Limit and Continuity
The development of calculus by Newton and Leibniz. The concept of a
“limit”. An informal, intuitive notion to a precise mathematical definition of limit.
Application of limits to study “continuous” curves.
Derivative
The Derivative Function. Introduction to techniques of differentiation. The
product and quotient rules. Derivatives of trigonometric functions. Topics in
differentiation. The derivative in graphing and applications.
Integration
Applications
of
the
definite
integral
in
geometry,
science, and engineering. Area between two curves. Volumes by slicing. Disks
and washers. Volumes by cylindrical shells. Length of a plane curve. Area of a
surface of revolution. Work. Principles of integral evaluation.
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