GSC-110 Applied Calculus 
                 Course Title:                   Applied Calculus 
                 Course Code:                    GSC-110 
                 Pre-Requisites:                  
                 Credit Hours Theory:            3 
                                                 0 
                 Credit Hours Lab (If 
                 Applicable): 
                 Course Objectives:              This freshmen level course has been designed to provide an 
                                                 introduction to the ideas and concepts of Calculus that would serve 
                                                 as a foundation for subsequent computer engineering courses. The 
                                                 primary objective is to endow the knowledge of basic concepts of 
                                                 calculus and geometry. Purpose of this course is to build the 
                                                 student’s knowledge of differential/integral calculus of 
                                                 multivariable functions based on their past experience of 
                                                 differential/integral calculus and analytic geometry of functions of 
                                                 one independent variable, at the Intermediate level.  
                 Learning Outcomes:              After the successful completion of course, the students will be able 
                                                 to: 
                                                  
                                                 CLO 1: To make students   familiar to real value functions of one 
                                                 and several variables 
                                                 CLO 2: Learn to analyze and solve problems relating analytical 
                                                 geometry, vector analysis & vector calculus and initial value 
                                                 problems.   
                 Contents (Catalog 
                 Description):                   Introductory Concepts – six lectures 
                                                        Introduction to real numbers 
                                                        Techniques of integration 
                                                        Indeterminate forms, L’Hopital Rule, Improper Integrals 
                                                          
                                                 Real value Functions of One & several variables – 
                                                 nine lectures 
                                                        Brief Introduction of Two and Three Coordinate System 
                                                        Domain  and Range of Functions with Two Variables 
                                                        Slope of A Line 
                                                        Bounded and unbounded regions in 2-D & 3-D 
                                                        Level Curves and Contour Lines of Functions with Two 
                                                         Variables, 
                                                        Real Valued    Functions of Two or More Variables with 
                                                         Concrete Examples 
                                                          
                                                 Three Dimensional Analytical Geometry & Vector 
                                                 Analysis and vector calculus – nine lectures 
                                                        Rectangular Coordinate system in space, vectors in plane 
                                                        Equation of lines and planes 
                                                                      Norms, Direction Cosines, Dot and Cross products 
                                                                      Scalar & vector fields, gradient & directional derivatives 
                                                                       Cylindrical, spherical &p polar coordinates 
                                                                      Divergence and Curl of vector field(divergence & Stoke’s 
                                                                       theorem)    
                                                                         
                                                              Infinite Sequence & series –six  lectures 
                                                                      Introduction to series and sequences 
                                                                      Convergence & Divergence of infinite series 
                                                                      Integral test/limit comparison test/alternating series test 
                                                                      Ratio and root tests 
                                                                      Absolute Convergence & Divergence  
                                                                      Taylor & McLaurin series  
                                                               Differential Calculus of Multivariable functions, 
                                                              limits & Continuity – nine lectures 
                                                                      Functions of several variables 
                                                                                                st  nd
                                                                      Partial derivatives (1 ,2  & higher order PDs of two/three 
                                                                       variables) 
                                                                      Chain rule 
                                                                      PD of Implicit functions 
                                                                      Linearization & Total differentials 
                                                                      Limits and continuity of function of several variables 
                                                                      Theorems on limits  
                                                              Multiple Integrals – nine lectures 
                                                                      Introduction to Double & Triple Integrals 
                                                                      Double Integrals over Rectangular & non-rectangular 
                                                                       Regions 
                                                                      Fubini’s Theorem 
                                                                      Methods of calculating limits over non-rectangular 
                                                                       regions 
                                                                      Applications of double integrals 
                                                                      Triple Integrals (calculating area and volumes) 
                                                                      Applications of triple integrals 
                                                                      Line Integrals 
                                                                      Path independence 
                                                                        
                                                               
                      Recommended Text Books:                 Calculus and Analytical Geometry, 9th Ed. by George B. Thomas, 
                                                              Jr. and Ross L. Finney 
                                                               
                      Reference Books:                        Calculus, 10th Edition by Anton, Bivens, Davis 
                                                              Calculus and Analytical Geometry, 10th Ed. by George B. 
                                                              Thomas, Jr. and Ross L. Finney 
                      Helping Web Sites:                       
                                                                                   Attendance is mandatory. Every class is important. All deadlines 
                                                                                   are hard. Under normal circumstances late work will not be 
                                                                                   accepted. Students are required to take all the tests. No make-up 
                                                                                   tests will be given under normal circumstances. There is 0 tolerance 
                                                                                   for plagiarism. Any form of cheating on 
                                                                                   exams/assignments/quizzes is subject to serious penalty. 
                                                                                   Attendance 
                             General Instructions for                                    75% attendance is mandatory. Latecomers will be marked as 
                             students:                                                   absent. 
                                                                                   Evaluation Criteria 
                                                                                         Assignments/projects                                       20% 
                                                                                         Quizzes                                                    10% 
                                                                                         Mid-Term                                                   20% 
                                                                                         Final                                                      50% 
                                                                                    
                            
               CONTRIBUTION OF COURSE LEARNING OUTCOMES (CLOs) TO PROGRAMME 
               LEARNING OUTCOMES (PLOs) 
                
                
                BS Software Engineering                   Applied Calculus
                No    Program Learning Outcomes           Course Learning Outcomes
                                                             12345 
                1     Engineering Knowledge                                                       
                2 Problem analysis                                                                  
                                                                               
                3     Design/Development of solutions                                          
                4 Investigation                                                                     
                                                                                      
                5     Modern tool usage                                                             
                6     Engineer and society   
                7     Environment and sustainability                                                
                8 Ethics                                                                        
                9     Individual and Team work                                                      
                10 Communication                                                                
                11    Project Management                                                            
                12 Lifelong learning