CALCULUS 1 SMS 1102. SMS 1102 CALCUUS 1 Instructor : Suryadi Monday 11:30 C-2-01 Wednesday 8:30...
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Transcript of CALCULUS 1 SMS 1102. SMS 1102 CALCUUS 1 Instructor : Suryadi Monday 11:30 C-2-01 Wednesday 8:30...
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