This course aims to teach the basic mathematical techniques, introducing mathematical skills to analyzes problems. With many examples of math emphasis is on the practical usability.

Learning Outcomes

CTPO

TOA

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

LO - 1 :

learn the concepts of limit and continuity of functions

LO - 2 :

learn the concepts of derivatives of functions

LO - 3 :

learn the concepts of integral of functions

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

Mid-term

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