1928464 - Newton PDF

Preview

Summary

Newton...

Description

F L IMPOPO UN YO IV ERSIT Faculty of Science and Agriculture

SCHOOL OF MATHEMATICAL AND COMPUTER SCIENCES

Department of Mathematics and Applied mathematics

MODULE OUTLINE

DIFFERENTIAL AND INTEGRAL CALCULUS

SMTH011

2021

MODULE OUTLINE DIFFERENTIAL AND INTEGRAL CALCULUS Module Title Module Code Department

Pre-requisites Module Code

SMTH011

12

No. of Credits

Mathematics and Applied Mathematics None

School

SMCS

Co-requisites Module Code

None

Mr Twala N.T (Office 2008 Maths Building) Module Lecturers

Mr Malatji T.L (Office 3021 Maths Building) Ms Takalani N.A (Office 3017 Maths Building) Mr Malatji T.L

Module Coordinator Office Addresses

2008, 3021 & 3017 Maths Building [email protected]

Emails

[email protected]

Telephone Numbers

[email protected]

015 268 2906 015 268 2290 015 268 2166

Tuesday: 14H00 – 16H00 Consultation Times Lecture Periods

Thursday: 10H00 – 12H00 Monday: 07h30 – 09h10 Wednesday: 07h30 – 09h10 Friday: 09h20 – 11h00

Tutorials

Monday: 14h50 – 17h25

ii

ONLINE VENUES ONLINE

Wednesday: 14h50 – 17h25

ONLINE

Thursday: 14h50 – 17h25 Important Dates

Tests dates will be as per the FACULTY OF SCIENCE AND AGRICULTURE tests dates.

Learning Hours

First semester: 23 March – 21 July 29 March (Monday) lectures commence 02 April GOOD FRIDAY 05 April FAMILY DAY 27 April FREEDOM DAY 01 May WORKER’S DAY 16 June Youth Day 25 June (Friday) Lectures cease 28 June (Monday) Revision week starts

Semester

Quarter/Semester Module Structure

No. of Lectures: Six (06) No. of Practical Sessions: One 2.5 hours tutorial per group

Assessment Method

Description

Weighting

1. Quizzes 2. Tests

Quizzes will contribute at most

20%

Tests will contribute (at least two tests)

80%

Min formative assessment mark for exam admission

40%

Weighting towards final mark

60%

Minimum summative assessment mark

40%

Weighting towards final mark

40%

Formative Assessment

Summative assessment

Min Final Assessment mark to pass (%)

50%

MODULE DESCRIPTION

iii

6

The following topics will be covered: Limits, Continuity, Differentiation and Integration.

MODULE OBJECTIVES

The purpose of this part of the curriculum is to equip students with a good foundation in calculus to use it in their later academic and professional work.

MODULE CONTENT • Limits. • Continuity. • Differentiation and its application. • Integration and its application.

LEARNING OUTCOMES

At the end of the module a student should be able to: • • • • • • •

Evaluate limits with ease since the notion of limit lies at the foundation of calculus. Understand continuity of functions. Differentiate a wide range of functions. Find extreme values of functions and sketch curves Integrate a wide range of functions. Find the area between any two curves in the xy-plane. Calculate arc lengths for a wide range of curves.

ASSESSMENT CRITERIA

At the end of the lesson students should be able to: • Evaluate the limits using limit laws. • Understand continuity of functions. • Understand and prove the theorems on continuity. iv

• Differentiate functions using different techniques of differentiation. • Use differentiation to sketch the curves. • Use the different methods of integration to solve problems. • Find the area between the curves. • Find the arc length of the curve. Prescribed book: J Stewart, Calculus, Metric version, 8th edition, Cengage learning

REFERENCE MATERIALS FOR THE MODULE

• J Stewart, Calculus 7e/6e/5e • William Briggs, Lyle Cochran, Bernard Gillett, Calculus, 2nd Edition. • ANTON, H.: Calculus. 5th ed. John Wiley and Sons. 1995 • ELLIS, R., GULICK, D.; Calculus with Analytic Geometry • STEIN, S.K; Calculus and Analytic Geometry. 5th ed. • THOMAS G.B. and FINNEY L.F. Calculus and Analytic Geometry

STUDENT FEEDBACK ON MODULE

Test marks: Feedback and Test Scripts will be given to students after 14 days from the test date.

MODULE POLICY (Including plagiarism, academic honesty, attendance etc.) 1. 2. 3. 4. 5.

Attendance of Lectures and Tutorials is Compulsory. Students must always be Punctual. Use of Cell phones during lectures and tutorials is prohibited. Students must stay in the allocated group for all lectures and tutorials. Students absent from a previously announced test should report to the lecturers. In the case of illness a medical certificate from a registered medical practitioner must be submitted. In case of domestic circumstances such as serious illness or death of a close family member (as described in the general rules G15) satisfactory proof of such circumstances must be produced. 6. Students are given seven days (after the release of results) to complain about their marks. 7. Announcements and Important Notices will be communicated via University Blackboard and notice boards. Students are expected to make use of this facility.

v

ADDITIONAL MODULE INFORMATION TENTATIVE SCHEDULE OF LECTURES

WEEK

TOPIC

TUTORIAL TESTS/QUIZZES

WEEK 1

Introduction. Introduction to limits, Theorems and Examples

WEEK 2

One-sided Limits, Infinite Limits, Continuity, Bounds

Tutorial 1

WEEK 3

Intermediate Value Theorem and formal definition of a limit.

Tutorial 2

WEEK 4

The formal definition of a limit. Theorems on limits.

Tutorial 3

WEEK 5

Definition of a derivative, examples and rules for differentiation.

Tutorial 4

WEEK 6

Derivatives of special functions, Implicit differentiation, Higher order derivatives, derivatives of inverse trigonometric functions.

Tutorial 5

WEEK 7

L’Hôpitals’s rule, Rolle’s Theorem, Mean Value Theorem.

Tutorial 6

WEEK 8

Curve Sketching, The indefinite Integral.

Tutorial 7

WEEK 9

The indefinite Integral. Methods of integration.

Tutorial 9

WEEK 10

Area, Fundamental Theorem of Integration, Properties of Definite Integrals.

Tutorial 10

WEEK 11

Application of Integration

Tutorial 11

vi

WEEK 12

Applications of integration

WEEK 13

Revision week

vii...