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
Student Learning Outcomes for a Quantitative Reasoning (Q) Course:
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Interpret and draw inferences from mathematical models such as formulas, graphs, and diagrams or tables.
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Represent mathematical information numerically, symbolically, and visually.
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Employ quantitative methods in symbolic systems such as arithmetic, algebra, or geometry to solve problems.