Fu Jen Catholic University Huei-Yu Chiu (n=Ø) Department of Economics Office: SL 321
Spring 2012 Office tel: 2905-2706
Class hours: 9:10-12:00, Tuesday Email: hychiu@mail.fju.edu.tw
Calculus II ( } II)
Calculus is one branch of mathematics that has widespread applications in many fields. In economics, we frequently utilize the skill of Calculus to do comparative- static and dynamic analyses, to solve optimization problems, etc. This course is designed to provide a firm understanding of the fundamental theorems of Calculus.
We will attempt to cover integral calculus in this semester. The first and second fundamental theorem of calculus will be first studied. Some important techniques of integration will be introduced, too. We will also pay attention to some useful functions such as logarithm and exponential function and some useful series such as Taylor and Maclaurin series. After learning the fundamental ideas, vector, double and triple integrals will be discussed as well.
Required Reading
Varberg, D., Purcell, E. J. and S. E. Rigdon (2007), Calculus, Prentice Hall.
Supplemental Reading
1. Šm ˜pp ÏÙª (2008) }, Mœz|
2. Larson, R., Hostetler, R. and B. H. Edwards (2008), Calculus: Early Tran- scendental Functions, Houghton Mifflin Company.
3. Hoffmann, L. D., and G. L. Bradley (2008), Applied Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill.
4. Tomas, G., Weir, M. and J. Hass (2009), Calculus, Addison Wesley.
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Course Outline
Week 1 (2/14): (Review) Definite integral & the first and second fundamental theorem of calculus (Varberg, Ch 4)
Week 2 (2/21): Mean value theorem for integrals and area integration of regions (Varberg, Ch 4)
Week 3 (2/28): Holiday
Week 4 (3/06): Logarithm function (Varberg, Ch 6) Week 5 (3/13): Exponential function (Varberg, Ch 6)
Week 6 (3/20): Techniques of integration: basic rules & integration by parts (Varberg, Ch 7)
Week 7 (3/27): Techniques of integration: integration of rational functions &
indeterminate forms (Varberg, Ch 7 & Ch 8) Week 8 (4/03): Holiday
Week 9 (4/10): Midterm exam
Week 10 (4/17): Improper integrals (Varberg, Ch 8) Week 11 (4/24): Infinite series (Varberg, Ch 9)
Week 12 (5/01): Taylor and Maclaurin series (Varberg, Ch 9)
Week 13 (5/08): The Taylor approximation to a function (Varberg, Ch 9) Week 14 (5/15): Vectors (Varberg, Ch 11)
Week 15 (5/22): Partial derivatives (Varberg, Ch 12)
Week 16 (5/29): The method of Lagrange multipliers (Varberg, Ch 12)
Week 17 (6/05): Multiple integrals: double & triple integrals (Varberg, Ch 13) Week 18 (6/12): Final exam
Grading
1. Class participation: (5%) 2. Homework: (10%)
3. TA class: 13:40-15:30, Friday (25%) 4. Midterm exam: 4/10 (30%)
5. Final exam: 6/12 (30%)
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