Leseprobe
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Honors Calculus
Charles R. MacCluer
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This is the first modern calculus book to be organized axiomatically and to survey the subject's applicability to science and engineering. A challenging exposition of calculus in the European style, it is an excellent text for a first-year university honors course or for a third-year analysis course. The calculus is built carefully from the axioms with all the standard results deduced from these axioms. The concise construction, by design, provides maximal flexibility for the instructor and allows the student to see the overall flow of the development. At the same time, the book reveals the origins of the calculus in celestial mechanics and number theory.
The book introduces many topics often left to the appendixes in standard calculus textbooks and develops their connections with physics, engineering, and statistics. The author uses applications of derivatives and integrals to show how calculus is applied in these disciplines. Solutions to all exercises (even those involving proofs) are available to instructors upon request, making this book unique among texts in the field.
- Focuses on single variable calculus
- Provides a balance of precision and intuition
- Offers both routine and demanding exercises
Kundenbewertungen
Disjoint union, Maxima and minima, Open set, Quantity, Countable set, Mean value theorem, Compact space, Empty set, Line segment, Addition, Antiderivative, Axiom, Improper integral, Religion, Taylor series, Infimum and supremum, Second derivative, Boundary (topology), Continuum hypothesis, Newton's law of universal gravitation, Harmonic series (mathematics), Wave function, Fixed point (mathematics), Power set, Mathematics, Bijection, Real number, Borel set, Calculation, Cantor's diagonal argument, World War II, Theorem, Tangent, Quantum mechanics, Rational number, Existential quantification, Subset, Intermediate value theorem, Surjective function, Proportionality (mathematics), Bisection, Differentiable function, Integer, Riemann integral, Linear function, Summation, Axiom of choice, Natural number, Neighbourhood (mathematics), Loss function, Acceleration, Standard deviation, Convergent series, Upper and lower bounds, Riemann zeta function, Series (mathematics), Continuous function (set theory), Interval (mathematics), Permutation, Cardinality, Derivative, Result, Connected space, Differential equation, Probability, Cartesian coordinate system, Inverse function, Sign (mathematics), Function (mathematics), Polynomial