Advanced Calculus for Applications The text provides advanced undergraduates with the necessary background in advanced calculus topics, providing the foundation for partial differential equations and analysis. Readers of this text should be well-prepared to study from graduate-level texts and publications of similar level. KEY TOPICS: Ordinary Differential Equations; The Laplace Transform; Numerical Methods for Solving Ordinary Differential Equations; Series Solutions of Differential Equations: Special Functions; Boundary-Value Problems and Characteristic-Function Representations; Vector Analysis; Topics in Higher-Dimensional Calculus; Partial Differential Equations; Solutions of Partial Differential Equations of Mathematical Physics; Functions of a Complex Variable; Applications of Analytic Function Theory MARKET: For all readers interested in advanced calculus. |
Common terms and phrases
a₁ analytic analytic function approximation arbitrary assumed Bessel functions branch points c₁ c₂ Chapter characteristic functions circle coefficients complex considered constant converges coordinates corresponding cosh d2y dx2 deduce defined denote determined differential equation divergence theorem dx dy dy dx Example expansion expression finite flow follows formally formula Fourier function f(x given Green's function hence imaginary infinite interval Laplace transform Laplace's equation linear mapping method notation notice obtain odd function partial differential equation polynomial positive integer prescribed R₂ region regular singular point replaced result of Problem right-hand member Section singular point sinh Taylor series temperature tend to zero theorem tion u₁ u₂ upper half-plane values vanish variable vector velocity Verify write xy plane ди ду дх მდ