MAT421: Sept 2013 – Jan 2014


Calculus I

Class Schedule

CSB1Aq, CSB1Bq

  • Tuesday – 0800-0950 – F141
  • Wednesday – 1000-1050 – F021/Lab01 (CSB1Aq only)
  • Wednesday – 1530-1620 – A218/Lab02 (CSB1Bq only)
  • Thursday – 1430-1520 – F141

Contents

WeekDateTopic
19 Sept - 13 Sept 20131
FUNCTIONS, LIMITS AND CONTINUITY
1.1Functions
οProperties of functions
οOperations on functions
οGraphs (family) of functions
216 Sept - 20 Sept 20131.2Limits
16 Sept (Malaysia Day)οIntroduction (An intuitive approach)
οOne sided limits and two sided limits
οInfinite limits and limits at infinity
οComputing limits
323 Sept - 27 Sept 2013οComputing limits: End behaviour
1.3Continuity
οContinuity at a point
οLimits abd continuity of trigonometric functions
Quiz 1
430 Sept - 4 Oct 20132
DIFFERENTIATION
2.1An Introduction to the Derivative: Tangents
2.2The Definition of Derivative
οDifferentiation from the first principle
οDifferentiability and continuity
2.3Techniques of Differentiation
57 Oct - 11 Oct 20132.4"Derivatives of Trigonometric, Exponential and Logarithmic Functions"

2.5The Chain Rule
Test 1
14 Oct - 20 Oct 2013Semester Break
15 & 16 Oct 2013Raya Qurban
621 Oct - 25 Oct 20132.6Implicit Differentiation
2.7Linear Approximations and Differentials
3
APPLICATIONS OF DIFFERENTIATION
3.1Related Rates
728 Oct - 1 Nov 20133.2Analysis of Functions I:
οIntervals of increasing and decreasing functions
οConcavity and inflection points
Quiz 2
84 Nov - 8 Nov 20133.3Analysis of Functions II:
5 Nov Awal MuharramοRelative maxima and minima
οCritical numbers
οFirst and Second Derivative Test
οGraphs of polynomial functions
911 Nov - 15 Nov 2013οGraphs of rational functions (linear/linear)
3.4Maximum and Minimum Values
οAbsolute maxima and minima
3.5Applied Maximum and Minimum Problems
Quiz 3
1018 Nov - 22 Nov 20133.6Rolle's Theorem; Mean Value Theorem
4
INTEGRATION
4.1Antiderivatives
4.2The Indefinite Integral of Algebraic Functions and Trogonometric Functions, Exponential and Logarithmic Functions
Test 2
1125 Nov - 29 Nov 20134.3Integration by Substitution
4.4Sigma Notation
4.5Area As a Limit and The Definite Integrals
122 Dec - 6 Dec 2013οProperties of Definite Integrals
4.6The Fundamental Theorem of Calculus
οFirst Fundamental Theorem of Calculus
οThe Second Fundamental Theorem of Calculus
139 Dec - 13 Dec 2013οEvaluating Definite Integrals by Substitution
5
APPLICATIONS OF INTEGRATION
5.1Area Between Two Curves
1416 Dec - 20 Dec 20135.2Volume: Solids of revolution
οVolume by Disks Method
Volume by Washers Method
5.3Volume by Cylindrical Shells Method
Test 3

Assessment

Final examination – One 3-hour paper : 60%

Continuous assessments: 40%
  1. Test 1 : 10%
  2. Test 2 : 10%
  3. Test 3 : 10%
  4. Quizzes (3) : 6%
  5. Lab Assignments (2) : 4%

Textbook

Stewart, J. (2012). Calculus (7th Edition). Brooks/Cole, Cengage Learning.
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