Math 113: Calculus 2
(Credit Hours:Lecture Hours:Lab Hours)
F, W, Sp, Su
Math 112 or equivalent.
Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates.
Desired Learning Outcomes
This course is designed for students majoring in the mathematical and physical sciences, engineering, or mathematics education and for students minoring in mathematics or mathematics education. Calculus is the foundation for most of the mathematics studied at the university level. The mastery of calculus requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. Calculus 2 develops techniques of integration, applications of integration, infinite sequences and series, parametric curves, polar coordinates, and conic sections. This course contributes to all the expected learning outcomes of the Mathematics BS (see ).
Minimal learning outcomes
Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor. Previous final exams (see ) give specific examples of the level of understanding that is expected.
- Techniques of integration
- Integration by parts
- Trigonometric substitution
- Partial fractions
- Integration using a computer algebra system
- Approximation of integrals including Simpson’s and trapezoidal rules
- Improper integrals
- Applications of integration
- Area between curves
- Volumes from slice method (includes washer method) and shell method
- Average value of a function
- Arc Length
- Area of a surface of revolution
- Hydrostatic force
- Moments and centers of mass for regions in the plane
- Using centroids to compute volume, hydrostatic force, and work.
- Infinite sequences and series
- Infinite sequences including definition, limit laws, and the theorem on monotonic sequences
- Infinite series including definition with partial sums, the geometric and harmonic series
- Tests for convergence of series including the test for divergence, and the integral, comparison, limit comparison, ratio and root tests.
- Alternating series test and bounding the sum of an alternating series between successive partial sums
- Absolute and conditional convergence
- Functions defined by power series including the radius of convergence, differentiation, and integration
- Taylor and Maclaurin series
- Parametric equations and polar coordinates
- Curves defined by parametric equations
- Tangent lines, arc length and area for curves defined by parametric equations
- Polar coordinates including graphs, tangent lines, arc lengths and areas
- Conic sections in Cartesian and polar coordinates
Possible textbooks for this course include (but are not limited to):
These are at the instructor's discretion as time allows. Some suggested topics are applications to economics and biology, probability, centroids of curves and solids, and the logarithm defined as an integral.