Department of Mathematics: Advice on the course MAT 1000 Calculus
1. The Course MAT 1000 titled Calculus is offered every semester by the Mathematics Department. It is mandatory for all students who wish to take Mathematics as their major, minor or concentration subject. It is a prerequisite for most other courses in mathematics. It may also be required for other mathematics-intensive subjects. Students are advised to take it as early as possible.
2. The course is designed for students who have done Mathematics in their Classes 11 and 12 in school. That means they have already learnt some calculus. College level calculus is quite different with its emphasis on concepts, rigour and reasoning in addition to calculations based on some standard techniques. Students should be prepared for this jump.
3. A few students who have not done class 11 and 12 mathematics request that they may be allowed to take this course. The Department is willing to allow such students to try this course provided they satisfactorily perform in a diagnostic test conducted by the department. The purpose is to test whether they have enough background to follow the course. This test is conducted at the beginning of every semester. For detailed information on the diagnostic test and its syllabus please refer to the department handbook. The following paras are addressed to students who wish to try this.
(a) This is going to be very difficult but not impossible. It will work out only if you learn and master some topics of school mathematics before the course begins. You may need an intensive four to six months of study to achieve this.
(b) For your guidance a list of such topics is given below
i. Algebra: linear equations, quadratic equations, binomial theorem, sets and functions, graphs of functions, elementary functions like x^n, exponential and logarithmic functions, arithmetic and geometric progressions.
ii. Trigonometry: the sin, cos and tan functions, their basic properties, trigonometric identities, addition formulas
iii. Coordinate Geometry: Equations of straight lines, circles, and other curves, slopes and tangents.
At different points the course will draw on these topics and if you do not know them, you will find it very difficult to proceed.
4. To decide whether you are reasonably prepared you could look at a standard college level textbook. One such book is Calculus by James Stewart.
Some of these books discuss the prerequisites for a Calculus course and also give some tests to check whether a student is reasonably well prepared.
You will find other resources on the web. It is recommended that you test yourself and decide whether you are prepared.
Syllabus: Number systems. Sequences and series. Functions of a real variable. Graphs of functions. Limits and continuity. Differentiation. Mean value theorem. L’Hospital rule. Maclaurin and Taylor series. Curve tracing. Riemann integral. Definite and indefinite integrals. Fundamental theorem of calculus. Applications of differential and integral calculus in areas such as optimization and mechanics.
References:
- J. Stewart: Calculus, Cengage Publishers, 2012.
- K. A. Ross: Elementary Analysis, The Theory of Calculus, Second Edition, Undergraduate Texts in Mathematics, Springer, 2013.
- G. B. Thomas and R. L. Finney: Calculus and Analytic Geometry, Second Edition, Addison-Wesley Publishing, 1998.
