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
analytic applied approximation arbitrary assumed axis becomes boundary branch c₁ Chapter characteristic circle closed coefficients complex considered constant continuous converges coordinates corresponding curve deduce defined definition dependent derivatives determined differences differential equation direction equal Example exist expansion expression fact Figure finite flow follows formally formula function given gives hence homogeneous independent infinite initial integral interval involving known length limit linear mapping method notice obtain operator origin partial particular plane positive prescribed Problem region relation replaced represents respect result result of Problem satisfies Section simple singular sinh solution Suppose surface temperature tends tion transform u₁ u₂ unit values vanish variable vector Verify whereas write written zero ду