**List of Figures**.

**List of Tables.**

**List of Examples**.

**Foreword**.

**Preface to Volume 1**.

**I.1 Basic Calculus for Finance**.

I.1.1 Introduction.

I.1.2 Functions and Graphs, Equations and Roots.

I.1.3 Differentiation and Integration.

I.1.4 Analysis of Financial Returns.

I.1.5 Functions of Several Variables.

I.1.6 Taylor Expansion.

I.1.7 Summary and Conclusions.

**I.2 Essential Linear Algebra for Finance**.

I.2.1 Introduction.

I.2.2 Matrix Algebra and its Mathematical Applications.

I.2.3 Eigenvectors and Eigenvalues.

I.2.4 Applications to Linear Portfolios.

I.2.5 Matrix Decomposition.

I.2.6 Principal Component Analysis.

I.2.7 Summary and Conclusions.

**I.3 Probability and Statistics**.

I.3.1 Introduction.

I.3.2 Basic Concepts.

I.3.3 Univariate Distributions.

I.3.4 Multivariate Distributions.

I.3.5 Introduction to Statistical Inference.

I.3.6 Maximum Likelihood Estimation.

I.3.7 Stochastic Processes in Discrete and Continuous Time.

I.3.8 Summary and Conclusions.

**I.4 Introduction to Linear Regression.**

I.4.1 Introduction.

I.4.2 Simple Linear Regression.

I.4.3 Properties of OLS Estimators.

I.4.4 Multivariate Linear Regression.

I.4.5 Autocorrelation and Heteroscedasticity.

I.4.6 Applications of Linear Regression in Finance.

I.4.7 Summary and Conclusions.

**I.5 Numerical Methods in Finance**.

I.5.1 Introduction.

I.5.2 Iteration.

I.5.3 Interpolation and Extrapolation.

I.5.4 Optimization.

I.5.5 Finite Difference Approximations.

I.5.6 Binomial Lattices.

I.5.7 Monte Carlo Simulation.

I.5.8 Summary and Conclusions.

**I.6 Introduction to Portfolio Theory**.

I.6.1 Introduction.

I.6.2 Utility Theory.

I.6.3 Portfolio Allocation.

I.6.4 Theory of Asset Pricing.

I.6.5 Risk Adjusted Performance Measures.

I.6.6 Summary and Conclusions.

**References**.

**Statistical Tables**.

**Index**.