BS ( I ) PROGRAM

(MORNING)

COURSE OUTLINES

Course Title: Calculus-I Semester: Fall 2009

Number: MTS101 Credit Hrs: 3

Note: Class meets twice a week each time for a 75 minute session

Text Book:

Ø  Calculus by Howard Anton, 5th Edition, John Wiley and Sons.

Reference Book:

Ø  Calculus by Swokowski, 5th Edition, PWS Publishing Company.

Ø  A First Course in Differential Equations by Denis G. Zill, 5th Edition, PWS Publishing Company.

Course Plan:

Assessment Scheme:

Two Tests each of 20 marks during semester = 40 marks

Quizzes & Assignment (around 5 marks each) = 20 marks

Terminal Examination = 40 marks

Total = 100 marks

Lec. No / Topics covered
1 / Real numbers, real line, intervals, open and closed intervals, lower and upper bounds, absolute value and its properties,
2 / Inequalities, Rectangular/Cartesian coordinate systems, some linear and non-linear equations and their graphs.
3 / Definition of function, domain, range, natural and restricted domain, piecewise functions,
4 / Arithmetic operations on functions, composite functions, polynomial, rational, trigonometric,
5 / Exponential and logarithmic functions, implicit and explicit functions,
6 / Graphs of functions (absolute, sgm(x), floor/ceiling, unit step functions etc),
7 / Graphs of functions (absolute, sgm(x), floor/ceiling, unit step functions etc), (Continue)
8 / Translation of function, even and odd function, vertical line test.
9 / Applications of (piecewise) functions in a programming language.
10 / Concept of approaching/tending, existence of limit graphically and analytically, properties of limits,
11 / Some basic limits, limits of polynomials, rational, and , radicals functions etc,
12 / One sided limit, limit of piecewise functions.
13 / Definition of continuity, continuity at a point, continuity on a close interval,
14 / Intermediate value theorem, root existence theorem, squeezing theorem.
15 / Geometrical and physical significance of derivative, rate of change, First principle, existence of derivatives graphically and analytically.
16 / Rules for differentiation, chain rule, implicit differentiation
17 / Higher derivatives, Leibnitz’s theorem,
18 / Critical values (Maxima, Minima, Point of inflections)
19 / Rolle’s theorem, Mean value theorem
20 / L’ Hospital rule (0/0, ∞/∞ forms)
21 / L’ Hospital rule (0 ∞, 00 , ∞0, 1∞, ∞ - ∞ forms)
22 / Introduction to indefinite integration, Substitution Techniques of integration
23 / Techniques of integration (cont)
24 / Reduction formulae
25 / Definite integral, the fundamental theorem of Calculus, Improper integrals,
26 / Improper Integrals (cont)
27 / Applications of Integration
28 / Maclourin’s and Taylor’s series.
29 / Separable variable method for First order ODE
30 / Review and Discussion.