Unit Course book
Calculus
Course code: Mth 101 CC
Unit Coordinator
Nawzad M. Ahmed
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 1
Education Aims:
To provide an introduction to calculus encompassing limits, differentiation extrema, curve sketching, definite and indefinite integration. An understanding of sets, relations, algebraic and nonalgebraic functions is essential to many aspects of calculus. The module content also provides valuable intermediate ground between the calculus II and differential equation.
Course outline and objectives
To make the students grasp the concepts of real analysis, limit points, interior points, closed intervals, open intervals. Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second derivative tests for local extrema. Concavity and inflection points. Curve sketching. Applied extrema problems. Role’s theorem. The Mean Value Theorem and applications. The Riemann integration (an introduction). Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Hyperbolic functions. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals.
This two semesters course is designed to emphasize conceptual understanding of calculus using a multi-representational approach (graphical, numerical, analytical and verbal), the use of technology and unifying mathematical themes such as derivatives, integrals, limits, applications/modeling and approximation. Every concept covered will build upon the previous one. Therefore, it is very important that you do not get left behind. Homework assignments, projects, quizzes and tests will be designed to continually reinforce and challenge your ability to apply the concepts discussed in class. A topical outline for the course, is provided by The Fauclty Board. The more general objective of this course is to continue providing a deeper understanding and working knowledge of mathematics.
Communications with Academic Staff
This handbook gives information on how to contact and communicate with staff.
We provide room numbers and email addresses of staff to you. The staffs in this department want to help you as much as possible so that you will be successful in your programme. We also want to encourage you to take responsibility for yourselves and for your learning so it will help you in your future careers.
The email rules
* Write your email in acceptable English.
* In your emails you must include: full name, stage, department and the unit title.
* We only respond to queries from students using genuine/Soran University email accounts.
* Appointments can be arranged through the email system, if you wish.
* We respond to genuine problems and queries as soon as possible, normally within 7 days.
* We will not respond to emails which do not have a subject line.
Staff associated with the unit:
Staff
Room Number
Email
Nawzad M. Ahmed
Head of Mathematic Dep. Room
Nawzad.A@soranu.com
Soran University
Department of Mathematics
Unit: Calculus
Credit 4 for one semester
Method of Assessment:
2x 2 h lectures and 1 x 1 h Tutorial per week.
Examination and grading
Month’s exam: 30%
Classroom participation and assignments and homework 10% Final exam: 60%
Marking System
The grades for each piece of assessed work are as follows:
* 90-100 % is excellent
* 80-89% is very good
* 70-79% is good
* 60-69% is a moderate pass
* 50-59% is a pass
* <49% is a fail
Unit Timetable/Content
University Academic Week
Lecture Title & Content
1,2Some property of a set of real numbers and inequalities and Absolute Value and solving equations involving absolute values.
Function, identify function.
3point and line and distance between them,
point – slope equation, Circle and Parabola and Ellipse and Hyperbolas.
4Graphs of second- degree equations.
Trigonometric equation
Examination.
.
5Limits, One-Sided Limits,
Infinite Limits
6
Limits of special Trigonometric functions and asymptote
7Continuity
8Examination.
Derivatives
9. Derivatives of Exponential Functions, some property of Exponential Functions
Derivative of Logarithmic Function, some property of Logarithmic Function.
10Implicit Differentiation
Parametric Derivatives, Differentiation with Polar Curves.
11Derivatives of Inverse Functions
Differentiability & Continuity
12
End of semesters one
Application of the Derivative
Examination.
13Tangent, Position, Velocity, & Acceleration, Related rates.
Relative Extreme & the First Derivative Test
.
14Absolute Extreme
Role’s Rule & the Mean Value Theorem and I. L'Hopital's Rule15
Graph of the function by using derivative
16
Examination
Definite Integrals.
17The Chain Rule for Integrals
Exponential Integrals
18Integrals & the Natural Log. Integrals on Inverse Trigonometric Functions
19
Technique of integration
20Improper integrals
Application of Integrals.
Course of Action
1. There are penalties for late submission of coursework.
2. There are penalties for plagiarism and collusion.
Recommendation
Keeping a wall diary is recommended to enter all deadline dates so you can see what assignments are due in. It is also essential to leave yourself sufficient time to complete the work.
Recommended Reading
1- Thomas Calculus, 2005 (Eleventh edition) George. Thomas.
2- Calculus 5th Edition - James Stewart.
3- Calculus III, 1985 (Second edition) Jerrold Marsden and Alan Weinstein.
4- Calculus Demystified, 2003 Steven G. Krantz . and other textbooks in Calculus