1.
Limit of a sequence
§1.
Convergence and Divergence of Sequences 9
§2.
Limit of Geometric Sequence 16
Practice Problem 1 21
2.
water supply
§1.
Grade 23
§2.
Geometric series 30
§3.
Applications of Geometric Series 35
Practice Problem 2 43
3.
Addition theorem of trigonometric functions
§1.
Definition of Trigonometric Functions 47
§2.
Trigonometric Addition Theorem 50
§3.
Composition of Trigonometric Functions 57
§4.
Double and Half-Width Formula 62
§5.
Formula for Sum or Difference 71
Practice Problem 3 76
4.
limit of a function
§1.
Limit of a function 80
§2.
Limits of Trigonometric, Exponential, and Logarithmic Functions 85
§3.
Determination of the undetermined coefficient 93
§4.
Continuous Function 97
Practice Problem 4 103
5.
Differentiation of a function
§1.
Differentiation and Derivatives 106
§2.
Differential Calculus Formula 112
§3.
Differentiation of Composite Functions 116
§4.
Differentiation of Implicit and Inverse Functions 120
§5.
Differentiation of parametric functions 125
Practice Problem 5 129
6.
Derivatives of various functions
§1.
Derivatives of Trigonometric Functions 131
§2.
Derivatives of Exponential and Logarithmic Functions 135
Practice Problem 6 141
7.
Tangents and differentiation of curves
§1.
Geometric Meaning of Differential Coefficients 143
§2.
Equation of Tangent Line 146
Practice Problem 7 154
8.
Properties of derivatives
§1.
Differentiability and Continuity 157
§2.
Mean Theorem 160
Practice Problem 8 169
9.
Maxima, minima, and differentiation
§1.
Increasing and decreasing functions 170
§2.
Maxima and Minima of Functions 173
§3.
Concavity and Convexity of Curves and Inflection Points 182
§4.
Curve Reform 189
Practice Problem 9 194
10.
Maximum, minimum and differentiation
§1.
Maximum and minimum of functions 197
§2.
Maximum and Minimum Utilization 202
Practice Problem 10 206
11.
Equations, Inequalities, and Differentiation
§1.
Equations and Differentiation 208
§2.
Inequalities and Differentiation 212
Practice Problem 11 216
12.
Velocity, acceleration, and differentiation
§1.
Speed ​​and acceleration 218
§2.
Instantaneous rate of change of a function with respect to time 221
§3.
Motion on a Plane 226
Practice Problem 12 231
13.
indefinite integral
§1.
Definition and Calculation of Indefinite Integrators 233
§2.
Indefinite integrals of various functions 239
Practice Problem 13 242
14.
Substitution integral and integration by parts
§1.
Substitution Integration Method 243
§2.
Integration by Parts 254
Practice Problem 14 260
15.
Calculation of definite integrals
§1.
Definition and Computation of Definite Integrators 262
§2.
Substitution and Partial Integration of Definite Integrals 270
Practice Problem 15 279
16.
Various problems regarding definite integrals
§1.
Section 282
§2.
Definite Integrals and Series 286
§3.
Functions defined by definite integrals 293
§4.
Definite Integrals and Inequalities 301
Practice Problem 16 304
17.
Area and integrals
§1.
Area between curve and coordinate axes 306
§2.
Area between two curves 313
§3.
Curves and Areas Represented by Parameters 319
Practice Problem 17 321
18.
Volume and Integration
§1.
Volume of regular solids 324
§2.
Volume of the rotating body 329
Practice Problem 18 338
19.
Speed, distance, and integration
§1.
Speed ​​and distance 340
§2.
Motion on a Plane 345
Practice Problem 19 350