COURSE CODE: COURSE NAME: CALCULUS I CREDIT HOURS: 3 (theory) + (practical) = 4 CONTACT HOURS: 48 (theory) + 48 (practical) = 96 PREREQUISITES: None MODE OF TEACHING: Lectures and Problem-Solving Activities INTRODUCTION: CALCULUS I is a first-year, first-semester General University Requirement (GUR) Course at NUTECH. This course is mainly focused on Single Variable Calculus. ) Required Skills: a) High school algebra and geometry (especially, Equations of Lines, Conic Sections, Trigonometry). b) Prior experience with Calculus is helpful but not essential. 2) Course Overview a) Calculus plays an important role in the understanding of science, engineering, and technology among other disciplines. It is 6 weeks long single term course of 5 Credit Hours (2 Unites) (Theory: 3Units, Lab: 3Units, Outside Preparation: 6 Units). b) This course mainly covers differentiation, and integration of functions of single variables along with their applications. Topics include: c) Concepts of functions, Limits, and Continuity. d) Differentiation rules, Application to graphing, Rates, Approximations, Extremum problems. e) Definite and Indefinite integration. f) The fundamental theorem of Calculus. g) Applications (Area, Volume, Arc Length, Average values, Work, etc.). h) Techniques of integration. i) Infinite series, Tests for convergence of infinite series. j) Approximation of definite integrals, Improper integrals, and l Hôpital s Rule. 3) Makeup Course Students interested in a Makeup Course for CALCULUS are advised to get themselves registered for PRE-CALCULUS. This makeup course primarily covers concepts related to high school algebra. (Contact your Course Advisor for more details.) COURSE DESCRIPTION: Differentiation and integration of functions of one variable, with applications. Informal treatment of limits and continuity. Differentiation: definition, rules, application to graphing, rates, approximations, and
extremum problems. Indefinite integration; separable first-order differential equations. Definite integral; fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Polar coordinates. L Hospital s rule. Improper integrals. Infinite series: geometric, p-harmonic, simple comparison tests, power series for some elementary functions. COURSE OBJECTIVES: ) To provide students a deeper understanding of the basic concepts of functions, limits and the derivatives and to familiarize students with the proper use of the differentiation formulae and integration of algebraic and transcendental functions. 2) To provides students sufficient knowledge and skills in solving relevant problems in engineering. 3) To strengthen and broaden students knowledge in differentiation and indeterminate forms of functions which they may encounter in solving different types of differentiation problems. COURSE LEARNING OUTCOMES: Upon successful completion of the course, the student should be able to: CLO Explain the concept of functions, limits and continuity, differentiation, integration, and infinite series with real life examples. Apply the principles of differentiation to solve maximaminima (extreme value) problems. Calculate the area of an irregular shape and volume of solids of revolution, using the techniques of integration. Solve first order separable differential equations of simple real-life problems. Perform the simulations of fairly complex engineering problems using MATLAB / Mathematica. Learning Domain Taxonomy Level PLO Cognitive 2 Cognitive 3 Cognitive 3 Cognitive 3 Psychomotor 3 5 RELEVANT PROGRAM LEARNING OUTCOMES (PLOs): The course is designed so that students will achieve the following PLOs: Engineering Knowledge: R 7 Environment and Sustainability: 2 Problem Analysis: 8 Ethics: 3 Design/Development of Solutions: 9 Individual and Team Work: 4 Investigation: 0 Communication: 5 Modern Tool Usage: R Project Management: 6 The Engineer and Society: 2 Lifelong Learning:
RELEVANCE OF COURSE TO REAL LIFE (PRACTICAL APPLICATIONS): In all aspects of engineering, when confronted with a problem, one usually defines the problem with a model using mathematical equations describing the relationships of different aspects of the problem, usually through calculus. Basic things that occur all the time in engineering are rates of change with respect to time, or space of such variables as heat, wave, gas, electromagnetic fields, conductivity, vibrations in solids like bridges and buildings, and many others. Calculus, at least the concepts developed from Calculus, are used all the time in civil engineering. Any time there is a rate of change of something then the derivative is an efficient way to characterize it. Any time there is an area under some function describing behavior then the integral is an efficient way to quantify it. The basic problems seek to maximize or minimize a quantity (such as surface area of some object, or the distance a projectile can achieve). Structural reliability is one very broad application of calculus in Civil Engineering. You can determine the probability of failure of the structure with respect to the loads and other variables which influence the same. A basic example of the use of Calculus in Civil Engineering is, for example, the simple beam formula to calculate the stress in a beam with various forms of end attachment from fixed (buried in concrete for example) to pinned like the attachment points on many bridge supports and with various loads from distributed loads to point loads. The derivation of each comes from a combination of Algebra and Calculus. You can derive the shear stress distribution from algebra and get the moment distribution by integrating the shear stress. INSTRUCTOR (S): Name: Office: Email: Dr. Abdul Wahab (Course Lead), Dr. Muhammad Ubaid Nisar (Lab Instructor) NUTECH School of Applied Sciences and Humanities (NUSASH), Academic Block. wahab@nutech.edu.pk, ubaidahmed@nutech.edu.pk CLASS HOURS: Check weekly training programs for class timings. LAB HOURS: Check weekly training programs for class timings. OFFICE HOURS: Thu: 2:00 3:00 (and by appointments). INSTRUCTOR S EXPERIENCE I have PhD in Applied Mathematics from École Polytechnique Paris and have research interests in direct and inverse scattering of (electromagnetic, acoustic, elastic) waves in complex media. I usually seek solutions of inverse problems related to Biomedical Imaging, Non-Destructive Testing, and Exploration Geophysics. I have vast experience of teaching a number of courses including Ordinary Differential Equations, Partial Differential Equations, Numerical Analysis, Calculus and Analytic Geometry, Discrete Mathematics, and Mathematical Methods for Physics. TEXT AND MATERIAL: Textbook (s). Thomas Calculus, th Edition, Addison-Wesley, 2005. References Material:
) Thomas, G. B. and Finney, R. L. Calculus and Analytic Geometry, 9th Edition, Pearson, 996. 2) Swokowski, E. W. Calculus with Analytic Geometry, Alternate Edition, PWS Publishers 983. 3) Anton, H. Calculus. John Wiley and Sons, 202. 4) Stewart, J. Calculus, 5th Edition, Brooks/Cole, 2002. 5) Simmons, G. F. Calculus with Analytic Geometry. 2nd Edition, McGraw-Hill, 996. EXAMS AND GRADIG: There will be 3 Homework Assignments, 3 Quizzes, Midterm and one comprehensive Final Exam. Date of submission of assignments will be reflected. Late submission will have a penalty (deduction of 20% marks for each day of late submission, zero marks for submission delayed more than 5 days). To encourage reading (reading assignments are reflected in course schedule) and discourage copying of homework assignments, all quizzes will be 50% from reading assignments and 50% from problem sets in assignments. Type of Exam % age weight Assignments 0% Quizzes 0% Midterm 30% End Semester Exam 50% CONDUCT IN THE CLASS: Students are not allowed to chat with each other Students are not allowed to do work of any other subject during the class Students are not allowed to do text messaging in class Your cell phones should be on silent/vibration mode Everyone should be seated in the class -2 minutes ahead of start time of the class You are not allowed to leave the class without permission You are not allowed to enter class without permission after class has started If I am late for class or absent for some reason, still students are required to be in the class and no one is allowed to stand outside the class. Parade state will be submitted -2 minutes before start of the class
TOPICSCOVERED WITH THEIR CONTRIBUTION TO PLOs: Week Topic Covered Reading Assignment/ Home Work Introduction to Calculus, Functions, Limits of functions. 2., 2.2, 2.4, 2 Continuity of functions and graphical representation. 2.5 to 2.7. 3 Derivatives, Techniques of Differentiation. 3. to 3.7 4 Applications of Derivatives, 5 6 7, 8 Extrema of Functions Mean Value Theorem, Concavity. Intermediate Forms and L Hopital s Rule Integration, Techniques of Integration. Midterm Exam 9 Applications of Integration, Area under/between the curves. 0, Volume of solids of revolution. Arc length, surface of revolution, Centre of mass. 2 Improper Integrals 3 Differential Equations, Classification of Differential Equations. Applications of st order separable differential equations 4 Sequences, Series and types. 5 Convergence of series by Basic comparison test, Limit comparison test, Ratio test. 3.8, 4. 4.2 to 4.5 Assignment 4.6 Quiz 4.8, 5. to 5.3, 8. to 8.5 Ref, Sect. 5.4 to 5.6 Assignment 2 Ref, Sec 6. to 6.7, Quiz 2 8.8. Assignment 3 Ref., Chap. 9 Quiz 3 CLO No. 2 2 3 3 4 Ref., Sec.. Ref., Sec..2-.6 PLO No. Assessment Methodology Assignment, Quizzes, Midterm, Formative Assessments Learning Domain Cognitive Domain Level of Learning -6-3
6 Power series of elementary functions Final Exam Ref., Sec..7 End Semester Exam Written by: Dr. Abdul Wahab Reviewed by: Dr. Muhammad Mudassar Gulzar Approved by: Dr. Shahid Iqbal