MTH101 Lecture-05

MTH101 Lecture-05

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Course Synopsis

Single variable calculus, which is what we begin with, can deal with motion of an object along a fixed path. The more general problem, when motion can take place on a surface, or in space, can be handled by multivariable calculus. So single variable calculus is the key to the general problem as well.

The course in Calculus and Analytical Geometry MTH101 covers the following topics:

Preliminary material:

·        Real numbers, set theory, intervals and inequalities

·        Lines, functions and graphs are reviewed briefly

Limits and Continuity:

·        The limit and continuity are introduced through rates of change and intuitive way then it is presented formally.

      Differentiation:

·        Techniques of differentiation

·        Applications of the differentiation ( Exterema / Minima, Mean Value Theorem, the fundamental theorems of calculus , the Newton’s method, the Roll’s theorem )

Integration:

·        Techniques of integration

·        Application of definite integral

      Sequence and Series:

·        Sequences and types of sequences

·        Infinite Series and types of series

·        Tests for convergence

The study of calculus is normally aimed at giving you the "mathematical sophistication" to relate to such more advanced work. Calculus and Analytical Geometry MTH101 is pre-requisite course for Calculus II (MTH301)