Mathematics
MTH001
Elementary Mathematics
MTH100
General Mathematics
MTH101
Calculus And Analytical Geometry
MTH201
Multivariable Calculus
MTH202
Discrete Mathematics
MTH301
Calculus II
MTH302
Business Mathematics & Statistics
MTH303
Mathematical Methods
MTH401
Differential Equations
MTH501
Linear Algebra
MTH601
Operations Research
MTH603
Numerical Analysis
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.

Course Related Links

For carrying out exercises
For more calculus
Problems and puzzles for calculus
Calculus and Differential Equations
Numerical Introduction to Limits
Graphical Representation of Limits
A valuable link!!
Derivative Rules(Examples)
composition of function
Very valuable computational browser
Course Instructor

Dr. Faisal Shah Khan
PhD. Mathematical Sciences
Portland State University (USA)

Books

Calculus with Analytic Geometry by Howard Anton

Calculus and Analytic Geometry by George B. Thomas and Ross L. Finney