Topic - Bentley University GR526
GR526 is a graduate course at Bentley University that gives an overview of Calculus from a computational viewpoint, for students who plan to study quantitative finance. The description from the course catalog can be found here.
Topics include limits, derivatives, integrals, differential equations, implicit differentiation, Taylor series, and continuous probability. By-hand computation is minimized and the use of a computer algebra system is required, such as Maxima or SymPy.
Basic Symbolic Mathematics
- How to do basic mathematical computations
- How to create symbolic variables
- How to substitute a value for a symbolic variable
Functions and Graphs
- How to compute the domain of a function
- How to graph mathematical functions
- How to graph curves that are not functions
- How to write a piecewise-defined function
- How to graph a two-variable function as a surface
Equations and Systems
- How to write symbolic equations
- How to solve symbolic equations
- How to isolate one variable in an equation
Limits, Sequences, and Series
- How to compute the limit of a function
- How to define a mathematical sequence
- How to graph mathematical sequences
- How to define a mathematical series (and evaluate it)
Differentiation
- How to compute the derivative of a function
- How to compute the Taylor series for a function
- How to compute the error bounds on a Taylor approximation
- How to do implicit differentiation
- How to find the critical numbers of a function
- How to find the critical points of a multivariate function
Antidifferentiation
- How to write and evaluate indefinite integrals
- How to write and evaluate definite integrals
- How to write and evaluate Riemann sums
Differential Equations
Content last modified on 03 August 2023.
Contributed by Nathan Carter (ncarter@bentley.edu)