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Math 220-2: Kursobjekt

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