UID:
edoccha_9958074228702883
Format:
1 online resource (622 p.)
ISBN:
0-12-800491-6
Content:
This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, and basic numerical methods. The easily-understandable text of "Introduction to Actuarial and Mathematical Methods" features examples, motivations, and lots of practice from a large number of end-of-chapter questions. Questions range from short calculations to large project-based assignments, all designed to promote independent thinking and the application of mathematical ideas. Model solutions are included. The intuitive organization of "Introduction to Actuarial and Mathematical Methods" maximizes its usefulness as a means of self-study and as a reference source. Financial concepts and terminology introduce every mathematical concept and theory. For readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute, "Introduction to Actuarial and Mathematical Methods" can provide a consistency of mathematical knowledge from the outset. -- From book cover.
Note:
Description based upon print version of record.
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Front Cover; Introduction to Actuarial and Financial Mathematical Methods; Copyright; Dedication; Contents; Preface; Part I: Fundamental Mathematics; Chapter 1: Mathematical Language; 1.1 Common Mathematical Notation; 1.1.1 Number systems; 1.1.2 Mathematical symbols; 1.2 More Advanced Notation; 1.2.1 Set notation; 1.2.2 Interval notation; 1.2.3 Quantifiers and statements; 1.3 Algebraic Expressions; 1.3.1 Equations and identities; 1.3.2 An introduction to mathematics on your computer; 1.3.3 Inequalities; 1.4 Questions; Chapter 2: Exploring Functions; 2.1 General Properties and Methods
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2.1.1 Mappings2.1.2 Functions; Functions vs. mappings; Odd and even functions; Roots; 2.1.3 Root finding on your computer; 2.1.4 Plotting functions; 2.2 Combining Functions; 2.2.1 Simple combinations; 2.2.2 Composite functions; 2.3 Common Classes of Functions; 2.3.1 Polynomial functions; 2.3.2 Rational functions; 2.3.3 Exponential functions; 2.3.4 Logarithmic functions; 2.3.5 Circular (trigonometric) functions; 2.4 Inverse Functions; 2.5 Actuarial Application: The Time Value of Money; 2.6 Questions; Chapter 3: Differential Calculus; 3.1 Continuity; 3.1.1 Limits; 3.1.2 Continuity
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3.2 Derivatives3.2.1 Gradients; 3.2.2 Derivatives of polynomials; 3.2.3 Derivatives of exponential functions; 3.2.4 Derivatives of circular functions; 3.3 Derivatives of More Complicated Functions; 3.3.1 Sums of functions; 3.3.2 Product rule; 3.3.3 Chain rule; 3.3.4 Quotient rule; 3.3.5 Derivatives of inverse functions; 3.4 Algebraic Derivatives on Your Computer; 3.5 Actuarial Application: The Force of Interest; 3.6 Questions; Chapter 4: Differential Calculus II; 4.1 An Introduction to Smoothness; 4.2 Higher-Order Derivatives; 4.3 Stationary and Turning Points; 4.3.1 Stationary points
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4.3.2 Classification via second derivatives4.3.3 Application to ranges; 4.4 Higher-Order Derivatives and Stationary Points on Your Computer; 4.5 Actuarial Application: Approximating Price Sensitivities; 4.6 Questions; Chapter 5: Sequences and Series; 5.1 Sequences; 5.2 Series and Summations; 5.2.1 Concepts and notation; 5.2.2 Properties of summations; 5.3 Evaluating Summations; 5.3.1 Arithmetic and geometric progressions; 5.3.2 Evaluating finite sums; 5.3.3 Evaluating infinite sums; 5.4 Taylor and Maclaurin Series; 5.4.1 Concepts; 5.4.2 Convergence and function approximation
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5.4.3 Further uses5.5 Series and Summations on Your Computer; 5.6 Actuarial Application: Annuities; 5.7 Questions; Chapter 6: Integral Calculus I; 6.1 Indefinite Integrals of Basic Functions; 6.2 Change of Variables Approach; 6.3 Indefinite Integrals of Products of Functions; 6.3.1 Change of variables; 6.3.2 Integration by parts; 6.4 Indefinite Integrals of Rational Functions; 6.5 Indefinite Integrals on Your Computer; 6.6 Questions; Chapter 7: Integral Calculus II; 7.1 Definite Integrals; 7.2 Integration Strategies; 7.2.1 Change of variables; 7.2.2 Integration by parts
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7.3 Area Between Curves
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English
Additional Edition:
ISBN 0-12-800156-9
Language:
English
