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# Introduction to Actuarial and Financial Mathematical Methods

- 1st Edition - April 7, 2015
- Author: Stephen Garrett
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 8 0 0 1 5 6 - 1
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 0 4 9 1 - 3

This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, an… Read more

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## Institutional subscription on ScienceDirect

Request a sales quoteThis 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. 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.

- Presents a self-study mathematics refresher course for the first two years of an actuarial program
- Features examples, motivations, and practice problems from a large number of end-of-chapter questions designed to promote independent thinking and the application of mathematical ideas
- Practitioner friendly rather than academic
- Ideal for self-study and as a reference source for readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute

- Dedication
- Preface
- Part 1: Fundamental Mathematics
- Chapter 1: Mathematical Language
- Abstract
- 1.1 Common mathematical notation
- 1.2 More advanced notation
- 1.3 Algebraic expressions
- 1.4 Questions

- Chapter 2: Exploring Functions
- Abstract
- 2.1 General Properties and Methods
- 2.2 Combining Functions
- 2.3 Common Classes of Functions
- 2.4 Inverse Functions
- 2.5 Actuarial Application: The Time Value of Money
- 2.6 Questions

- Chapter 3: Differential Calculus
- Abstract
- 3.1 Continuity
- 3.2 Derivatives
- 3.3 Derivatives of More Complicated Functions
- 3.4 Algebraic Derivatives on Your Computer
- 3.5 Actuarial Application: The Force of Interest
- 3.6 Questions

- Chapter 4: Differential Calculus II
- Abstract
- 4.1 An Introduction to Smoothness
- 4.2 Higher-Order Derivatives
- 4.3 Stationary and Turning Points
- 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
- Abstract
- 5.1 Sequences
- 5.2 Series and Summations
- 5.3 Evaluating Summations
- 5.4 Taylor and Maclaurin Series
- 5.5 Series and Summations on Your Computer
- 5.6 Actuarial Application: Annuities
- 5.7 Questions

- Chapter 6: Integral Calculus I
- Abstract
- 6.1 Indefinite Integrals of Basic Functions
- 6.2 Change of Variables Approach
- 6.3 Indefinite Integrals of Products of Functions
- 6.4 Indefinite Integrals of Rational Functions
- 6.5 Indefinite Integrals on Your Computer
- 6.6 Questions

- Chapter 7: Integral Calculus II
- Abstract
- 7.1 Definite Integrals
- 7.2 Integration Strategies
- 7.3 Area Between Curves
- 7.4 Definite Integrals on Your Computer
- 7.5 Actuarial Application: The Force of Interest as a Function of Time
- 7.6 Questions

- Chapter 1: Mathematical Language
- Part II: Further Mathematics
- Chapter 8: Complex Numbers
- Abstract
- 8.1 Imaginary and Complex Numbers
- 8.2 Simple Operations on Complex Numbers
- 8.3 Complex Roots of Real Polynomial Functions
- 8.4 Argand Diagrams and the Polar Form
- 8.5 A Simplified Polar Form
- 8.6 Complex Numbers on Your Computer
- 8.7 Questions

- Chapter 9: Probability Theory
- Abstract
- 9.1 Fundamental Concepts
- 9.2 Combinations and Permutations
- 9.3 Introductory Formal Probability Theory
- 9.4 Conditional Probabilities
- 9.5 Probability on Your Computer
- 9.6 Actuarial Application: Mortality
- 9.7 Questions

- Chapter 10: Introductory Linear Algebra
- Abstract
- 10.1 Basic Matrix Algebra
- 10.2 Matrix Multiplication
- 10.3 Square Matrices
- 10.4 Solving Matrix Equations
- 10.5 Solving Systems of Linear Simultaneous Equations
- 10.6 Matrix Algebra on Your Computer
- 10.7 Actuarial Application: Markov Chains
- 10.8 Questions

- Chapter 11: Implicit Functions and ODEs
- Abstract
- 11.1 Implicit Functions
- 11.2 Ordinary Differential Equations
- 11.3 Algebraic Solution of First-Order Boundary Value Problems
- 11.4 Implicit Functions and ODEs on Your Computer
- 11.5 Questions

- Chapter 12: Multivariate Calculus
- Abstract
- 12.1 Partial Derivatives and Their Uses
- 12.2 Critical Points of Bivariate Functions
- 12.3 The Method of Lagrange Multipliers
- 12.4 Bivariate Integral Calculus
- 12.5 Multivariate Calculus on Your Computer
- 12.6 Questions

- Chapter 13: Introductory Numerical Methods
- Abstract
- 13.1 Root Finding
- 13.2 Numerical Differentiation
- 13.3 Numerical Integration
- 13.4 Actuarial Application: Continuous Probability Distributions
- 13.5 Questions

- Chapter 8: Complex Numbers
- Part III: Worked Solutions to Questions
- Chapter 1 Solutions
- Chapter 2 Solutions
- Chapter 3 Solutions
- Chapter 4 Solutions
- Chapter 5 Solutions
- Chapter 6 Solutions
- Chapter 7 Solutions
- Chapter 8 Solutions
- Chapter 9 Solutions
- Chapter 10 Solutions
- Chapter 11 Solutions
- Chapter 12 Solutions
- Chapter 13 Solutions

- Appendix A: Mathematical Identities
- A.1 Trigonometric Identities
- A.2 Derivatives of Standard Functions

- Appendix B: Long Division of Polynomials
- B.1 Motivation
- B.2 Performing the Long Division
- B.3 Questions
- B.4 Solutions

- Bibliography
- Index

- No. of pages: 624
- Language: English
- Edition: 1
- Published: April 7, 2015
- Imprint: Academic Press
- Hardback ISBN: 9780128001561
- eBook ISBN: 9780128004913

SG

### Stephen Garrett

*Introduction to Actuarial and Financial Mathematical Methods*on ScienceDirect