By the end of this course, you should be able to:
- Construct systems of linear equations and how to solve them, by hand and by using a computational engine, in order to answer questions in various contexts.
- Geometrically interpret the solutions of systems of linear equations, and how to characterize systems of linear equations with more than one solution.
- Create polynomial, trigonometric, exponential, logarithmic, and piecewise functions to model abstract and applied phenomena.
- Use limits to analyze the behaviour of a function for both finite and infinite values.
- Use limits to find the derivative of polynomial, trigonometric, exponential, and logarithmic functions.
- Use the rules for finding derivatives of polynomial, trigonometric, exponential, and logarithmic functions, and to interpret the meaning of the value of the derivative.
- Use derivatives to analyze the properties of a function, including extreme points, regions where the function is increasing and decreasing, and finding the regions of concavity. You will apply these properties to describe the phenomenon a given function is representing.
- Use derivatives to employ the technique of optimization in a variety of contexts, both abstract and applied.
- Use derivatives to describe rates of change, solve related rates problems, and approximate functions.