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Course Pro FormaProgram Ijazah Sarjana Muda Perguruan Dengan Kepujian

(Matematik Pendidikan Rendah)

Course Title Basic Calculus(Kalkulus Asas)

Course Code MTE 3108

Credit 3(3+0)

Contact Hours

45 hours

Language Of Delivery

English

Prerequisite to entry

Nil

Semester One/ Two

Learning outcomes

1. Differentiate between functions and non- functions

2. Sketch graphs of elementary functions manually and/or using graphing calculator

3. Determine the inverse of a function

4. Recognise patterns and relationships

5. Find the first and second derivatives of functions

6. Apply the concepts of derivatives and integrals in problem solving

Synopsis This course focuses on the key concepts of Calculus which includes functions and graphs, basic understanding of limits and limit theorem, derivatives and integrals, and patterns and relationships. At this point, students are able to find the first and second derivatives of functions and minimum and maximum points of graphs. The applications and use of technology is also emphasized through graphing calculator and software such as Geometer’s Sketchpad to sketch and interpret the graphs of functions.

Kursus ini memfokuskan kepada konsep utama dalam Kalkulus; fungsi dan graf, kefahaman asas mengenai had dan teorem had, ‘derivatif’ dan ‘integral’ serta pola dan perhubungan. Pelajar boleh mencari derivatif pertama dan kedua bagi fungsi serta titik minimum dan maksimum bagi graf. Penggunaan dan aplikasi teknologi dijelaskan melalui kalkulator grafik dan perisian seperti Geometer Sketchpad untuk melakar dan membuat interpretasi graf fungsi.

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Topic Content Hours

1 Functions and graphs Patterns and relationships Use of variables to express relationships Pattern recognition Concepts of functions

o Composition of functions Domain and range Inverse of functions Graph sketching

o by hando graphing calculator o GSP

9

2 Limits and continuity Definition of limits Properties and theorems of limit One-sided and two-sided limits Concepts of continuity Properties and theorems of continuous function

12

3 Derivatives Definition: Slope of a tangent to a curve at a

point Definition of a differentiable function at a point First derivatives The first principle Formula Second derivatives Applications of derivatives

12

4 Integrals The concept of anti-derivatives Indefinite and definite integrals Applications of integrals

12

Total 45

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Assessment Coursework 50%Examination 50%

Main References

Bittinger, M. L. (2004). Calculus and its applications. 8th ed. Boston: Pearson/Addison-Wesley.

Clements, C., Pantozzi, R. & Steketee, S. (2002). Exploring calculus with the Geometer’s Sketchpad. Emeryville, CA: Key Curriculum Press.

Finney.et.al. (2000). Calculus : A Complete Course. 2nd ed. USA: Addison Wesley.

Additional References

Barnet et.al. (2000). Precalculus: A graphing approach. NY: Mc Graw Hill.

Berlinski, D. (1995). A tour of the calculus. New York: Pantheon Books.

Brodie, Ross (2002).. New Mathematics IIB. USA: Thomson & Nelson.

De Temple, D., & Robertson, J. (1991). The CALC handbook: Conceptual activities for learning the calculus. Palo Alto, CA: Dale Seymour Publications.

Foerster, P. A. (1998). Calculus concepts and applications. Emeryville, CA: Key Curriculum Press.

Key, Stewart. J. (2005). Single variable calculus: Concepts and contexts. Belmont, CA: Thomson Higher Education.

___ _____ (2001). The Geometer’s sketchpad: Dynamic geometry software for exploring mathematics. Version 4. [Computer software] Emeryville, CA: Key Curriculum Press.