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Introduction to Actuarial and Financial Mathematical Methods
1st Edition - April 7, 2015
Author: Stephen Garrett
Hardback ISBN:9780128001561
9 7 8 - 0 - 1 2 - 8 0 0 1 5 6 - 1
eBook ISBN:9780128004913
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, and… Read more
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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. 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
Actuarial and finance students worldwide who need to learn or revisit fundamental applied mathematical tools and techniques
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
7.5 Actuarial Application: The Force of Interest as a Function of Time
7.6 Questions
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
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
Published: April 7, 2015
Imprint: Academic Press
Hardback ISBN: 9780128001561
eBook ISBN: 9780128004913
SG
Stephen Garrett
Prof. Stephen Garrett is Professor of Mathematical Sciences at the University of Leicester in the UK. He is currently Head of Actuarial Science in the Department of Mathematics, and also Head of the Thermofluids Research Group in the Department of Engineering. These two distinct responsibilities reflect his background and achievements in both actuarial science education and fluid mechanics research. Stephen is a Fellow of the Royal Aeronautical Society, the highest grade attainable in the world's foremost aerospace institution.
Affiliations and expertise
Professor of Mathematical Sciences, University of Leicester, UK