Capstone Project Course Outline - University of Sargodha

Course Title: Capstone Project

Course Code: CMP-4970

Course Structure: Lectures: 0/Labs: 6

Credit Hours: 6

Prerequisites:None

Course Objectives:

The Capstone Project is an opportunity for participants to put their leadership competencies into
practice. Capstone Project allows the student to identify and develop a project that puts into
practice the leadership skills and competencies learned during the courses of study. Detailed
guideline and documentation temples are available with the Department.

Contents of Computing Supporting Area Elective Courses

Course Title: Calculus and Analytical Geometry

Course Code: MATH-2213

Course Structure: Lectures: 3, Labs: 0

Credit Hours: 3

Prerequisites: None

Course Objectives:

To provide foundation and basic ground for calculus and analytical geometry background.
Course Syllabus:

Real Numbers and the Real Line. Functions. Shifting Graphs, Trigonometric Functions. Limits
and Continuity. Tangent Lines. Derivatives. Differentiation Rules. Derivatives of Trigonometric
Functions. The Chain Rule. Implicit Differentiation and Rational Exponents. Applications of
Derivatives. Integration. Numerical Integration. Applications of Integrals. Transcendental
Functions. Inverse Trigonomic Functions. Derivatives of Inverse Trigonometric Functions.
Integrals. Hyperbolic Functions. Conic Sections, Parametrized Curves, and Polar Coordinates.
Vectors and Analytic Geometry in Space.

Course Outline:

1.     Real Numbers and the Real Line, Coordinates, Lines, and Increments, Functions, Shifting
Graphs, Trigonometric Functions. [TB: Preliminaries]

2.      Limits and Continuity: Rates of Change and Limits, Rules for Finding Limits, Target
Values and Formal Definitions of Limits, Extensions of the Limit Concept, Continuity,
Tangent Lines. [TB: Ch. 1]

3.      Derivatives: The Derivative of a Function, Differentiation Rules, Rates of Change,
Derivatives of Trigonometric Functions, The Chain Rule, Implicit Differentiation and
Rational Exponents. [TB: Ch. 2]

4.      Applications of Derivatives: Extreme Values of Functions, The Mean Value Theorem,
The First Derivative Test for Local Extreme Values, Graphing with y' and y''. [TB: Ch.
3]

5.      Integration: Indefinite Integrals, Integration by Substitution—Running the Chain Rule
Backward, Estimating with Finite Sums, Riemann Sums and Definite Integrals,
Properties, Area, and the Mean Value Theorem. Substitution in Definite Integrals.
Numerical Integration. [TB: Ch. 4]

6.      Applications of Integrals: Areas between Curves, Finding Volumes by Slicing, Volumes
of Solids of Revolution—Disks and Washers. Cylindrical Shells. Lengths of Plan Curves,
Areas of Surfaces of Revolution, Moments and Centers of Mass. [TB: Ch. 5]

7.      Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms,
The Exponential Function, a^x and log_a^x, Growth and Decay, L'Hopital's Rule, Relative Rates of Growth, Inverse Trigonometric Functions, Derivatives of Inverse Trigonometric

Functions; Integrals. Hyperbolic Functions. [TB: Ch. 6]

8.      Conic Sections, Parameterized Curves, and Polar Coordinates: Conic Sections and
Quadratic Equations. Classifying Conic Sections by Eccentricity. Quadratic Equations
and Rotations. Parameterizations of Plan Curves. Calculus with Parameterized Curves.
Polar Coordinates. Graphing in Polar Coordinates. Polar Equations for Conic Sections.
Integration in Polar Coordinates. [TB: Ch. 7, 9]

9.      Vectors and Analytic Geometry in Space, Vectors in the Plane Dot Products, Vector-
Valued Function Cartesian (Rectangular) Coordinates and Vectors in Space. Dot
Products. Cross Products. Lines and Planes in Space. Cylinders and Quadric Surfaces.
Cylindrical and Spherical Coordinates. [TB: Ch. 9, 10]

Textbook(s):

•          Calculus and Analytic Geometry by George B. Thomas and Ross L. Finney, Addison
Wesley; 10^th Edition (1995) ISBN-10: 0201531747

Reference Material:

•          Calculus and Analytical Geometry by Swokowski, Olinick and Pence, 6^th Edition, (1994),
Brooks/Cole Publishers.

•          Calculus by Howard Anton, Irl C. Bivens, Stephen Davis, Wiley; 10^th Edition (2012),
ISBN-10: 0470647728

•          Calculus with Analytic Geometry: Student Solution Manual by Howard Anton, Wiley;
5^th Edition (1995). ISBN-10: 0471105899

Note: This content is obtained from official documents of University of Sargodha and applied on BS Computer Science for Main Campus, Sub Campuses, and Affiliated Colleges.