Calculus I (MTBS1013)

Linear Algebra (MTC-1033)

Thomas, Calculus And Analytical Geometry,  11^th Edition.
Schaum’s Series, Calculus And Analytical Geometry
Earl W. Sowkowski , Calculus.

The main aim of this course is to give students some basic ideas of calculus, which is the mathematics of motion. The purpose is not just making the students learn these ideas but to enable them apply these ideas to solve problems of practical nature. It will help the students of engineering, computer science and bioinformatics to understand and solve the problems of mathematical and logical nature in other courses of these disciplines.

Course Objective

Preliminaries

Real Numers
Inequalities
Absolute Value
Functions
Graphs
Shifting of the Graphs

Limits and Continuity

 Rates of Change and Limits
Limits of Function Values
Rules for Finding Limits
Extensions of the Limit Concepts
Infinite Limits
Continuity
Continuity at a Point
Continuity on an Interval

Derivatives

Definition and Examples
Relation Between Differentiability and Continuity
Rates of Change
The Chain Rule

Applications of Derivatives

 Extreme Values of Functions
The Max-Min Theorem for Continuous Functions
Local and Absolute (Global) Extrema
Increasing and Decreasing Functions
Finding Extrema
The Mean Value Theorem
Concavity
Points of Inflection
Optimization
Linearization

Integration

Indefinite Integrals
Different Techniques of Integration
Reduction Formulas
Definite Integrals
Area Under the Graph of a Nonnegative Function
Improper Integrals