. L’Hôpital’s Rule
Part 18: Integrals
171. Indefinite Integrals
172. Definite Integrals
173. Fundamental Theorem of Calculus
174. Integration by Substitution
175.
176. Finding Areas by Integration
177. Integral of the Exponential Function
178. Integral of Trigonometric Functions
179.
180. Trigonometric Substitution for Integrals
181. Improper Integrals
182. Riemann Integrability Criteria
Part 19: Differential equations
183. Differential Equations
Part 20: Probability and statistics
184. Probability and Statistics
185. Probability and Statistics
186. Probability and Statistics
187. Probability and Statistics
188. Root Mean Square
189. Median and Quantiles
190. Variance
191. Discrete Random Variables
192. Continuous Random Variables
193. Mean or Expected Value of a Random Variable
194. Variance and Covariance of a Random Variable
195.
196. Binomial Distribution
197. Hypergeometric Distribution
198. Geometric Distribution
199. Poisson Distribution
200. Uniform Distribution
201. Beta Distribution
202. Normal Distribution
203. Standard Normal Z Table
204. Gamma Distribution
205. Chi-square Distribution
206. Student’s t Distribution
207. Exponential Distribution
208. Sampling Distributions
209. Bayes’ Theorem
210. Confidence Intervals
Part 21: Kinematics
211.
212.
213. Simple Harmonic Motion
Part 22: Other topics
214. Cosine Similarity
215. Propositional Logic
216. The Backpropagation Algorithm
References
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Contents
Part 13: Series
Chapter 121.
Power Series
Next: Series › Chapter 122.
Taylor Series
Previous: Series › Chapter 120.
Function Series