Definite integrals, Fundamental Theorems of Calculus, area of plane regions, volumes of solids, length of arcs. Mean Value Theorem for integrals, other applications of the definite integral. Techniques of integration, numerical integration, improper integrals. Sequences, monotonic and bounded sequences, Newton's method. Infinite series, tests for convergence and divergence, alternating series, absolute and conditional convergence. Power series, differentiation and integration of power series, Taylor series, Taylor's formula, binomial series, Fourier series.
Comments
Limits are very important in this course, and if you are not good with limits, then it's going to be a very rough journey in Calculus II, since limits are important in almost every part of the course (Riemann sum, arc length, sequences, series). So revise Calculus I if necessary. Also, a good understanding of numbers and common functions are extremely important, (For example, one has to know that the curve y = arctan(x) approaches pi/2 when x approaches infinity) otherwise it will be very difficult to do even one question of the series test, which stands for quite a significant proportion in the course.
Recommended as UE? Only if you love integration and strange series. :)
The bell curve for the CA component (40%) is very steep, since half of the CA is homework and simple quizzes, so finals is the one that determines where you stand. My cohort skipped quite a lot of content like Maclaurin,Power,Taylor Series.
The midterm and finals are quite rushed papers. The final exam has 7 questions, and has an unusually high occurence of trigo questions in almost every part. But overall, if you somewhat understand the theorems, then it should not be difficult to do the paper as not many proofs are required, and it's really just applying the formulas and stuff. Some of the questions come from the Stewart textbook, so it's advisable to try them. (The simpson rule and the arithmetic/geometric mean)
Programme: MATH(SPS)
Definite integrals, Fundamental Theorems of Calculus, area of plane regions, volumes of solids, length of arcs. Mean Value Theorem for integrals, other applications of the definite integral. Techniques of integration, numerical integration, improper integrals. Sequences, monotonic and bounded sequences, Newton's method. Infinite series, tests for convergence and divergence, alternating series, absolute and conditional convergence. Power series, differentiation and integration of power series, Taylor series, Taylor's formula, binomial series, Fourier series.