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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