Computer-age Calculus with R
Table of contents
Preface
1
Representing mathematical functions
1.1
Numbers, quantities, and names
1.2
R-language functions
1.3
Literate use of arguments
1.4
With respect to …
2
Graphing functions
2.1
Graphing mathematical functions
2.1.1
Exercises
2.2
Making scatterplots
2.2.1
Exercises
2.3
Graphing functions of two variables
2.3.1
Exercises
3
Parameters and functions
3.1
Parameters versus variables
3.2
Parameters of modeling functions
3.3
Polynomials and parameters
3.4
Parameters and
makeFun()
3.5
Functions without parameters: splines and smoothers
3.5.1
Exercises
4
Solving
4.1
Functions vs equations
4.1.1
From Equations to Zeros of Functions
4.1.2
Multiple Solutions
4.1.3
Setting up a Problem
4.1.4
Exercises
5
Modeling with linear combinations
5.1
Linear algebra
5.1.1
Example: Atomic bomb data.
5.1.2
Exercises
6
Fitting functions to data
6.0.1
Exercises
6.1
Curves and linear models
6.1.1
Exercises
6.2
fitModel()
6.3
Functions with nonlinear parameters
6.4
Exponential functions
6.5
Optimizing the guesses
6.5.1
Exercises
7
Derivatives and differentiation
7.1
Formulas and Numerical Difference
7.2
Symbolic Parameters
7.3
Partial Derivatives
7.3.1
Second derivatives
7.3.2
Exercises
8
Integrals and integration
8.1
The anti-derivative
8.2
One variable becomes two arguments
8.3
The integral
8.3.1
Exercises
9
Dynamics
9.1
Solving differential equations
9.2
Systems of differential equations
9.2.1
Example: Diving from the high board
9.2.2
Exercises
Project MOSAIC Books
Computer-age Calculus with R
Computer-age Calculus with R
Daniel Kaplan
2020-05-25
Table of contents