1.
Limit of a sequence
§1.
Convergence and Divergence of Sequences 7
§2.
Limit of Geometric Sequence 15
Practice Problem 1 20
2.
water supply
§1.
Grade 22
§2.
Geometric series 28
§3.
Applications of Geometric Series 34
Practice Problem 2 43
3.
Addition theorem of trigonometric functions
§1.
Definition of Trigonometric Functions 46
§2.
Trigonometric Addition Theorem 50
§3.
Composition of Trigonometric Functions 58
§4.
Double and Half Angle Formula 63
Practice Problem 3 72
4.
limit of a function
§1.
Limits of Functions 75
§2.
Limits of Trigonometric, Exponential, and Logarithmic Functions 84
§3.
Continuous Function 95
Practice Problem 4 102
5.
Differentiation of a function
§1.
Differentiation and Derivatives 105
§2.
Differential Calculus Formula 113
§3.
Differentiation of Composite Functions 117
§4.
Differentiation of Implicit and Inverse Functions 122
§5.
Differentiation of parametric functions 127
Practice Problem 5 131
6.
Derivatives of various functions
§1.
Derivatives of Trigonometric Functions 133
§2.
Derivatives of Exponential and Logarithmic Functions 138
Practice Problem 6 144
7.
Tangents and differentiation of curves
§1.
Geometric Meaning of Differential Coefficients 146
§2.
Equation of Tangent Line 149
Practice Problem 7 156
8.
Properties of derivatives
§1.
Differentiability and Continuity 158
§2.
Mean Theorem 161
Practice Problem 8 169
9.
Maxima, minima, and differentiation
§1.
Increasing and decreasing functions 171
§2.
Maxima and Minima of Functions 174
§3.
Graph modification 185
Practice Problem 9 193
10.
Maximum, minimum and differentiation
§1.
Maximum and minimum of the function 196
§2.
Maximum and Minimum Utilization 201
Practice Problem 10 204
11.
Equations, Inequalities, and Differentiation
§1.
Equations and Differentiation 206
§2.
Inequalities and Differentiation 211
Practice Problem 11 214
12.
Velocity, acceleration, and differentiation
§1.
Speed ​​and acceleration 215
§2.
Instantaneous rate of change of a function with respect to time 218
§3.
Motion on a Plane 222
Practice Problem 12 227
13.
indefinite integral
§1.
Definition of Indefinite Integral 229
§2.
Calculating Indefinite Integrators 232
§3.
Indefinite integrals of various functions 236
Practice Problem 13 241
14.
Substitution integral and integration by parts
§1.
Substitution Integration Method 242
§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 273
Practice Problem 15 279
16.
Various problems regarding definite integrals
§1.
Section 282
§2.
Definite Integrals and Series 287
§3.
Functions defined by definite integrals 295
Practice Problem 16 303
17.
Area and integral
§1.
Area between curve and coordinate axes 305
§2.
Area between two curves 313
Practice Problem 17 319
18.
Volume and Integration
§1.
Volume of regular solids 321
§2.
Volume of the rotating body 327
Practice Problem 18 337
19.
Speed, distance, and integration
§1.
Speed ​​and Distance 339
§2.
Motion on a Plane 344
Practice Problem 19 348