Honors Calculus I, II (MATH-UA 221–222) (offered fall and spring terms, respectively).
Honors Calculus I, II (MATH-UA 221–222) (offered fall and spring terms, respectively).
This sequence is intended for well-prepared students who are considering majoring in mathematics or a closely related subject such as economics, physics, or computer science. It covers the essential elements of Calculus II (MATH-UA 122), Calculus III (MATH-UA 123), and Linear Algebra (MATH-UA 140) in just two semesters.
Honors Calculus I assumes mastery of the material in the Advanced Placement (AP) Calculus AB syllabus. In particular, students should know how to differentiate elementary functions and evaluate standard integrals; in addition, they should know the basic properties and applications of differentiation and integration (e.g. graphing, optimization, and finding areas). Students whose background is limited to Calculus I (MATH-UA 121) will have learned most of this material; they may register for Honors Calculus I, but may have to do some catch-up reading about methods of integration.
Honors Calculus I,II is significantly more difficult than Calculus II, Calculus III, and Linear Algebra, both because of its more rapid pace, and because it is intended for very well-prepared students.
Honors Calculus I,II are not alternatives to Calculus I,II. Students who do well in Calculus I and who wish to take Honors Calculus should consider Honors Calculus I as the correct subsequent course, not Honors Calculus II.
The full course descriptions are provided below.
Honors Calculus I (MATH-UA 221): Accelerated Calculus with Linear Algebra I (offered fall term). 5 points.
Prerequisite: One of the following: (a) a score of 4 or higher on the Advanced Placement Calculus BC exam or 5 on the AB exam; or (b) Calculus I (MATH-UA 121) and permission of the instructor.
This is the first semester of a year-long course that covers the essential content of Calculus II, Calculus III and Linear Algebra. The first 1/3 semester discusses sequences and series, Taylor's theorem, and power series. The next 1/3 semester introduces concepts from linear algebra including: linear systems of equations; matrices and LU decomposition; determinants; vector spaces; eigenvalues and eigenvectors. The last 1/3 semester introduces topics from vector calculus including: functions of several variables; vector-valued functions; partial derivatives; various applications including maxima and minima.
Honors Calculus II (MATH-UA 222): Accelerated Calculus with Linear Algebra II (offered spring term). 5 points.
Prerequisite: Honors Calculus I (MATH-UA 221) with a B or better.
This is the second semester of a year-long course that covers the essential content of Calculus II, Calculus III and Linear Algebra. Topics covered in the spring are multidimensional differentiation (e.g. differentials, gradients, Taylor expansions, applications), multidimensional integration (e.g. double and triple integrals, Green's theorem, divergence theorem, applications), differential equations (e.g. first-order linear equations, second-order linear equations, applications), and additional topics in linear algebra (e.g. inner products, orthogonality, applications).