Fozia Tauqeer

Assistant Professor

Computer science Department

* MATHEMATICSGSC-105(3:00Hrs)BSCS 1A&1B

Marks distribution as;

Assessment Methods and Weightage

Quizzes 10

Assignments/Projects 20

Mid-Term Examination 20

Final Examination 50

Total 100

1. Calculus by Thomas Finney 8th Edition

2. Calculus An applied Approach by Ron Larson Eighth Edition

3. Instructor’s Lectures

*Textbooks

The objective of this course as;

1. To understand the basic concept of real number and number system.

2. To know about the inequalities and their solutions.

3. To understand the concept of function its types, domain and range.

4. Circle equation, parabola, distance formula and their application.

5. Derivatives for different functions.

6. Understand the Basic Techniques of integration.

7. Concept of Complex number.

*Course Objectives

* Lecture Plan (16 Weeks)

Week # and Date

Lecture/Hour #

Topic to be covered

1 1 Introduction

2 Number system, real numbers, solution of inequalities, Linear and Quadratic

3 Absolute value, properties and solution of absolute values

2 1 Exponent and radicals

2 Function, domain and range

3 Graphs of functions

3 1 Transformation of functions

2 Inverse function

3 composite function and logarithmic function

4  

1 Application of different functions

2 Quiz # 1

3 Equation of circle and its sketch

Lecture plan

5th week 1 Sketch of parabola

  2 Distance formula and its application

  3 Application of graphs for circle and parabola

6th week 1 Analytical trigonometry

  2 Graphs of trigonometry

  3 Fundamental relations

7th week 1 Limit of a function

  2 Application of limit

  3 Continuity of function

8th week 1 Application of continuity

  2 Quiz#2

  3 Revision

9th week   MID TERM EXAM

Lecture plan:10th week 1 Derivatives, basic formulas

  2 Derivatives and slope of graph

  3 Differentiability and continuity

11 1 Product rule

  2 Chain rule

  3 Equation of tangent line

12 1 Implicit differentiation

  2 Rate of change, velocity and Marginal

  3 Quiz#3

13 1 Derivatives of trigonometric function

  2 Derivatives of exponential function

  3 L. Hopital rule

14 1 Techniques of integration

  2 Basic rules of integration

  3 Quiz#4

Lecture plan:15th week 1 Integration by parts

  2 Application of by part integration

  3 Introduction to complex number

16 1 Properties, application

  2 Demoivre’s theorem

  3 Application of Demoivre’s theorem

17 1 Presentation by students

  2 Presentation

  3 Revision and Guest lecture

18   Final Exam

Objectives:

1. Represent , classify and order real numbers

2. Use in equalities to represent sets of real numbers

3. Solve in equalities

4. Use inequalities to model and solve real life problems

*Number system

1. Positive direction

2. Coordinate of point

3. Origin

4. Negative direction

5. Non-negative

6. One to one correspondence

7. Rational numbers

8. Irrational numbers

*Real number line

1. Open interval

2. Interval that neither open nor closed

3. Infinite intervals

4. Closed intervals

* Order and interval on Real number line

1.

* Solving inequalities

Let a, b, c and d be real numbers;

1. Transitive property:

2. Adding property:

3. Multiplying by positive constant:

* Properties of inequalities

4. Multiplying by negative constant:

5. Adding a constant:

6. Subtracting a constant:

Use to describe conditions occur in business and science:

1. Production level

2. Physiology

3. Profit

4. Annual operating cost

* Application

In addition to fixed overhead costs of $500 per day , cost of producing x units of an item is $2.50 per unit. During the month of August , the total cost of production varied from high of $1325 to low of $1200 per day, Find the high and low production levels during the month?

* Production level

Objectives:

1. Find absolute value on real numbers

2. Properties

3. Distance between two real numbers

4. Intervals on real numbers

5. Midpoint of an interval

6. Using interval to model and solve real life problems

* Absolute value and distance

Definition:

the absolute value of real number a is:

* Absolute value of real numbers

1.Multiplication:

2.Division

3.Power

4.Square root

* Properties

1. Directed distance from a to b is:

b-a

2. Directed distance from b to a is:

a-b

3. Distance between a and b is:

|a-b| or |b-a|

4.

* Distance on real number line

1.

2.

* Two basic types of inequalities involving absolute

1. Quality control

2. Chemistry

3. Stock price

4. Heights of population

5. Biology

6. Production

7. manufacturing

* Application