MATH 115 Calculus for Business and EconomicsSpring 2013 Class time Section 02: UT 12:30-13:45, F1-2126 Section 57: MW 12:30-13:45, C6-1037 Instructor info 0B Instructor 2B 1B Dr. Viktor Bodi
[email protected] F1-0075 (Male campus) TBA E-mail 4B 3B Office 5B 6B Office Hours 7B Course Description This course introduces the concepts of differential and integral calculus useful to students in business, economics. Among the topics studied are: curve sketching for some functions relevant to business and economics applications, derivatives and techniques of differentiation, exponential growth, anti-derivatives and methods of integration, definite and indefinite integrals with applications. The course also covers topics on partial derivatives and matrices, in addition to many applications in Business and Economics. Prerequisite: MATU 1332 Textbook Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, 11th Ed. by Hoffmann, Bradley, Sobecki, and Price, McGraw-Hill, 2013. Course coordinator Dr. Ana Vasilic, Department of Mathematical Sciences, Office F1-0079
[email protected] Page 1 of 4 Calculus for Business and Economics 21/04/2013 7:00-8:00 PM Saturday. students who are absent from 4 classes (10%) will receive 2nd warning. Attendance Attendance is mandatory for all classes. Define. Solve practical problems involving marginal cost and marginal revenue. Understand the concept of differentiation. Students who are absent from 3 classes (5%) will receive 1st warning. graph. Assessment Weight Quizzes Homework Test 1 Test 2 Midterm 10 % 10 % 10 % 10% 20 % Date TBA TBA TBA TBA Sunday. apply differentiation rules.15/06/2013 3:30-5:30 PM In class In class TBA Location In class Final 40 % TBA Page 2 of 4 Calculus for Business and Economics . Sketch graphs using critical points.Course Objectives/Learning Outcomes Upon successful completion of this course the student should be able to: • • • • • • • • • • Graph and identify basic properties of various elementary functions. Understand basic matrix operations and their applications in solving linear systems. compute derivatives. Understand the concept of integration. compute indefinite and definite integrals and apply these concepts to solve practical problems. extrema. and concavity. and find the derivatives of the exponential and logarithmic functions. Understand the concept of multivariate functions. use these functions to model different practical problems. Interpret real-world problems in terms of calculus concepts: inventory problems. Understand the physical and graphical interpretation of derivatives. Students who are absent for 5 or more classes (15%) are prohibited from participating in subsequent exams and fail the course. Use mathematical models to describe some concepts relevant for business and economics applications. Use derivatives to find extrema and study concavity of a function. marginal analysis and other business problems. 2.4.7 1. 45 1-6.2.2.5 2.8. 2. 57-62 4-38. 43-45 (do after 2.16 1.3 (only concavity). 3.2. 1.5.1. 21-34.2.2. 45-48 1-8.3. 34. 66 1-6.2.5 (do after 2.5. Graphs.2. 1.1.1.2.6 Examples 2. 39-40. 2.5. 1.1. 29-68.3.4. 35-42 1-6.2.2. While some of those problems will be covered in class.1-3.4.2.14-A. 1.1-1. 83-88 15-26. A. 13-20. 3. 23-29. 1.1-2.2.1.2) 2. 37.4.1. 1.Course contents Below is an outline of sections to be covered and a tentative weekly schedule.8 A.4. A. Numbers in bold red denote word problems related to business and economics applications and should be studied with a great care.1.6. and Limits 1 A1 A Brief Review of Algebra (Exponents and Roots) A2 Factoring Polynomials.7. Additional Applications of the Derivative 7 1 Increasing and Decreasing Functions. 15-26.5.1. 12-13 2 3 4 Functional Models 5 Limits 4 6 One-Sided Limits and Continuity 2.2.5a.2. 4347. 56. 3438 1-38 1-10.5.7.1-1. 42-45. Functions. 43-46 8 Midterm Review Page 3 of 4 Calculus for Business and Economics . Relative Extrema 2 Concavity and Points of Inflection Examples 3.1.2.2.1-1.1. 2.2.3.1. 39. 3. 21-28.4.1.1. the others are left for students to complete on their own.5.3. 31-38 Exercises 1-12.6.3.1. 32.4. 1.4.1. 1.6. 2.1. 1. 2. 55. 35.10 1. 1.6 1.4-2.2) 1-25. 38 16-18. It lists the examples from the textbook and suggested exercises.3. 1.1-1. 29-39 1-15. 29.4.6-2.3.10. Quadratic formula 1 Functions 2 The Graph of a Function 3 Linear Functions Examples A.3. A.4. 1.4.2 Exercises 19-30.5-A.2.1-2.6 1.5.5. 48 1-8.7 1.8 2. 1.5. 13-18.3. A. 35-41.2.3.5. Properties of fractions. Differentiation: Basic Concepts 5 1 The Derivative 2 Techniques of Differentiation 3 Product and Quotient Rules 6 4 The Chain Rule 5 Marginal Analysis & Approximations Using Increments 3.3.3.5.1. 27-29. 30-32.6 2. 40.5 Exercises 9-15.4 3. 2.3.9 3 Curve Sketching 4 Optimization. 53 5.1.1.2.3.1. 47-48.1-7. 66 5.3.10.3.3.2.3.4.3.1.1-5.2.3. 19.6 7.1-4. Continuous Compounding 2 Logarithmic Functions 3 Differentiation of Exponential and Logarithmic Functions Examples 4. 4. 17-20.7.5.2.1.1.2.4.1-4. 20.3.8 4. 25.3. 35-44 3-8. 29 Exercises *** *** *** *** 7. 69-72 Exercises 5. 17. Exponential and Logarithmic Functions 10 1 Exponential Functions.3. 4. 7.b 4.4. 4. Page 4 of 4 Calculus for Business and Economics . 39.1. 15-32. 21-27.40 1-7.1-5. 7.1. Elasticity of Demand 3. 5.8.10-4.1-7.4 (asymptotes only) 3.4 1-15 5.7 Examples *** *** *** *** Exercises 1-7.1-3. 43-48 1-24.2.4.2.1. 3. 13-16. Homework problems covering this material will also be provided in class. 52.5 1-24.1.4.3.4. 4. 27.3.7.9 Examples 7.64.5.11 Examples 5.12 4.3. Functions of several variables 13 1 Functions of Several Variables 2 Partial Derivatives Matrices ⃰ 14 1 Basic Matrix Operations 2 Matrix Inversion 15 3 Determinants and Cramer’s Rule 4 Solving Systems of Linear Equations 16 Final Review ⃰ A handbook covering material on systems of linear equations and matrices will be provided in class. 3. 4.3. 5.5. 3.1. Integration 11 1 Antidifferentiation: The Indefinite Integral 2 Integration by Substitution 12 3 The Definite Integral and the Fundamental Theorem of Calculus 1-15. 31a. 22.3.2. 5.3.1.1-4.3. 21. 4. 5.5 Exercises 5-28.2. 4. 20 1-8.2.