Mathematics

MTH101 - Calculus And Analytical Geometry
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Course Category:	Mathematics
Course Level:	Undergraduate
Credit Hours:	3
Pre-requisites:	N/A

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 topics which will be covered in the course 'Calculus and Analytical Geometry MTH101' are Real numbers, set theory, intervals and inequalities, Lines, functions and graphs, Limits and Continuity, Differentiation, Integration and Sequence and Series. 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).

Course Learning Outcomes

At the end of the course, you should be able to:

Use a variety of methods in solving real-life, practical, technical, and theoretical problems
Select and use an appropriate problem-solving strategy
Explain the limit process and that calculus centers around this concept
Identify the two classical problems that were solved by the discovery of calculus, The tangent problem and the area problem
Describe the two main branches of calculus, Differential calculus and Integral calculus

Course Contents

Absolute value ,Coordinates plane and graphs , Distance; Circles, Quadratic Equations, Limits, Continuity, Differentiation, Tangent Lines, Rates of Change, The Derivative, Derivatives of Trigonometric Functions Maximum and Minimum Values of Functions, Newton's Method, Roll's Theorem and the Mean Value Theorem, Integration by Substitution, Sigma Notation, Definite Integral, First and second Fundamental Theorem of Calculus, Applications of the Definite Integral: ,.Area between two curves, Volumes by Cylindrical Shells, Length of Plane Curves, Improper Integral , L'Hopital's Rule, Improper Integral, Infinite Series, Sequence and Monotone Sequences, Alternating Series; Conditional Convergence, Taylor and Maclaurin Series.