CALCULUS 1SMS 1102

SMS 1102 CALCUUS 1

Instructor : Suryadi

Monday 11:30 C-2-01Wednesday 8:30 C-2-01

Level YEAR 1Prerequisite NIL

COURSE OBJECTIVE

Calculate and prove limits of the elementary mathematical functions and the combinations

Determine continuity of the elementary mathematical functions and the combinations

Calculate derivatives of the elementary functions and the combinations

Analyze mathematical functions in terms of its extreme points and certain specific behavior

ReferencesTextbook:

“Thomas’ Calculus” by Thomas G.B.Jr., Finney R.L., Wier M.D., Giordano F.R., 11th edition (Addison-Wesley)

Other recommended books: 1. “Calculus and Analytical Geometry” by

Thomas G.B.Jr. et al., 9th edition (Addison-Wesley)

2. “Calculus with Analytical Geometry” by Repka J. Morton, 1993

3. “Calculus with Analytical Geometry” by Ellis R & Gulick D. 5th Edition, Harcout Brace & Co, 1990

Course outline

W:1 Introduction to CalculusW:2-5 Limit

Thomas’ Calculus, Chap 2W:6 Continuity

Thomas’ Calculus, Chap 2W:7-9 Derivative

Thomas’ Calculus, Chap 3W:10-14 Application of Derivatives

Thomas’ Calculus, Chap 4

Q-1

FE-1

ME-1

Q-1

Course outline

LIMITLimit from graph and by substitution. Limit laws. Definition Limits. Proving Limit. One-sided limits. Limits at infinity.

INFINITE LIMITInfinite limit. Vertical & horizontal asymptote.

Graphing rational function. Continuity at a point and continuous functions.

CONTINUITYDefinition of continuity at a point. Continuity test. Continuous functions. Composite of continuous functions.

Course outline

DERIVATIVESDerivative as a function. Definition of one-sided derivatives. Differentiation rules. Derivatives as a rate of change. Derivatives of trigonometry function. The chain rule and parametric equations. Derivatives of a composite function outside-inside rule. Implicit differential. Linearization and differential.

Course outline

APPLICATION OF DERIVATIVESExtreme value theorem. First derivative theorem for local extreme values. Critical points. Mean value theorem. First and second derivative test. Concavity. Applied optimization problems. Example from business and industry, math and physics, and economics. Newton’s method. Procedure applying Newton’s method convergence. Modeling and Optimization.

Administrative

Assessment:• 10% Assignments• 20% Quizzes / Tests• 30% Mid-term test• 40% Final examination

Administrative

1. Two quizzes: Quiz 1 / tests – week 5/6 – (in class) Quiz 2 / tests – week 10/11 – (in class)

2. Mid-term test and Final exam:Scheduled by the RegistrarComprehensive on everything covered in class

3. Absence from class/quizzes/mid/final: University policies apply

4. Grading: University definitions apply

Total Student Learning Time(SLT)

Face To FaceIndependent

Learning AssessmentTeacher CenteredLearning

StudentCenteredLearning

26.5 14.5 70.5 8.5

22% 12% 59% 7%Total Hours of Learning (THoF) 120

Conversion of SLT into tentative credit (THoF / 40) 3

Credit to be assigned to the course 3

... suggestions welcome ...

Using the technology

Using the technology

Using the technology

http://www.wolframalpha.com/