Calculus early transcendentals(metric edition) (9版)
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【簡介】
Calculus:Early Transcendentals, Metric Edition
ISBN13:9780357113516
出版社:Cengage Learning; Inc
作者:James Stewart (McMaster University);Saleem (California State University Watson Long Beach);Daniel K. Clegg (Palomar College)
【目錄】
Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.
2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Derivatives of Logarithmic Functions and Inverse Trigonometric Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Approximations and Differentials. Discovery Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. What Derivatives Tell Us about the Shape of a Graph. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Technology. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton's Method. Antiderivatives. Review. Problems Plus.
5. INTEGRALS.
The Area and Distance Problems. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.
6. APPLICATIONS OF INTEGRATION.
Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus.
7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Technology. Discovery Project: Patterns in Integrals. Approxi
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Introduction to Time-Dependent Quantum Mechanics with Python
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Computational spectroscopy and computational quantum chemical dynamics is a vast field in physical chemistry. Significant part of this field is developed based on the concepts of time-dependent quantum mechanics and its numerical implementations.
This book gives an introduction to the Time-Dependent Quantum Chemistry for use with any introductory college/university course in optics, spectroscopy, kinetics, dynamics, or experimental physical chemistry or chemical physics of the kind usually taken by undergraduate and graduate students in physical chemistry. In this book, different concepts of time-dependent quantum mechanics are systematically presented by first giving emphasis on the contrasting viewpoint of classical and quantum mechanical motion of a particle, then by demonstrating the ways to find classical flavour in quantum dynamics, thereafter by formally defining the wavepacket which represents a quantum particle and finally by demonstrating numerical methods to explore the wavepacket dynamics in one dimension. Along with the analytical theory, accompanying Python chapters in this book take readers to a hands-on tour with Python programming by first giving them a quick introduction to the Python programming, then by introducing the position-space grid representation of the wavefunction, thereafter, by making them familiarized with the Fourier transform to represent the discretized wavefunction in momentum space, subsequently by showing the Python-based methodologies to express Hamiltonian operator in matrix form and finally by demonstrating the entire Python program which solves the wavepacket dynamics in one dimension under influence of time-independent Hamiltonian following split-operator approach.
Rigorous class-testing of the presented lecture notes at the Indian Institute of Science, GITAM University and at NPTEL platform reveals that physical chemistry students, after thoroughly going through all chapters, not only develop an in-depth understanding of the wavepacket dynamics and its numerical implementations, but also start successfully writing their own Python code for solving any one dimensional wavepacket dynamics problem.
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