# sap course 1434120350

## Course Code & Number:

## Course Title:

## Level of Course:

## Credits:

## Catalog Description:

## Pre-requisites & Co-requisites:

Quiz - 5%

Homework - 10%

Exam 1 - 15%

Exam 2 - 15%

Exam 3 - 20%

Final - 35%

Concept of Limit, Limit Theorems, Continuity, Limits of Sequences, Exponential and Logarithmic Functions, Derivative, Rules for Differentiation, Chain Rule, Derivatives of Inverse Functions, Implicit Differentiation, Differentials, Related Rates, The Mean Value Theorem, Maxima and Minima of Functions, Graphing, L'Hopital's Rule, Anti-differentiation. Integration, Rules for Integration, The Fundamental Theorem of Calculus, Techniques of Integration, Improper integrals, Volumes, Arc Length and Surface Area, Series, Tests for Convergence, Power Series, Representing Functions by Power Series, Taylor Series.

Upon succesful completion of this course, a student will be able to

1. recall basic principles of mathematical writing, mathematical conventions, notation and fundamental definitions related to one variable functions.

2. recognize elementary and transcendental functions of one variable and their properties.

3. explain the concepts of limit and continuity and continuity implications such as the Intermediate and Extreme Value Theorems.

4. calculate limits, derivatives and definite integrals of one variable functions algebraically, graphically and numerically,

5. use the Mean Value Theorem (MVT) and implications of the MVT on limits, monotonocity, concavity and extrema,

6. solve problems of related rates, optimization, and approximation, which model physical quantities that involve instantaneous rates of change.

7. relate indefinite integral and definite integral via the Fundamental Theorem of Calculus.

8. solve problems of planar area, volume, arc length, which model physical quantities that involve total change.

9. use tests of convergence, differentiation and integration to represent functions of one variable as Taylor or Maclaurin Series.