APEX Calculus I

... etc., are standard topics of study for students today just as they were then. However, the areas of arbitrary shapes could not be computed, even if the boundary of the shape could be described exactly. Rates of change were also important. When an object moves at a constant rate of change, then “dist ...

... etc., are standard topics of study for students today just as they were then. However, the areas of arbitrary shapes could not be computed, even if the boundary of the shape could be described exactly. Rates of change were also important. When an object moves at a constant rate of change, then “dist ...

Contents - CSI Math Department

... A function in mathematics is defined as ”a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.” That is a general definition. Specialized to mathematical functions of one real variable returning a real value, we can de ...

... A function in mathematics is defined as ”a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.” That is a general definition. Specialized to mathematical functions of one real variable returning a real value, we can de ...

Multidimensional Calculus. Lectures content. Week 10 22. Tests for

... on (−1, 1), but the convergence is not uniform. It will be uniform if we restrict our attention to [−%, %] for % ∈ (0, 1). P → Theorem. Let fk →f on M . (i) If all fk are continuous on M , then also f is continuous there. (ii) If all fk have a derivative on M , then also f has it there and f 0 = ...

... on (−1, 1), but the convergence is not uniform. It will be uniform if we restrict our attention to [−%, %] for % ∈ (0, 1). P → Theorem. Let fk →f on M . (i) If all fk are continuous on M , then also f is continuous there. (ii) If all fk have a derivative on M , then also f has it there and f 0 = ...