Appendix B Definitions
1.1 Antiderivatives
Definition 1.1.2 Antiderivative
Definition 1.1.11 Indefinite integral
1.3 Riemann sums
Definition 1.3.1 Sigma notation
Definition 1.3.7 Riemann sums
Definition 1.3.8 Riemann sum types
1.4 Definite integral
Definition 1.4.1 Definite integral
Definition 1.4.8 Area and signed area of regions defined by functions
1.5 Fundamental theorem of calculus
Definition 1.5.4 Difference evaluation notation
1.6 Fundamental theorem (cont.)
Definition 1.6.1 Integral function
1.8 More substitution; area between curves
Definition 1.8.3 Area between curves: functions of \(x\)
Definition 1.8.4 Area between curves: functions of \(y\)
1.9 Volume via cross sections
Definition 1.9.1 Volume via cross sections
Definition 1.9.5 Solid of revolution
1.10 Inverse functions
Definition 1.10.1 One-to-one function
Definition 1.10.2 Inverse function
Definition 1.10.4 Monotonic
1.11 The natural logarithm
Definition 1.11.1 Natural logarithm
Definition 1.11.5 Euler’s number
1.12 Exponential functions
Definition 1.12.1 Exponential function
Definition 1.12.3 Base-\(a\) exponential function
Definition 1.12.4 Base-\(a\) logarithm
1.13 Separable differential equations
Definition 1.13.1 Exponential growth and decay
Definition 1.13.3 First-order differential equation
Definition 1.13.4 Separable first-order differential equation
1.14 L’Hôpital’s rule
Definition 1.14.1 Indeterminate forms
1.15 More on indeterminate forms
Definition 1.15.1 More indeterminate forms
1.16 Inverse trigonometric functions
Definition 1.16.1 Inverse trigonometric functions
1.21 Rational functions
Definition 1.21.1 Rational function
1.22 Numerical integration: techniques
Definition 1.22.1 Trapezoidal rule
Definition 1.22.2 Simpson’s rule
1.24 Improper integrals
Definition 1.24.1 Improper integral of type I: infinite intervals
Definition 1.24.6 Improper integrals of type II: discontinuities
Definition 1.24.7 Area interpretation of improper integrals
1.26 First-order linear differential equations
Definition 1.26.1 First-order linear equation
Definition 1.26.2 Integrating factor