The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

clasify numbers and understand functions and their properties

1,3

1

LO - 2 :

know the concepts of limit and continuity of functions

1,3

1

LO - 3 :

know the concepts of derivatives of functions

1,3

1

LO - 4 :

apply of the derivative to some engineering problems

1,3

1

LO - 5 :

know the concepts of integral of functions

1,3

1

LO - 6 :

apply the integration to some engineering problems and to some applications

1,3

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Functions (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Definition of function,
Introduction to function types,
Summation, subtraction etc. properties of functions,

Week 2

Graphs of basic functions and shifting graphs,
Inverse functions

Limit, limit computation rules.
Formal definition of limit
One-sided limits

Week 6

Continuity, properties of continuous functions, Intermediate Value Theorem
Limits at infinity and infinite limits, asymptotes of graphs

Week 7

Derivative of a function, geometrical meaning of derivative,
Differentiation rules,
Derivatives of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions.

Week 8

Chain rule,
Implicit differentiation
Higher order derivatives
L?hospital?s rule

Week 9

Midterm exam.

Week 10

Applications of differentiation (maximum-minimum and Mean Value Theorem)
First and second derivative tests

Week 11

Sketching the graph of a function by analyzing changes.

Week 12

Optimization problems

Week 13

Indefinite integrals (Anti-derivatives)
Methods of integration (change of variables, integration by parts)

Week 14

Partial fractions,
Integrals of trigonometric (rational) functions.

Week 15

Elimination of incomplete parts, general assessment