Calculus I. What is Calculus? Calculus is the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions‚ by methods originally based on the summation of infinitesimal differences. a. Differential Calculus - concerned with the determination‚ properties‚ and application of derivatives and differentials. b. Integral Calculus - concerned with the determination‚ properties‚ and application of integrals. II. Brief History of Calculus Calculus was
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position in intraday‚ in overnight position. Moreover the salary of the top management official were linked excessively to the speculated profit which promoted the top management official under the guidance of Leeson to take excessive position in derivative trades even risking the loss limits when led to huge losses incurred. Moreover the absence of any formal internal audit system allowed the bank to take unauthorized path of settling the huge loss in the error account (Rogue
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• It is easy to use the Excel Solver to solve NLPs. • The process is similar to a linear model. • For NLPs having multiple local optimal solutions‚ the Solver may fail to find the optimal solution because it may pick a local extremum that is not a global extremum. 22 Example 2 • Trucko is trying to determine where they should locate a single warehouse. The positions in the x‐y plane of their four customers and the number of shipments made annually to each customer are given. Trucko
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Fluid Dynamics and Electromagnetic fields. (iii) to solve ordinary differential equations directly and also use transform methods where its possible Unit 1 Mutivariable Calculus 9L+4P hours Functions of two variables-limits and continuity-partial derivatives –total differential–Taylor’s expansion for two variables–maxima and minima–constrained maxima and minima-Lagrange’s multiplier method- Jacobians Unit 2 Mutiple Integrals 9L+4P hours Evaluation of double integrals–change of order of integration–
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AP Calculus Name ____________________________ Period _____ Functions Defined by Integrals The graph below is‚ the derivative of. The graph consists of two semicircles and one line segment. Horizontal tangents are located at and and a vertical tangent is located at. 1. On what interval is increasing? Justify your answer. 2. For what values of x does have a relative minimum? Justify. 3. On what intervals is concave up? Justify 4. For what values of x is undefined? 5. Identify
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of integral We can write [pic] where G(x) is an anti-derivative (indefinite integral) of g(x) (ii) Let [pic] where [pic]‚ that is f(x‚y) can be written as the product of two functions‚ one function of variable x and other of y. Equation [pic] can be written as [pic] By integrating both sides we get [pic] where [pic] or [pic] where H(y) and G(x) are anti-derivatives of [pic]and [pic]‚ respectively. Example 2.1: Solve the differential
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5 11. Corporate Finance 12. Securities Markets 13. Equity Investments 14. Fixed Income Investments 15. Derivatives Chapter 6 - 10 Chapter 11 - 15 Chapter 16 - 17 15.29 Interest Rate Options vs. FRAs 15.30 Interest Rate Caps and Floors 15.31 Minimum and Maximum Values for Options 15.32 Straddles and Strangles 15.33 Option Prices and the Time to Expiration Derivatives - Interest Rate Caps and Floors Interest Rate Cap An interest rate cap is actually a series of European interest
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Actuarial Common Entrance Test (ACET) The FAC course The Foundation Course consists of a set of eight chapters of notes covering the following ideas: Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Notation Numerical Methods I Mathematical constants and standard functions Algebra Numerical Methods II Differentiation Integration Vectors and matrices We recommend that you work through the sections that you are unsure of‚ completing the questions
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Australian School of Business School of Banking and Finance FINS 3635 OPTIONS‚ FUTURES AND RISK MANAGEMENT TECHNIQUES Course Outline Semester 1‚ 2012 Part A: Course-Specific Information Part B: Key Policies‚ Student Responsibilities andSupport Table of Contents PART A: COURSE-SPECIFIC INFORMATION 1 2 2.1 2.2 2.3 2.4 2.5 3 STAFF CONTACT DETAILS COURSE DETAILS Teaching Times and Locations Units of Credit Summary of Course Course Aims and Relationship to Other Courses Student Learning Outcomes
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Algebraic Fractions An algebraic fraction can always be expressed in different‚ yet equivalent forms. A fraction is expressed in its simplest form by cancelling any factors which are common to both the numerator and the denominator. Algebraic Fractions can be simplified by cancelling down. To do this‚ numerators and denominators must be fully factorised first. If there are fractions within the numerator/denominator‚ multiply by a common factor to get rid of these and create an equivalent fraction:
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