Course Syllabus

Department : Department of Mathematics

Course Prefix and Number : Maths 121

Course Title : Calculus I

Number of : Credit Hours 3 Lecture Hours 3 Lab Hours 0

Catalog Description : Algebra. Functions and graphs. Trigonometry. Conic sections. Limits and continuity. Derivatives and integrals. Applications of derivatives which include mean value theorem, extrema of functions and optimization. Definite integrals and the Fundamental Theorem of Calculus. Derivatives and integrals of exponential, logarithmic and inverse Trigonometric functions

Pre-requisite(s) : No pre-requisites for this course.

Text(s) : Calculus, by Smith and Minton. Third Edition (McGraw-Hill).

Reference : Calculus, by James Stewart. Fifth Edition (Thomson Brooks/Cole).

Course Objectives : The main objectives of this course are:

  1. Explain (theoretically, analytically and graphically) the main concepts of Calculus, namely: limits, continuity, differentiation and integration.
  2. Teach the various techniques of computing limits, derivatives and integrals in order to develop the student's problem-solving ability.
  3. Introduce the concept of mathematical modeling and physical applications through various applications of derivatives, namely: related rates, optimization problems, curve sketching and area under a curve.

Measurable Learning Outcomes: On Successful completion of this course, student

should be able to

a.  Demonstrate ability to explain the various concepts of calculus: Limits Continuity, Derivative and Integration theoretically, algebraically and geometrically through graphs.

b.  Demonstrate knowledge of the various computational techniques and rules to compute limits, derivatives, indefinite and definite integrals.

c.  Demonstrate a through understanding of the physical applications of derivatives in real life problems such as optimization problems and related rates.

d.  Know how to use derivative to analyze functions and how to sketch their graphs.

Topical outline:

·  Inverse functions, trigonometric and inverse

trigonometric functions, exponential and logarithmic

functions.

·  Limits and continuity.

·  Differentiation.

·  Applications of differentiation.

·  Integration.

Prepared by: Mohammed Abdullah Ali

University of Bahrain

College of Science

Department of Mathematics

First Semester 2007/2008

Math 101

Calculus I (For IT students and Engineers)

Topics covered and weekly teaching Plan

Week

/ Beginning / Sec. # / Examples / Suggested Problems (*)
1 / 16 /09/ 2007 / 0.1 Polyn. & rational functions.
0.3 Inverse functions.
0.4 Trig. &inverse trig. functs. / 1.17—1.19,
3.3—3.5
4.5,4.7,4.10 / 36,38,40,42,44,46.
6,12,14.
57,58.
2 / 23/09/2007 / 0.5 Exp. & log. functions.
1.2 The concept of limit. / 5.3—5.12
2.1—2.5 / 32,38,42,48.
2,5,6.
3 / 30/09/2007 / 1.3 Computation of limits. / 3.1—3.7, 3.9 / 1—34.
4 / 07/10/2007 / 1.4 Continuity. / 4.1, 4.4 —4.7. / 13—24, 27,28,31,32,34,35
5 / 14/10/2007 / 1.5 Limits involving infinity. / 5.1—5.7, 5.9,5.10. / 5—24, 64.
6 / 21/10/2007 / 2.1 Tangent lines & velocity.
2.2. The derivative. / 1.1,1.2,1.5.
2.1—2.4, 2.7. / 17,18,21,22.
5, 7, 9, 11, 39.
7 / 28/10/2007 / 2.3 Computation of derivatives.
2.4 The product & quotient rules / 3.1—3.6.
4.1, 4.3. / 5,10,19,23,33,34.
1—16, 21—24.
8 / 04/11/2007 / 2.5 The chain rule.
2.6 Derivatives of trig. functions / 5.1—5.5.
6.1—6.4. / 5—28, 33—36.
3—20.
9 / 11/11/ 2007 / Mid-Semester Break
10 / 18/11/ 2007 / 2.7 Der. of exp. & log. functs.
2.8 Implicit diff. & inverse trig. / 7.3, 7.4, 7.6.
8.1, 8.2, 8.5. / 1—30, 39—44, 49, 52.
5,6,12,13, 29—38.
11 / 25/11/ 2007 / 3.3 Maximum & min. values. / 3.1, 3.6, 3.10, 3.11. / 11—14, 22, 25, 31—35.
12 / 02/12/2007 / 3.4 Increasing & decreasing / 4.3, 4.4. / 1,9,10,12,14,27,28.
13 / 09/12/ 2007 / 3.5 Concavity & the SDT.
3.7 Optimization. / 5.1—5.5.
7.1—7.3. / 1,3,7,8,9,11,14,15,16.
3,9,16,33.
14 / 16/12/ 2007 / National Day + Arafat Day +Eid Al-Adha
15 / 23/12/ 2007 / 4.1 Antiderivatives.
4.2 Sums & sigma notation. / 1.1—1.10.
2.1—2.5. / 5—30.
9,10,17,18,19,20.
16 / 30/12/2007 / 4.3 Area.
4.4 The definite integral. / 3.1, 3.3.
4.3. / 15, 18, 19, 20.
5,8,11,12,21,22.
17 / 06/01/2008 / 4.5 The fundamental theorem of
4.6 Integration by substitution. / 5.1—5.9.
6.2—6.11. / 1—20, 27—34, 45, 53—58.
5—40, 45, 46.
18 / 13/01/2008 / 4.7 Numerical integration. / 7.1, 7.5, 7.6. / 1—4, 20, 21.
19 / 23/01/ 2008 / Final Exams

Student Achievement & Evaluation Tools:

Exam / Weight / Date / Time / Material / Location
Test 1 / 25 % / 24/10/2007 / 4-5 / Chapters 0 and 1. / Hall 18
Test 2 / 25 % / 05/12/2007 / 4-5 / Chapter 2. / Hall 18
Final exam / 50 % / 23/01/2008 / 14:30-16:30 / Comprehensive / TBA