Note: F,S,Su 4 cr. LEC 4 PREREQUISITE: M151, ACT 27 or better, SAT 620 or better, MPLEX level 5 within the past 12 months.

## Functions

• elementary transcendental functions
• limits and continuity
• differentiation
• applications of the derivative
• curve sketching
• integration theory

## Course Learning Outcomes

### Upon completion of this course, a student will be able to:

• Explain the definition of limit, how to compute it in elementary cases, and how to determine the limits of transcendental, rational and piecewise defined functions;
• Define infinite limits, limits at infinity, asymptotes, indeterminate forms and how to use L’Hopital’s Rule;
• Explain the limit definition of continuity;
• Explain the limit definition of the derivative of a function, how it related to the function itself, and how to use it to compute derivatives;
• Use derivatives to find tangent lines to curves and velocity for particle motion;
• Apply the power, sum, product, quotient and chain rules of differentiation;
• Use the derivatives of exponential, logarithmic , trigonometric and hyperbolic functions;
• Explain implicit and logarithmic differentiation;
• Apply the Intermediate and Mean Value Theorems;
• Graphically analyze functions including using continuity and differentiation to determine local and global extrema, concavity, and inflection points;
• Use the derivative to solve challenging related rate and optimization word problems;
• Explain Newton’s Method for estimating zeros of a function;
• Explain the Riemann integral, areas under graphs, antiderivatives the Fundamental Theorem of Calculus;
• Apply integration using the method of substitution

## Core 2.0 Quantitative Reasoning (Q)

### Students completing a Core 2.0 Quantitative Reasoning (Q) course should demonstrate an ability to:

• Interpret and draw inferences from mathematical models such as formulas, graphs, diagrams or tables.
• Represent mathematical information numerically, symbolically and visually.
• Employ quantitative methods in symbolic systems such as, arithmetic, algebra, or geometry to solve problems.