Financial Calculus from First Principles

Reactive Publishing

Financial Calculus from First Principles offers a rigorous, self-contained introduction to the mathematical foundations of modern finance. Written for readers who want to truly understand the "why" behind the models rather than just memorize formulas, this book builds the core tools of calculus, limits, derivatives, and integrals, directly from first principles and applies them to essential problems in pricing, hedging, and risk management.

Starting with foundational concepts in real analysis and progressing through differentiation, integration, and multivariable calculus, the book develops the mathematical machinery needed for key financial applications: option pricing, sensitivity analysis (Greeks), dynamic hedging, portfolio optimization, and basic stochastic processes.

• A clear, step-by-step derivation of financial calculus concepts without unnecessary abstraction
• Concrete examples connecting limits, derivatives, and integrals to real pricing and risk problems
• Insight into how mathematical rigor translates into practical trading and risk-management decisions
• A solid platform for further study in quantitative finance, stochastic calculus, or derivatives modeling

Ideal for aspiring quants, finance students, self-taught practitioners, and professionals seeking a deeper mathematical understanding of the tools they use daily. No prior advanced calculus knowledge is assumed, only basic algebra and a willingness to engage with formal reasoning.