BS Math 1st Semester

BS Mathematics (Semester Plan)

The BS Mathematics degree program is divided into eight semesters as follows.

Code

Course Title

CrHr

Pre-Req

 

Code

Course Title

CrHr

Pre-Req

Year 1 Semester 1

 

Year 1 Semester II

XXX***

UR-I

4(3+1)

None

 

MATH102

Calculus-II

3(3+0)

MATH101

MATH101

Calculus-I

3(3+0)

None

 

MATH103

Discrete Mathematics

3(3+0)

None

XXX***

UR-II

3(3+0)

None

 

XXX***

UR-IV

3(3+0)

None

XXX***

UR-III

3(3+0)

None

 

XXX***

UR-V

3(3+0)

None

XXX***

FR-I

3(3+1)

None

 

XXX***

FR-II

4(3+1)

None

Year 2 Semester III

 

Year 2 Semester IV

MATH201

Calculus-III

3(3+0)

MATH102

 

MATH211

Group Theory

3(3+0)

None

XXX***

FR-III

3(3+0)

MATH101

 

MATH271

Ordinary Differential Equations

3(3+0)

MATH101

MATH202

Number Theory

3(3+0)

None

 

MATH212

Linear Algebra

3(3+0)

None

XXX***

FR-IV

3(3+0)

None

 

XXX***

FR-V

3(3+0)

None

XXX***

UR-VI

3(3+0)

None

 

XXX***

FR-VI

3(3+0)

None

XXX***

UR-VII

3(3+0)

None

 

XXX***

FR-VII

3(2+1)

None

Year 3 Semester V

 

Year 3 Semester VI

MATH325

Vector and Tensor Analysis

3(3+0)

MATH212

 

MATH322

Real Analysis – II

3(3+0)

MATH321

MATH321

Real Analysis-I

3(3+0)

MATH101

 

MATH331

Numerical Analysis – I

4(3+1)

MATH321

MATH351

General Topology

3(3+0)

None

 

MATH332

Complex Analysis

3(3+0)

MATH321

MATH371

Partial Differential Equations

3(3+0)

MATH271

 

MATHxxx

Elective-II

3(3+0)/4(3+1)

MATHxxx

MATH313

Rings & Fields

3(3+0)

MATH211

 

MATHxxx

Elective-III

3(3+0)/4(3+1)

MATHxxx

MATHxxx

Elective-I

3(3+0)/4(3+1)

MATHxxx

 

 

 

 

 

Year 4 Semester VII

 

Year 4 Semester VIII

MATH471

Mathematical Modeling

3(3+0)

MATH271/MATH212

 

MATH472

Integral Equations

3(3+0)

MATH271

MATH424

Functional Analysis

3(3+0)

MATH212

 

MATH451

Differential Geometry

3(3+0)

MATH351

MATH431

Numerical Analysis-II

4(3+1)

MATH331

 

MATHxxx

Elective-IV

3(3+0)/4(3+1)

MATHxxx

MATHXXX/
MATH493

Elective/Report Writing & Presentation
Skills

3(3+0)/4(3+1)

MATHxxx

 

MATHxxx

Elective-V

3(3+0)/4(3+1)

MATHxxx


MATHXXX/
MATH499

Elective/Senior Design Project-I

3(0+9)/3(3+0)/4(3+1)

MATHxxx

 


MATHXXX/
MATH499

Elective/Senior Design Project-II

3(0+9)/3(3+0)/

4(3+1)

MATHxxx

                   

Note:   UR:          University Requirement Courses,    FR: Faculty Requirement Courses

 

*****************************************************************************************************************************************************

BS 1st Semester

 Course Code:  MATH101

Course Title:               Calculus-I

Credit Hours:              (3 0 3)

Pre-requisite(s):         None

 Course Objectives:

  The objectives of this course are:

  1. To learn about limits and their central role in calculus.
  2. To learn about derivatives and their relationship to instantaneous rates of change.
  3. To understand practical applications of derivatives.
  4. To learn about integrals: their origin in the area problem and their relationship to derivatives.

 Reading list:

  1. Anton, I. C. Bivens, S. Davis, “Calculus, Early Transcendental”, 11th edition, John Wiley, New York, 2016.
  2. Stewart, “Calculus”, 8th edition, Brooks/Cole, 2016.
  3. B. Thomas, A. R. Finney, “Calculus”, 14th edition, Pearson, USA, 2017.

 Lecture-wise distribution of the Contents

Lecture #

Topic

L1

Introduction to the course

L2

Functions and graphing techniques.

L3

Limit of a Function and Limit Laws, One sided Limits.

L4-L5

Continuity.

L7-L7

Limits Involving Infinity; Asymptotes.

L8-L9

Tangents and Derivatives at a Point, The Derivative by first principle.

L10

Left/Right Derivatives.

L11-L12

Differentiation Rules.

L13

Derivatives as a Rate of Change.

L14

Derivatives of Trig Functions.

L15

The Chain Rule, Implicit Differentiation.

L16

Derivatives of trigonometric and logarithmic functions.

L17

Derivatives of Inverse trigonometric and hyperbolic Functions

L18-L19

Related rates of change

L20-L21

Linearization and Differentials.

L22

MID EXAM

L23-L24

Extreme Values of Functions.

L25

The Mean Value Theorem.

L26-L27

Monotone Functions and the First Derivative Test.

L28-L29

Concavity and Curve Sketching.

L30-L32

Indeterminate Forms & L’Hopitals Rule.

L33-L35

Applied Optimization.

L36-L38

Anti-derivatives and techniques.

L39-L41

Area and Estimating with finite sums.

L42-L43

Definite Integral.

L44-L45

Fundamental Theorems of Calculus

L46-L48

Improper integrals.

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