Course Syllabus, Ma 19 (Applied Calculus for Business)

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COURSE SYLLABUS for Ma 19

Catalogue No.: Ma 19 Course

Title: Applied Calculus for Business

Department: Mathematics

School: Science and Engineering, Ateneo de Manila University

Semester: 2nd

School Year: 2008 – 2009

Credit: 6 units

Prerequisite: Ma 11

A. Course Description

Ma 19 is a 6-unit course taken primarily by BS Management majors both for the standard and honors programs. It aims to introduce students to differential and integral calculus in preparation for various topics in higher management areas such as Business Statistics, Operations Management and Financial Management. Topics include: limits and continuity; derivatives and differentials, some applications of derivatives, antidifferentiation, the definite integral, partial derivatives and the total differential of functions of more than one variable.

B. Course Objectives

At the end of the course, the student should be able to:

Have an intuitive notion of the concepts of limit and continuity of a function; apply the limit theorems and obtain the asymptotes of the graph of a function.

Find the derivative of algebraic, exponential and logarithmic functions; interpret the derivative as a measure of slope and as a rate of change; use derivatives as an aid in sketching the graph of a function and to solve optimization problems.

Determine both the definite and the indefinite integrals of functions; interpret the integral as a measure of an area of a region; apply different techniques of integration; solve differential equations.

Find the partial derivatives and the higher order partial derivatives of functions of more than one variable; determine the maximum and minimum values of multivariate functions and use the method of Lagrange multipliers to solve constrained optimization problems.

Course Outline and Timeframe (based on the textbook, Calculus for Business, Economics, Life Sciences, and Social Sciences (9^th ed), by Barnett and others)

Topics (# of hours does NOT include exam day)	Chapter/Section
The Derivative (14½ hours) Rate of Change and Slope Limits The Derivative Derivatives of Constants, Power Forms, and Sums Derivatives of Products and Quotients Chain Rule: Power Form Marginal Analysis in Business and Economics Long Exam #1 Tentative Schedule: Nov. 27 (Th)	3.1 3.2 3.3 3.4 3.5 3.6 3.7
Graphing and Optimization (14½ hours) Continuity and Graphs First Derivative and Graphs Second Derivative and Graphs Curve Sketching Techniques: Unified and Extended Optimization; Absolute Maxima and Minima Long Exam #2 Tentative Schedule: Dec. 18 (Th)	4.1 4.2 4.3 4.4 4.5
Additional Derivative Topics (14 hours) The Constant e and Continuous Compound Interest Derivatives of Logarithmic and Exponential Functions Chain Rule: General Form Implicit Differentiation Related Rates Long Exam #3 Tentative Schedule: Jan. 20 (T)	5.1 5.2 5.3 5.4 5.5
Midterm Exam Tentative Schedule: Jan. 23, 2009 (F) 6:00 – 8:00 pm
4. Integration (14½ hours) Antiderivatives and Indefinite Integrals Integration by Substitution Differential Equations – Growth and Decay (no slope fields) A Geometric-Numeric Introduction to the Definite Integral Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus (no error bounds) Long Exam #4 Tentative Schedule: Feb. 12, 2009 (Th)	6.1 6.2 6.3 6.4 6.5 *Goldstein can be used as supplement
Additional Integration Topics (10½ hours) Area between Curves Applications in Business and Economics (no probability density functions) Integration by Parts Long Exam #5 Tentative Schedule: Feb. 26, 2009 (Th)	7.1 7.2 7.3
Multivariable Calculus (14 hours) Functions of Several Variables Partial Derivatives Maxima and Minima Maxima and Minima Using Lagrange Multipliers Double Integrals Over Rectangular Regions Long Exam #6 Tentative Schedule: Mar 17, 2009 (T)	8.1 8.2 8.3 8.4 8.6
Final Exam Schedule: c/o Registrar’s Office week of Mar. 23-27, 2009

D. Required Textbook:

Calculus for Business, Economics, Life Sciences, and Social Sciences (9^th ed.), by R.A. Barnett, M.R. Ziegler and K.E. Byleen.

E. References:

Bittinger, M.L., Calculus (5^th ed.), Addison-Wesley, 1992

Edwards, C.H. and E. Penney, Calculus with Analytic Geometry (6^th ed.), Prentice-

Hall, 2002.

Goldstein, L.J., D.C. Lay and D.I. Schneider, Calculus and its Applications (7^th ed.),

Prentice-Hall, 1996.

Harshbarger, R.J. and J.J. Reynolds, Calculus with Applications, D.C. Heath and

Company, 1990.

Thomas, G.B. and R.L. Finney, Calculus and Analytic Geometry (9^th ed.), Addison-

Wesley, 1996.

F. Course Requirements and Grading System:

The final mark of the student will be based principally on the following:

• 6 long exams (100 pts. each),
  

• the departmental midterm exam (200 pts.),
  
• the departmental final exam (200 pts.)
  
• and (optional) quizzes/assignments (100 pts.).

Percentage of the total score	Equivalent letter grade
92% - 100%	A
86% - 91%	B+
77% - 85%	B
69% - 76%	C+
60% - 68%	C
50% - 59%	D
49% and below	F

Students whose class standing before the final exam is 90% or above (prior to cancellation of one (1) lowest long exam score) may be exempted from taking the final exam subject to the discretion of the teacher.

Some Dates to be noted:

Date	Day	Event
Nov. 10, 2008	Monday	2nd Semester Classes begin
Nov. 14, 2008	Friday	2nd Semester Faculty Day
Dec. 1, 2008	Monday	Bonifacio Day (Monday nearest Nov. 30) (Regular non-working holiday)
Dec. 8, 2008	Monday	Solemnity of the Immaculate Conception (Non-working School Holiday)
Dec. 20, 2008 – Jan. 4, 2009	Saturday to Sunday	C H R I S TM A S B R E A K
Jan. 5, 2009	Monday	Classes resume
Feb. 2, 2009	Monday	President’s Day (Non-working School Holiday)
March 23-28, 2009		Final Exam Week

H. General Classroom Policies

1. A student who misses an exam MAY be given a make-up exam depending on the student’s reason(s), and upon the Department Chairperson’s approval. Make-up exams are more difficult than the regular exam.

2. As a departmental policy, there will be no take home long exams and no bonuses.
   
   

I. Consultation Hours:

MW: 1500 - 1630

F: 1500 - 1600

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