Author | Estep, Donald. author |
---|---|
Title | Practical Analysis in One Variable [electronic resource] / by Donald Estep |
Imprint | New York, NY : Springer New York, 2002 |
Connect to | http://dx.doi.org/10.1007/b97698 |
Descript | XX, 623 p. online resource |
Numbers and Functions, Sequences and Limits -- Mathematical Modeling -- Natural Numbers Just Arenโt Enough -- Infinity and Mathematical Induction -- Rational Numbers -- Functions -- Polynomials -- Functions, Functions, and More Functions -- Lipschitz Continuity -- Sequences and Limits -- Solving the Muddy Yard Model -- Real Numbers -- Functions of Real Numbers -- The Bisection Algorithm -- Inverse Functions -- Fixed Points and Contraction Maps -- Differential and Integral Calculus -- The Linearization of a Function at a Point -- Analyzing the Behavior of a Population Model -- Interpretations of the Derivative -- Differentiability on Intervals -- Useful Properties of the Derivative -- The Mean Value Theorem -- Derivatives of Inverse Functions -- Modeling with Differential Equations -- Antidifferentiation -- Integration -- Properties of the Integral -- Applications of the Integral -- Rocket Propulsion and the Logarithm -- Constant Relative Rate of Change and the Exponential -- A Mass-Spring System and the Trigonometric Functions -- Fixed Point Iteration and Newtonโs Method -- Calculus Quagmires -- You Want Analysis? Weโve Got Your Analysis Right Here -- Notions of Continuity and Differentiability -- Sequences of Functions -- Relaxing Integration -- Delicate Limits and Gross Behavior -- The Weierstrass Approximation Theorem -- The Taylor Polynomial -- Polynomial Interpolation -- Nonlinear Differential Equations -- The Picard Iteration -- The Forward Euler Method