This unique book provides a new and well-motivated introduction to calculus and analysis that are historically significant fundamental areas of mathematics and widely used in many disciplines.
This unique book provides a new and well-motivated introduction to calculus and analysis that are historically significant fundamental areas of mathematics and widely used in many disciplines.
Contents: Tangents and Double Points Derivatives by Algebra Exponential Functions Completeness of Real Numbers The Base of the Natural Exponential and Logarithm Functions Continuity of Functions Differentiability Chain Rule and Other Rules for Derivatives Derivatives of Trigonometric Functions Mean Value Inequality and Theorem Basic Differential Equations Motion with Constant Acceleration Linear and Higher Order Approximations The Antiderivative Problem Definite Integrals Fundamental Theorem of Calculus Integrability of Monotonic Functions Integrability of Functions with Bounded Derivative Substitution Integration by Parts Taylor's Theorem Analytic Functions The Euler Identity
Contents: Tangents and Double Points Derivatives by Algebra Exponential Functions Completeness of Real Numbers The Base of the Natural Exponential and Logarithm Functions Continuity of Functions Differentiability Chain Rule and Other Rules for Derivatives Derivatives of Trigonometric Functions Mean Value Inequality and Theorem Basic Differential Equations Motion with Constant Acceleration Linear and Higher Order Approximations The Antiderivative Problem Definite Integrals Fundamental Theorem of Calculus Integrability of Monotonic Functions Integrability of Functions with Bounded Derivative Substitution Integration by Parts Taylor's Theorem Analytic Functions The Euler Identity
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