SCHOOL OF BUSINESS & ECONOMICS Department of Economics Spring 2018 Course Name: Applied Business Mathematics Course Code: BUS 135; Section: 1 Faculty: Naveen Abedin Office: NAC 824 Office Hours: Mid Term I Syllabus 1. Linear Programming: System of linear equations and system of linear inequalities, formulation of linear programming in business problems and their graphical solutions. 2. Limit: Limit and continuity of single variable functions with reference to business problems. 3. Differentiation: Slope of a single variable function (with an explanation of the first derivative as the rate of change) and their differentiation (up to chain rule), including examples involving business problems. Mid Term II Syllabus 4. Application of Differentiation: Convex and concave functions, minimization and maximization techniques of single variable functions and their applications in solving business problems. 5. Integral Calculus: Definition of integration and its explanation with a business example problem. Indefinite and definite integrals of functions (up to integration by parts) and their applications in business. Final Exam Syllabus 6. Differential Equation: First order differential equation and its application in business. 7. Non-linear Optimization: Introduction to non-linear functions and partial differentiation, hessian matrix and leading principal minors, unconstrained optimization of multi-variable functions, Lagrange multiplier method of optimization, and their applications to the solutions to business problems. ______________________________________________________________________________________ Text book Text Book Reading: Mathematics for Business, Finance and Economics ( by F.M.Wilkes) Course Evaluation Grading categories Quizzes Mid-term 1 Exam Mid-term 2 Exam Final Exam Attendance & Participation Total % contribution towards the final grade 15% (3 quizzes, each worth 5%) 25% 25% 30% 5% 100% Make-up Policy Make-up Midterm Exams will NOT be taken unless the student faces a severe crisis. The students must submit applications in advance including all supporting documents before appearing for make-up midterm exams. Make-up for quizzes and final exam are NOT allowed under any circumstances, unless advised by the authorities. __________________________________________________________________________________________ Rules of Conduct Switch off your cell phones when you enter the classroom If you disrupt or distract the class in any way, the instructor has the right to ask you to leave the classroom. Repeated misconduct will earn you a one-way ticket to the Proctor’s Office. BE ON TIME! Your attendance points will be heavily penalized for repeated tardiness. Please Refer to NSU Student CODE OF CONDUCT at www.northsouth.edu/student-code-of-conduct.html. Tentative Lecture Schedule Lecture No. 1 2 3 4 Topic Solutions to system of linear equations by Cramer’s Rule Linear inequalities and their graphical representation Formulation of linear programming problem; Solution to linear programming problem by graphical solution method Explanation of Limit, limit of functions and their graphical representation; left and right hand limits; explanation of continuity of functions by example problems 5 Explanation of Limit, limit of functions and their graphical representation; left and right hand limits; explanation of continuity of functions by example problems 6 Definition of first derivative of a single variable function and its explanation as its slope and rate of change at a point; introduction to the first derivative formulas of algebraic, exponential, logarithmic and trigonometric functions 7 Differentiation of product and quotient of functions, differentiation by chain rule 8 9 10 Partial differentiation; Combination derivative problems Mid Term I Exam Definition of convex and concave functions. Illustration of single variable convex and concave functions by using second derivative of the concerned function 12 Necessary and sufficient condition for optimization of a single variable function and their illustration by example problems Optimal solutions to business problems by the method of differentiation 13 Definition of integration as a summation and inverse of differentiation of a function 14 15 16 17 18 Integration by substitution Integration by parts Evaluation of definite integrals 11 19 20 21 22 23 24 Mid Term II Exam Definition of simple first order differential equations and their solutions Solution to differential equations by using integrating factors; solution to business problems by using differential equation Definition of multivariable functions including up to three variables; introduction to partial differentiation and hessian matrix; leading principal minors of a hessian matrix Unconstrained optimization of multivariable functions including up to three variables Presentation of non-linear optimization problem with equality constraints and formation of Lagrangian function and its hessian matrix Solution to non-linear optimization problem with equality constraints by Lagrangian multiplier method Practice class on solutions to non-linear optimization problem with equality constraints by Lagrangian multiplier method Final Exam by NSU schedule