Dec 02, 2022
MTH 252 - Calculus 2 (Integral Calculus)5 Credit(s)
Specific topics include conceptual development of the definite integral, properties of the definite integral, the first and second Fundamental Theorems of Calculus, constructing anti-derivatives, techniques of indefinite integration, approximating definite integrals, and applications. Analytical, graphical, and numerical methods are used to support one another in developing the course material. Opportunities are provided for students to work in groups, verbalize concepts with one another, and explore concepts and applications using technology.
Prerequisite: MTH 251 or equivalent course completed with a grade of C- or better completed within the past five years.
Upon successful completion of this course, the student should be able to:
- Estimate & calculate totals given information about rates of change
- Understand the definite integral as a limit of Riemann sums.
- Interpret the meaning of and use correct notation for a definite integral.
- Compute definite integrals using the first fundamental theorem of calculus.
- Understand how the definite integral and the average value of a function are related.
- Use properties and theorems pertaining to integrals.
- Graphically and numerically construct antiderivatives.
- Work with elementary differential equations.
- Work with functions defined in terms of definite integrals with a variable limit(s) of integration and apply the second fundamental theorem of calculus to the analysis of these functions.
- Understand that the indefinite integral represents a family of antiderivative functions.
- Find definite & indefinite integrals using basic rules, the substitution method, integration by parts, and trigonometric substitution.
- Use the midpoint, trapezoid, and Simpson's rule to approximate definite integrals.
- Identify improper integrals that converge or diverge and compute their values where possible.
- Use the methods & techniques of integral calculus to solve a variety of application problems.
- Use a programmable graphing calculator as an effective tool in confirming analytical work and obtaining numerical and graphical results related to integral calculus
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