MATH 231. Calculus with Functions I.

Goals of the Course

. To develop an understanding of the logical structure and style of mathematics by:
(a)  Using reason in an orderly, cogent fashion.
(b)  Writing clear, well organized solutions to problems.

Structure refers to the foundations of mathematics and to the techniques used to build on those foundations. Style refers to the clarity, elegance, efficiency, and precision desirable in mathematical expression.

2. To develop ability to use mathematical tools to solve problems and to transfer this knowledge to analogous situations by:
(a) Using algebra, limits, and derivatives to classify properties of power, polynomial, rational, and general algebraic functions.
(b) Using differentiation to solve problems involving optimization and rates of change.

3. To develop computational skills such as:
(a) Solving equations and inequalities, factoring, fraction manipulation, handling exponents.
(b) Calculating limits and derivatives.
(c) Finding maxima and minima of functions, and curve sketching of algebraic functions.

4. To develop an understanding of the theory of calculus and algebraic structures by knowing:
(a) The definitions of limit, derivative, and continuous function.
(b) The important results concerning continuous and differentiable functions including the Intermediate Value Theorem, Rolle's Theorem, the Mean Value Theorem, and the relationship between continuity and differentiability.
(c) The theory of maxima and minima of functions.