This course explores Riemann sums, definite integrals, and indefinite integrals for real-valued functions of a single variable. These topics will be explored graphically, numerically, and symbolically in real-life applications. This course emphasizes abstraction, problem-solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of technology.
This class is a foundational course for many STEM majors. Some topics are of particular importance for students continuing into MTH 253 including: using L’Hospital’s rule to evaluate limits, improper integrals, and error estimates for definite integrals. Students may be taking this course concurrently with calculus-based physics courses. Partial fractions are a particularly important technique for engineering students (which will be revisited in MTH 253). Students are not required to have physical graphing calculators in MTH 252Z but are required to have a scientific calculator. Where physically possible instructors will demonstrate using Desmos, GeoGebra, or other online programs in class. Assessments requiring the use of a graphing calculator will be done outside of the proctored exam grade component.
Upon completion of the course the students should be able to:
- Approximate definite integrals using Riemann sums and apply this to the concept of accumulation and the definition of the definite integral.
- Explain and use both parts of the Fundamental Theorem of Calculus.
- Choose and apply integration techniques including substitution, integration by parts, basic partial fraction decomposition, and numerical techniques to integrate combinations of power, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
- Use the integral to model and solve problems in mathematics involving area, volume, net change, average value, and improper integration.
- Apply integration techniques to solve a variety of problems, such as work, force, center of mass, or probability.
Equivalent placement test scores also accepted.
This course fulfills the following GE requirements: Science, Math, Computer Science/ASOT-B, Science, Math, Computer Science/AAOT, Science, Math, Computer Science/AAS, Science, Math, Computer Science/AGS, Science, Math, Computer Science/AS.