When we think of the material covered by a course, it’s common to think about the topics we cover: functions, rates of change, derivatives, etc. But doing math is more than this, and our focus in this course is on more than the individual topics in mathematics that appear in our textbook and video resources. Our course learning goals reflect this: by the end of the course, we expect that:
- Students will be able to appropriately choose and apply various problem solving strategies in the context of mathematical problems, such as identifying relevant data and appropriate mathematical tools, considering a simpler or special case of a given problem, testing specific parameter values, or considering an alternate representation of the scenario.
- Students will be able to effectively communicate mathematical solutions and arguments from calculus, choosing graphical, numerical, algebraic, and/or verbal points of view as appropriate, both with mathematical language, vocabulary, and precision, as well as with non-technical, context-appropriate language.
- And, of course, students will have mastered the mathematical content learning objectives; broadly, course topics include integration as an accumulation of change, antiderivatives, techniques of integration, applications of integration, and sequences and series.
Mathematical Content
This is a second course in single-variable Calculus, and it covers that content. This means that we learn about how change can accumulate and how this influences our understanding of mathematics and the real world. More formally, we cover:
- The First and Second Fundamental Theorems of Calculus, Antiderivatives, and Applications of these
- Techniques of Integration to Find Antiderivatives, and Numerical Approximation of Definite Integrals
- Applications of the Definite Integral, Including Volume, Mass, and Work
- Limiting Processes, Including L’Hopital’s Rule, Improper Integrals and Their Convergence, and Applications of These
- Sequences and Series, Including Series Convergence Tests with Mathematical Justification, Power and Taylor Series
- Parametric and Polar Curves in Two Dimensions, with Derivatives, Arc Length, and Area Considered
There are many aspects to these very large topics that are fundamental to the course we teach, not least of which are the connections between them that build deep understanding. Throughout Math 116 we seek to build conceptual understanding, emphasizing the meaning of the integral and how the Fundamental Theorems of Calculus provide insight on mathematics and real-world situations; modeling; and the application of concepts of calculus to sequence and series.
